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Research ArticleScrew Performance Degradation AssessmentBased on Quantum Genetic Algorithm and Dynamic FuzzyNeural Network
Xiaochen Zhang Hongli Gao and Haifeng Huang
School of Mechanical Engineering Southwest Jiaotong University Chengdu 610031 China
Correspondence should be addressed to Hongli Gao ghl2248hotmailcom
Received 16 April 2015 Revised 23 June 2015 Accepted 1 July 2015
Academic Editor Wahyu Caesarendra
Copyright copy 2015 Xiaochen Zhang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
To evaluate the performance of ball screw screw performance degradation assessment technology based on quantum geneticalgorithm (QGA) and dynamic fuzzy neural network (DFNN) is studied The ball screw of the CINCINNATIV5-3000 machiningcenter is treated as the study object Two Kistler 8704B100M1 accelerometers and a Kistler 8765A250M5 three-way accelerometerare installed to monitor the degradation trend of screw performance First screw vibration signal features are extracted both intime domain and frequency domain Then the feature vectors can be obtained by principal component analysis (PCA) Secondthe initialization parameters of the DFNN are optimized by means of QGA Finally the feature vectors are inputted to DFNNfor training and then get the screw performance degradation model The experiment results show that the screw performancedegradation model could effectively evaluate the performance of NC machine screw
1 Introduction
NC machine tool is an important foundation for mod-ern manufacturing which directly impacts the economicdevelopment [1 2] With the continuous development ofmodern manufacturing technology NC machine tool hasbeen widely used in aerospace automobile shipbuildingand other industries [3 4] In the manufacturing processthe continuous degradation of ball screw directly leads tothe decrease of NC machine toolrsquos static geometric accuracyand dynamic precision which means that enterprises shouldincrease their production and maintenance costs Since ballscrewrsquos performance would change greatly with the variationof working conditions and processing environment replace-ment of the ball screw regularly is neither scientific norreasonable [5 6] Therefore screw performance degradationneeds real-time assessment in order to cut down enterprisesrsquomaintenance costs
DFNN is a kind of information processing methodcombined with fuzzy set theory Its essence is a dynamicmapping network with fuzzy input signal and weights [7]
During the learning process network parameters and dimen-sion will change according to the rules Compared withthe traditional neural network DFNN is more suitable fordescribing dynamic system However it is difficult to choosethe initialization parameters of the DFNN which meansDFNN will easily fall into local optimum [8 9] To thedefect of DFNN this paper adopts the QGA which has theadvantage of the high efficiency and avoiding local optimumto select the best initialization parameters of the DFNN thatcan improve the performance of DFNN and increase theoperation stability of system
The purpose of this paper is to present a useful methodfor performance degradation assessment of ball screw basedon QGA and DFNN Meanwhile feature vectors selectionmethod is proposed here Particularly we extract screwvibration signal features both in time domain and frequencydomain The dimensionalities of the input signal featurespace are reduced with the help of PCA Then the initial-ization parameters of the DFNN are optimized by means ofQGA Screw performance degradation model can be gottenafter training with the feature vectors Finally we compare
Hindawi Publishing CorporationShock and VibrationVolume 2015 Article ID 150797 11 pageshttpdxdoiorg1011552015150797
2 Shock and Vibration
the prediction accuracies amongdifferent kinds of neural net-works to examine the effectiveness of the proposed method
2 Screw Vibration Feature Vectors
21 Screw Online Monitoring System Figure 1 shows thescrew onlinemonitoring system applied toCINCINNATIV5-3000 machining center Two Kistler 8704B100M1 one-wayaccelerometers are installed at two bearing chocks to mon-itor the radial vibration of screw ends while a Kistler8765A250M5 three-way accelerometer is installed on thescrew nut to monitor three-dimensional shaking of thescrew nut INV1870 is the signal conditioner connectedwith Advantech PCI1710 data acquisition card Industrycomputer can store the vibration data through the PCI1710data acquisition card and the sampling frequency is 256 kHzBall screw works in horizontal installation state meanwhilethe installation method of the ball screw is one-end fixedwhile the other end floated Ball screw reaches 45mm in axisdiameter 12mm in lead and 762mm in journey
22 Signal Analysis and Feature Extraction With the increaseof service life ball screwrsquos performance will gradually reducemeanwhile the vibration of the screw fixed end changesgradually After more than five years of service life thevibration increased significantly Failure occurs at the seventhyear of service life Vibrations of screw fixed end underdifferent service life are showed in Figure 2
Considering the distribution characteristics of the ballscrew vibration signal the original features consist of thefollowing parts Time domain or frequency domain features(such as root mean square value peak value and gravityfrequency) which are presently used to reflect the timedomain or frequency domain are extracted as a part ofthe original signal features By using the wavelet analysismethod the vibration signal is decomposed into 5 levelsselecting wavelet ldquodb1rdquo and distinct time-frequency featuresbased on wavelet packet energy are obtained Approximateentropy a recently developed statistic theory in mechanicalfault diagnosis has also been applied to enrich the originalfeatures here
The original features extracted by different methodswhich have characteristics of high dimension and heavycomputation are not conducive to the online modeling andevaluation Meanwhile considering the certain correlationamong the high dimensional original features eliminatingredundant information is one of the main focuses in theresearch of feature extraction
PCA is a statistical method that uses an orthogonaltransformation to convert a set of observations of possiblycorrelated variables into a set of values of linearly uncorre-lated variables The 119899-dimensional original features can beexpressed as X = [119909
1 1199092 119909
119899] By means of PCA linearly
uncorrelated feature vectors Y = [1199101 1199102 119910
119899] can be
obtained The contribution of the 119894th component 120578119894can be
expressed as follows
120578119894=
120582119894
sum119899
119896=1 120582119896 (1)
where 120582119894is the variance of the 119910
119894
Then the contributions of the first119898 principal component1205781015840
119898can be built as follows
1205781015840
119898=
sum119898
119894=1 120582119894
sum119899
119896=1 120582119896 (2)
The first ten principal component contributions are plot-ted as shown in Figure 3The first three principal componentcontributions are more than 20 and the accumulativecontribution of the first five principal components is over90 Taking into account the real-time operation speed andoperation precision this paper takes the first five principalcomponents as the feature vectors of the screw performanceassessment system
3 Screw Performance Degradation Assessment
31 Dynamic Fuzzy Neural Network The DFNN has fivelayers including input layer output layer and three hiddenlayers [10 11] Figure 4 shows the structure of DFNN InFigure 4 119909
1 1199092 119909
119903are the input variables 119910 is the system
output MF119894119895is the 119895th membership function of the 119894th input
variable119873119895is the 119895th normalized node and 119908
119895is the weight
of the 119895th rule The number of the system rules is 119906The main function of each layer can be explained as
follows(1) Input layerThe variables119909
1 1199092 119909
119903are input to the
corresponding nodes respectively(2) Membership function layer Each node represents a
membership function which can be expressed as follows
120583119894119895(119909119894) = exp[
[
minus
(119909119894minus 119888119894119895)
2
1205902
119895
]
]
(3)
where 120583119894119895(119894 = 1 2 119903 119895 = 1 2 119906) is the 119895th mem-
bership function of the 119909119894 119888119894119895and 120590
119895represent the center and
width of the 120583119894119895 respectively
(3) 119905-norm layer In the layer fuzzy rules are representedby nodes The output of the 119895th node 119877
119895is defined as
120601119895= exp[
[
minus
sum119903
119894=1(119909119894minus 119888119894119895)
2
1205902
119895
]
]
= exp[minusX minus C2
1205902
119895
]
119895 = 1 2 119906
(4)
(4) Normalized layer Normalization processing is madefor the output of the 119905-norm layer in this layer The output of119895th node119873
119895can be expressed as follows
120595119895=
120601119895
sum119906
119896=1120601119896
119895 = 1 2 119906 (5)
(5) Output layer The system output which is the super-position of the input variables can be formulated as
119910 (X) =119906
sum
119896=1119908119896sdot 120595119896 (6)
Shock and Vibration 3
8704B100M1
INV1870
8765A250M5
Industrialcomputer
8704B100M1
Figure 1 Screw online monitoring system
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(a)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(b)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(c)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(d)
Figure 2 Vibrations of screw fixed end under different service life (a) vibration of 05-year-service screw (b) vibration of 2-year-servicescrew (c) vibration of 5-year-service screw and (d) vibration of 7-year-service screw
Before generating the first rule DFNN should set theinitialization parameters of the network Ten parametersof DFNN need to be initialized including membershipfunction width of the first rule 120590
0 overlap factor of the radial
based function 119896 width renewal factor 119896119908 rule threshold
119896err decay constant 120574 convergence constant 120573 maximumdebugging standard 120576maxminimumdebugging standard 120576minmaximumoutput error 119890max andminimumoutput error 119890minThe specific details of the ten initialization parameters areintroduced in [12ndash15]
DFNN will easily fall into local optimum due to therandom initialization of the network parameters Thereforethis paper applies QGA to obtain the optimal initializationparameters of DFNN
32 Quantum Genetic Algorithm The main ideas of QGAcan be expressed as follows according to the parametercharacteristics of DFNN chromosomal genes with quantumbit coding system are constructed and the population thatincludes several chromosomes is generated By adopting
4 Shock and Vibration
1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
30
35
40
Principal component
Prin
cipa
l com
pone
nt co
ntrib
utio
n (
)
Figure 3 The first ten principal component contributions
layer layer layer layer layer
x1
xr
y
w1
wj
wu
MFru Ru Nu
First Second Third Fourth Fifth
Figure 4 The structure of DFNN
quantum cross variation and quantum rotation gate theoptimal initialization parameters of DFNN can be obtainedFigure 5 shows the algorithm flowchart of QGA
321 Population Initialization Thepopulation size of the ini-tialized population Q(119905
0) = q1199050
1 q11990502 q1199050
119873 is 119873 By means
of the quantum bit coding system arbitrary chromosome q1199050119895
of the initialized populationQ(1199050) can be expressed as follows
q1199050119895=[
[
120572119905011
120573119905011
120572119905012
120573119905012
sdot sdot sdot
sdot sdot sdot
120572119905011198961
120573119905011198961
120572119905021
120573119905021
120572119905022
120573119905022
sdot sdot sdot
sdot sdot sdot
120572119905021198962
120573119905021198962
sdot sdot sdot
sdot sdot sdot
12057211990501198981
12057311990501198981
12057211990501198982
12057311990501198982
sdot sdot sdot
sdot sdot sdot
1205721199050119898119896119898
1205731199050119898119896119898
]
]
(7)
where 119898 is the number of the chromosomal genes and1198961 1198962 119896
119898represent the quantum bit number of each
chromosomal gene respectively q1199050119895is the 119895th chromosome
of the 1199050generation In this paper chromosome q1199050
119895includes
ten genes which are respectively corresponding to teninitialization parameters of DFNN Initialization probability
amplitude [120572 120573]119879 is [1radic2 1radic2]119879 so that each chromosomeexpresses the same state The fitness function is built asfollows [16 17]
119891 = 1minus 1119904
119904
sum
119901=1
1003816100381610038161003816100381610038161003816100381610038161003816
1199101015840
119901minus 119905119901
119905119901
1003816100381610038161003816100381610038161003816100381610038161003816
(8)
Shock and Vibration 5
Beginning
Population initialization
Individual measurement
Individual fitness evaluation
Quantum cross and variation
Renewal of population with quantum rotation gate
Recording optimal individual
Meetingtermination conditions
Bestindividual
Yes
No
QGA DFNN
Initializing DFNN
Generating the first rule
Obtaining initialization parameters
Calculating distance and searching the
Generating new rule
Calculating error decreased rate
Training end
Adjusting width
Adjusting the parameters
Yes
Yes
Yes
Yes
No
No
No
No
No
Yes
minimum value dmin
Calculating output error ei
Arbitrary data (Xi ti)(i gt 1)
dmin gt kd
ei gt ke ei gt ke
120578i lt kerr
Rejecting the ith rule
Figure 5 Algorithm flowchart of QGA
where 1199101015840119901is the predictive value of the imitating prediction
sample 119905119901is the true value of the imitating prediction sample
and 119904 is the number of the imitating prediction samplesFor DFNN training processing the predictive values
of the testing samples are prone to distortion though thepredictive values of the training samples are very good Toavoid having a seriously distorted prediction the fitnessfunction and imitating prediction samples can be used Thefitness function takes into account the fitting degree of the
training samples and the portability of optimized DFNNTherefore the prediction accuracy of the optimized DFNNis guaranteed
322 Quantum Cross and Variation In order to avoid fallinginto population local optimum quantum cross has been usedhere With the help of quantum cross new chromosomesare generated which means information exchange amongchromosomes is realized The cross processes are as follows
6 Shock and Vibration
Table 1 The adjustment strategy of the quantum rotating angle
119909119894119887119894
119891(119909) gt 119891(119887) Δ120579119894
119904(120572119894 120573119894)
120572119894120573119894gt 0 120572
119894120573119894lt 0 120572
119894= 0 120573
119894= 0
0 0 TRUEFALSE 0 0 0 0 00 1 FALSE 120596 +1 minus1 0 plusmn10 1 TRUE 120596 minus1 +1 plusmn1 01 0 FALSE 120596 minus1 +1 plusmn1 01 0 TRUE 120596 +1 minus1 0 plusmn11 1 TRUEFALSE 0 0 0 0 0
(1) Two chromosomes are randomly selected from thepopulation and whether cross operation should beconsidered is determined by cross probability
(2) If it is necessary to consider the cross operationexchanging the random cross position informationbetween two chromosomes is applied here
(3) Examining chromosome feasibility cross operation isfinished
By using quantum variation we can disturb the currentevolution direction of the chromosome to avoid early matu-rity so good global search capacity can be obtained
323 Quantum Rotation Gate Quantum gate is the actuatorof the evolution process for QGA The update process ofquantum rotation gate is as follows
[
1205721015840
1205731015840] = [
cos (120579) minus sin (120579)sin (120579) cos (120579)
] [
120572
120573
] (9)
where [120572 120573]119879 and [1205721015840 1205731015840]119879 represent quantum bit proba-
bility amplitudes before and after updating respectively 120579 isthe quantum rotating angle The adjustment strategy of thequantum rotating angle is shown in Table 1
Where 119909119894and 119887119894are the 119894th bit of the current chromosome
and the best chromosome respectively Δ120579119894is the adjusting
angle step and 119904(120572119894 120573119894) is the rotating angle direction This
paper adopts dynamic adjustment strategy based on expan-sion coefficient for quantum rotation gate [18ndash21] rotatingangle 120596 is defined as follows
120596 = 120596min + (120596max minus120596min) [1minus(119905119894
119905max)
120576
] (10)
where 120596min and 120596max are the minimum value and maximumvalue of the 120596 respectively 119905
119894is the number of the current
genetic generations 119905max is the number of the maximumgenetic generations and 120576 is the expansion coefficient
33 Screw Performance Degradation Model Sensor signalsare acquired by screw online monitoring system and highdimension features are extracted in both time domain andfrequency domain Then the feature vectors can be obtainedby PCA Feature vectors are sent to feature vectors librarytogether with the real-time working conditions Trainingsamples and imitating prediction samples are randomlyselected from the feature vectors library and used for training
DFNN and QGA After training testing samples selectedfrom the feature vectors library are used to test the optimizedand trained DFNN If the prediction accuracy falls onthe system error allowable range this DFNN can be usedas screw performance degradation model Otherwise theDFNN must be retrained by means of increasing samples ormodifying network parameters until the prediction accuracycan be guaranteed Flowchart of building screw performancedegradation model is showed in Figure 6
4 The Experiment Results
Screw vibration signals are not only determined by screwperformance degradation degree but also determined byworking conditions Feature vectors library which includesreal-time working conditions is accumulated with the help ofthe screw online monitoring system In this paper one ballscrew of CINCINNATIV5-3000 is used as the experimentobject Four class performance degradation samples of theball screw are randomly selected from the feature vectorslibrary together with their working conditions The lengthof each screw performance sample is 10 seconds while thesampling frequency is 256 kHz Four class screw perfor-mance samples include 05-year-service screw samples 2-year-service screw samples 5-year-service screw samplesand 7-year-service screw samples Training samples include400 samples (100 samples from each class) imitating pre-diction samples include 400 samples (100 samples from eachclass) and testing samples include 400 samples (100 samplesfrom each class)
A mapping method used for describing the output of thescrew performance degradation model is presented In thismethod different output intervals of the screw performancedegradation model show different kinds of screw perfor-mance Interval [0 02) indicates good performance Interval[02 04) indicates the performance degraded slightly Inter-val [04 06) indicates middle degraded performance whichcan still ensure the machining accuracy Interval [06 08)presents serious degraded performance which means thescrew is easy to go wrong Interval [08 1] means screwwith failure Combined with the field experiences the modeloutput of the 05-year-service screw samples 2-year-servicescrew samples 5-year-service screw samples and 7-year-service screw samples is 01 025 07 and 09
The QGA population scale and the number of theiterations should be based on comprehensive considerationof training samples and searching efficiency The parametersof the quantum cross variation and rotation gate can bedetermined by experiences on the premise of fast searchingoptimization The initialization parameters range of DFNNcan be obtained with multiple algorithm running tests [22ndash25] In this paper parameters of the QGA are selectedas follows [26 27] population scale is 40 the number ofthe iterations is 100 the initialization parameters intervalof DFNN is [0 3] cross probability is 03 while variationprobability is 01 maximum rotating angle 120596max is 015120587and minimum rotating angle 120596min is 001120587 and expansioncoefficient 120576 is 2
Shock and Vibration 7
Sensor signals
High dimension features
Featureextraction
Training samples Testing samples
QGA
Training DFNN
Optimal initialization parameters
Trained DFNNTest
Meet the requirements
Screw performancedegradation model
Yes
No
Increase samples
Modify network
parameters
PCA
Feature vectors libraryReal-time working
conditions
Imitating prediction samples
Figure 6 Flowchart of building screw performance degradation model
Table 2 The prediction accuracies of two DFNN
1205900
119896 119896119908
119896err 120574 120573 120576max 120576min 119890max 119890minAccuracy of training
samplesAccuracy of testing
samplesUnoptimizedDFNN 2 15 2 01 09 09 2 01 2 01 07350 06975
OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175
Table 2 shows the prediction accuracies of two DFNNCompared with the unoptimized DFNN the optimizedDFNN has higher prediction accuracies in both trainingsamples and testing samples From the prediction accuraciesof training samples and testing samples it is clear that theoptimized DFNNmaintains a stable prediction accuracy
Figures 7 and 8 show the confusion matrixes of unopti-mized DFNN It can be found that unoptimizedDFNN couldnot distinguish 5-year-service screw very well especially fortesting samples Figures 9 and 10 are the confusion matrixesof optimized DFNN It can be seen that optimized DFNNshows better prediction accuracies Figures 11 and 12 showthe training and testing accumulated errors of two DFNN
It is clear that optimized DFNN presents better predictionaccuracies
In order to validate the effect of the optimized DFNNbackpropagation (BP) neural network and radial basis func-tion (RBF) neural network are trained and tested with thesame samples Table 3 shows the prediction accuracies ofthree networks According to the results presented in Table 3prediction accuracy of the optimized DFNN is better thanthat of BP neural network and RBF neural network
Figures 13 and 14 are the confusion matrixes of BPneural network while Figures 15 and 16 are the confusionmatrixes of RBF neural network From Figure 13 to 16 it isfound that 2-year-service screw and 5-year-service screw are
8 Shock and Vibration
Table 3 The prediction accuracies of three networks
Optimized DFNN BP neural network RBF neural networkAccuracy of training samples 08225 06950 06925Accuracy of testing samples 08175 06375 06450
87
16
1
0
12
73
31
5
1
11
55
16
0
0
13
79
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 7 Unoptimized DFNN confusion matrix for training sam-ples
86
25
3
1
14
65
45
2
0
10
43
12
0
0
9
85
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 8 Unoptimized DFNN confusion matrix for testing sam-ples
difficult to distinguish both for BP neural network and forRBF neural network It is known that screw performancedegradation would obey the rule of bathtub curve 2-year-service screw and 5-year-service screw are in random failureperiodTherefore it is not easy to predict 2-year-service screwand 5-year-service screw Compared with Figures 9 and 10the optimizedDFNN shows better prediction accuracies thanBP neural network and RBF neural network
Figures 17 and 18 show the training and testing accu-mulated errors of three networks As seen in Figures 17 and
90
9
1
0
9
81
21
4
1
10
68
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 9 Optimized DFNN confusion matrix for training samples
87
11
1
0
12
79
18
2
1
10
71
8
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 10 Optimized DFNN confusion matrix for testing samples
18 the accumulated errors of BP network and RBF networkare larger than those of the optimized DFNN As previouslydiscussed it can be concluded that the optimized DFNN canassess screw performance degradation effectively
5 Conclusion
Screw performance degradation assessment based on QGAand DFNN is studied in this paper The experiment resultsclassified by the optimized DFNN show that our proposed
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
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2 Shock and Vibration
the prediction accuracies amongdifferent kinds of neural net-works to examine the effectiveness of the proposed method
2 Screw Vibration Feature Vectors
21 Screw Online Monitoring System Figure 1 shows thescrew onlinemonitoring system applied toCINCINNATIV5-3000 machining center Two Kistler 8704B100M1 one-wayaccelerometers are installed at two bearing chocks to mon-itor the radial vibration of screw ends while a Kistler8765A250M5 three-way accelerometer is installed on thescrew nut to monitor three-dimensional shaking of thescrew nut INV1870 is the signal conditioner connectedwith Advantech PCI1710 data acquisition card Industrycomputer can store the vibration data through the PCI1710data acquisition card and the sampling frequency is 256 kHzBall screw works in horizontal installation state meanwhilethe installation method of the ball screw is one-end fixedwhile the other end floated Ball screw reaches 45mm in axisdiameter 12mm in lead and 762mm in journey
22 Signal Analysis and Feature Extraction With the increaseof service life ball screwrsquos performance will gradually reducemeanwhile the vibration of the screw fixed end changesgradually After more than five years of service life thevibration increased significantly Failure occurs at the seventhyear of service life Vibrations of screw fixed end underdifferent service life are showed in Figure 2
Considering the distribution characteristics of the ballscrew vibration signal the original features consist of thefollowing parts Time domain or frequency domain features(such as root mean square value peak value and gravityfrequency) which are presently used to reflect the timedomain or frequency domain are extracted as a part ofthe original signal features By using the wavelet analysismethod the vibration signal is decomposed into 5 levelsselecting wavelet ldquodb1rdquo and distinct time-frequency featuresbased on wavelet packet energy are obtained Approximateentropy a recently developed statistic theory in mechanicalfault diagnosis has also been applied to enrich the originalfeatures here
The original features extracted by different methodswhich have characteristics of high dimension and heavycomputation are not conducive to the online modeling andevaluation Meanwhile considering the certain correlationamong the high dimensional original features eliminatingredundant information is one of the main focuses in theresearch of feature extraction
PCA is a statistical method that uses an orthogonaltransformation to convert a set of observations of possiblycorrelated variables into a set of values of linearly uncorre-lated variables The 119899-dimensional original features can beexpressed as X = [119909
1 1199092 119909
119899] By means of PCA linearly
uncorrelated feature vectors Y = [1199101 1199102 119910
119899] can be
obtained The contribution of the 119894th component 120578119894can be
expressed as follows
120578119894=
120582119894
sum119899
119896=1 120582119896 (1)
where 120582119894is the variance of the 119910
119894
Then the contributions of the first119898 principal component1205781015840
119898can be built as follows
1205781015840
119898=
sum119898
119894=1 120582119894
sum119899
119896=1 120582119896 (2)
The first ten principal component contributions are plot-ted as shown in Figure 3The first three principal componentcontributions are more than 20 and the accumulativecontribution of the first five principal components is over90 Taking into account the real-time operation speed andoperation precision this paper takes the first five principalcomponents as the feature vectors of the screw performanceassessment system
3 Screw Performance Degradation Assessment
31 Dynamic Fuzzy Neural Network The DFNN has fivelayers including input layer output layer and three hiddenlayers [10 11] Figure 4 shows the structure of DFNN InFigure 4 119909
1 1199092 119909
119903are the input variables 119910 is the system
output MF119894119895is the 119895th membership function of the 119894th input
variable119873119895is the 119895th normalized node and 119908
119895is the weight
of the 119895th rule The number of the system rules is 119906The main function of each layer can be explained as
follows(1) Input layerThe variables119909
1 1199092 119909
119903are input to the
corresponding nodes respectively(2) Membership function layer Each node represents a
membership function which can be expressed as follows
120583119894119895(119909119894) = exp[
[
minus
(119909119894minus 119888119894119895)
2
1205902
119895
]
]
(3)
where 120583119894119895(119894 = 1 2 119903 119895 = 1 2 119906) is the 119895th mem-
bership function of the 119909119894 119888119894119895and 120590
119895represent the center and
width of the 120583119894119895 respectively
(3) 119905-norm layer In the layer fuzzy rules are representedby nodes The output of the 119895th node 119877
119895is defined as
120601119895= exp[
[
minus
sum119903
119894=1(119909119894minus 119888119894119895)
2
1205902
119895
]
]
= exp[minusX minus C2
1205902
119895
]
119895 = 1 2 119906
(4)
(4) Normalized layer Normalization processing is madefor the output of the 119905-norm layer in this layer The output of119895th node119873
119895can be expressed as follows
120595119895=
120601119895
sum119906
119896=1120601119896
119895 = 1 2 119906 (5)
(5) Output layer The system output which is the super-position of the input variables can be formulated as
119910 (X) =119906
sum
119896=1119908119896sdot 120595119896 (6)
Shock and Vibration 3
8704B100M1
INV1870
8765A250M5
Industrialcomputer
8704B100M1
Figure 1 Screw online monitoring system
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(a)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(b)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(c)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(d)
Figure 2 Vibrations of screw fixed end under different service life (a) vibration of 05-year-service screw (b) vibration of 2-year-servicescrew (c) vibration of 5-year-service screw and (d) vibration of 7-year-service screw
Before generating the first rule DFNN should set theinitialization parameters of the network Ten parametersof DFNN need to be initialized including membershipfunction width of the first rule 120590
0 overlap factor of the radial
based function 119896 width renewal factor 119896119908 rule threshold
119896err decay constant 120574 convergence constant 120573 maximumdebugging standard 120576maxminimumdebugging standard 120576minmaximumoutput error 119890max andminimumoutput error 119890minThe specific details of the ten initialization parameters areintroduced in [12ndash15]
DFNN will easily fall into local optimum due to therandom initialization of the network parameters Thereforethis paper applies QGA to obtain the optimal initializationparameters of DFNN
32 Quantum Genetic Algorithm The main ideas of QGAcan be expressed as follows according to the parametercharacteristics of DFNN chromosomal genes with quantumbit coding system are constructed and the population thatincludes several chromosomes is generated By adopting
4 Shock and Vibration
1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
30
35
40
Principal component
Prin
cipa
l com
pone
nt co
ntrib
utio
n (
)
Figure 3 The first ten principal component contributions
layer layer layer layer layer
x1
xr
y
w1
wj
wu
MFru Ru Nu
First Second Third Fourth Fifth
Figure 4 The structure of DFNN
quantum cross variation and quantum rotation gate theoptimal initialization parameters of DFNN can be obtainedFigure 5 shows the algorithm flowchart of QGA
321 Population Initialization Thepopulation size of the ini-tialized population Q(119905
0) = q1199050
1 q11990502 q1199050
119873 is 119873 By means
of the quantum bit coding system arbitrary chromosome q1199050119895
of the initialized populationQ(1199050) can be expressed as follows
q1199050119895=[
[
120572119905011
120573119905011
120572119905012
120573119905012
sdot sdot sdot
sdot sdot sdot
120572119905011198961
120573119905011198961
120572119905021
120573119905021
120572119905022
120573119905022
sdot sdot sdot
sdot sdot sdot
120572119905021198962
120573119905021198962
sdot sdot sdot
sdot sdot sdot
12057211990501198981
12057311990501198981
12057211990501198982
12057311990501198982
sdot sdot sdot
sdot sdot sdot
1205721199050119898119896119898
1205731199050119898119896119898
]
]
(7)
where 119898 is the number of the chromosomal genes and1198961 1198962 119896
119898represent the quantum bit number of each
chromosomal gene respectively q1199050119895is the 119895th chromosome
of the 1199050generation In this paper chromosome q1199050
119895includes
ten genes which are respectively corresponding to teninitialization parameters of DFNN Initialization probability
amplitude [120572 120573]119879 is [1radic2 1radic2]119879 so that each chromosomeexpresses the same state The fitness function is built asfollows [16 17]
119891 = 1minus 1119904
119904
sum
119901=1
1003816100381610038161003816100381610038161003816100381610038161003816
1199101015840
119901minus 119905119901
119905119901
1003816100381610038161003816100381610038161003816100381610038161003816
(8)
Shock and Vibration 5
Beginning
Population initialization
Individual measurement
Individual fitness evaluation
Quantum cross and variation
Renewal of population with quantum rotation gate
Recording optimal individual
Meetingtermination conditions
Bestindividual
Yes
No
QGA DFNN
Initializing DFNN
Generating the first rule
Obtaining initialization parameters
Calculating distance and searching the
Generating new rule
Calculating error decreased rate
Training end
Adjusting width
Adjusting the parameters
Yes
Yes
Yes
Yes
No
No
No
No
No
Yes
minimum value dmin
Calculating output error ei
Arbitrary data (Xi ti)(i gt 1)
dmin gt kd
ei gt ke ei gt ke
120578i lt kerr
Rejecting the ith rule
Figure 5 Algorithm flowchart of QGA
where 1199101015840119901is the predictive value of the imitating prediction
sample 119905119901is the true value of the imitating prediction sample
and 119904 is the number of the imitating prediction samplesFor DFNN training processing the predictive values
of the testing samples are prone to distortion though thepredictive values of the training samples are very good Toavoid having a seriously distorted prediction the fitnessfunction and imitating prediction samples can be used Thefitness function takes into account the fitting degree of the
training samples and the portability of optimized DFNNTherefore the prediction accuracy of the optimized DFNNis guaranteed
322 Quantum Cross and Variation In order to avoid fallinginto population local optimum quantum cross has been usedhere With the help of quantum cross new chromosomesare generated which means information exchange amongchromosomes is realized The cross processes are as follows
6 Shock and Vibration
Table 1 The adjustment strategy of the quantum rotating angle
119909119894119887119894
119891(119909) gt 119891(119887) Δ120579119894
119904(120572119894 120573119894)
120572119894120573119894gt 0 120572
119894120573119894lt 0 120572
119894= 0 120573
119894= 0
0 0 TRUEFALSE 0 0 0 0 00 1 FALSE 120596 +1 minus1 0 plusmn10 1 TRUE 120596 minus1 +1 plusmn1 01 0 FALSE 120596 minus1 +1 plusmn1 01 0 TRUE 120596 +1 minus1 0 plusmn11 1 TRUEFALSE 0 0 0 0 0
(1) Two chromosomes are randomly selected from thepopulation and whether cross operation should beconsidered is determined by cross probability
(2) If it is necessary to consider the cross operationexchanging the random cross position informationbetween two chromosomes is applied here
(3) Examining chromosome feasibility cross operation isfinished
By using quantum variation we can disturb the currentevolution direction of the chromosome to avoid early matu-rity so good global search capacity can be obtained
323 Quantum Rotation Gate Quantum gate is the actuatorof the evolution process for QGA The update process ofquantum rotation gate is as follows
[
1205721015840
1205731015840] = [
cos (120579) minus sin (120579)sin (120579) cos (120579)
] [
120572
120573
] (9)
where [120572 120573]119879 and [1205721015840 1205731015840]119879 represent quantum bit proba-
bility amplitudes before and after updating respectively 120579 isthe quantum rotating angle The adjustment strategy of thequantum rotating angle is shown in Table 1
Where 119909119894and 119887119894are the 119894th bit of the current chromosome
and the best chromosome respectively Δ120579119894is the adjusting
angle step and 119904(120572119894 120573119894) is the rotating angle direction This
paper adopts dynamic adjustment strategy based on expan-sion coefficient for quantum rotation gate [18ndash21] rotatingangle 120596 is defined as follows
120596 = 120596min + (120596max minus120596min) [1minus(119905119894
119905max)
120576
] (10)
where 120596min and 120596max are the minimum value and maximumvalue of the 120596 respectively 119905
119894is the number of the current
genetic generations 119905max is the number of the maximumgenetic generations and 120576 is the expansion coefficient
33 Screw Performance Degradation Model Sensor signalsare acquired by screw online monitoring system and highdimension features are extracted in both time domain andfrequency domain Then the feature vectors can be obtainedby PCA Feature vectors are sent to feature vectors librarytogether with the real-time working conditions Trainingsamples and imitating prediction samples are randomlyselected from the feature vectors library and used for training
DFNN and QGA After training testing samples selectedfrom the feature vectors library are used to test the optimizedand trained DFNN If the prediction accuracy falls onthe system error allowable range this DFNN can be usedas screw performance degradation model Otherwise theDFNN must be retrained by means of increasing samples ormodifying network parameters until the prediction accuracycan be guaranteed Flowchart of building screw performancedegradation model is showed in Figure 6
4 The Experiment Results
Screw vibration signals are not only determined by screwperformance degradation degree but also determined byworking conditions Feature vectors library which includesreal-time working conditions is accumulated with the help ofthe screw online monitoring system In this paper one ballscrew of CINCINNATIV5-3000 is used as the experimentobject Four class performance degradation samples of theball screw are randomly selected from the feature vectorslibrary together with their working conditions The lengthof each screw performance sample is 10 seconds while thesampling frequency is 256 kHz Four class screw perfor-mance samples include 05-year-service screw samples 2-year-service screw samples 5-year-service screw samplesand 7-year-service screw samples Training samples include400 samples (100 samples from each class) imitating pre-diction samples include 400 samples (100 samples from eachclass) and testing samples include 400 samples (100 samplesfrom each class)
A mapping method used for describing the output of thescrew performance degradation model is presented In thismethod different output intervals of the screw performancedegradation model show different kinds of screw perfor-mance Interval [0 02) indicates good performance Interval[02 04) indicates the performance degraded slightly Inter-val [04 06) indicates middle degraded performance whichcan still ensure the machining accuracy Interval [06 08)presents serious degraded performance which means thescrew is easy to go wrong Interval [08 1] means screwwith failure Combined with the field experiences the modeloutput of the 05-year-service screw samples 2-year-servicescrew samples 5-year-service screw samples and 7-year-service screw samples is 01 025 07 and 09
The QGA population scale and the number of theiterations should be based on comprehensive considerationof training samples and searching efficiency The parametersof the quantum cross variation and rotation gate can bedetermined by experiences on the premise of fast searchingoptimization The initialization parameters range of DFNNcan be obtained with multiple algorithm running tests [22ndash25] In this paper parameters of the QGA are selectedas follows [26 27] population scale is 40 the number ofthe iterations is 100 the initialization parameters intervalof DFNN is [0 3] cross probability is 03 while variationprobability is 01 maximum rotating angle 120596max is 015120587and minimum rotating angle 120596min is 001120587 and expansioncoefficient 120576 is 2
Shock and Vibration 7
Sensor signals
High dimension features
Featureextraction
Training samples Testing samples
QGA
Training DFNN
Optimal initialization parameters
Trained DFNNTest
Meet the requirements
Screw performancedegradation model
Yes
No
Increase samples
Modify network
parameters
PCA
Feature vectors libraryReal-time working
conditions
Imitating prediction samples
Figure 6 Flowchart of building screw performance degradation model
Table 2 The prediction accuracies of two DFNN
1205900
119896 119896119908
119896err 120574 120573 120576max 120576min 119890max 119890minAccuracy of training
samplesAccuracy of testing
samplesUnoptimizedDFNN 2 15 2 01 09 09 2 01 2 01 07350 06975
OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175
Table 2 shows the prediction accuracies of two DFNNCompared with the unoptimized DFNN the optimizedDFNN has higher prediction accuracies in both trainingsamples and testing samples From the prediction accuraciesof training samples and testing samples it is clear that theoptimized DFNNmaintains a stable prediction accuracy
Figures 7 and 8 show the confusion matrixes of unopti-mized DFNN It can be found that unoptimizedDFNN couldnot distinguish 5-year-service screw very well especially fortesting samples Figures 9 and 10 are the confusion matrixesof optimized DFNN It can be seen that optimized DFNNshows better prediction accuracies Figures 11 and 12 showthe training and testing accumulated errors of two DFNN
It is clear that optimized DFNN presents better predictionaccuracies
In order to validate the effect of the optimized DFNNbackpropagation (BP) neural network and radial basis func-tion (RBF) neural network are trained and tested with thesame samples Table 3 shows the prediction accuracies ofthree networks According to the results presented in Table 3prediction accuracy of the optimized DFNN is better thanthat of BP neural network and RBF neural network
Figures 13 and 14 are the confusion matrixes of BPneural network while Figures 15 and 16 are the confusionmatrixes of RBF neural network From Figure 13 to 16 it isfound that 2-year-service screw and 5-year-service screw are
8 Shock and Vibration
Table 3 The prediction accuracies of three networks
Optimized DFNN BP neural network RBF neural networkAccuracy of training samples 08225 06950 06925Accuracy of testing samples 08175 06375 06450
87
16
1
0
12
73
31
5
1
11
55
16
0
0
13
79
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 7 Unoptimized DFNN confusion matrix for training sam-ples
86
25
3
1
14
65
45
2
0
10
43
12
0
0
9
85
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 8 Unoptimized DFNN confusion matrix for testing sam-ples
difficult to distinguish both for BP neural network and forRBF neural network It is known that screw performancedegradation would obey the rule of bathtub curve 2-year-service screw and 5-year-service screw are in random failureperiodTherefore it is not easy to predict 2-year-service screwand 5-year-service screw Compared with Figures 9 and 10the optimizedDFNN shows better prediction accuracies thanBP neural network and RBF neural network
Figures 17 and 18 show the training and testing accu-mulated errors of three networks As seen in Figures 17 and
90
9
1
0
9
81
21
4
1
10
68
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 9 Optimized DFNN confusion matrix for training samples
87
11
1
0
12
79
18
2
1
10
71
8
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 10 Optimized DFNN confusion matrix for testing samples
18 the accumulated errors of BP network and RBF networkare larger than those of the optimized DFNN As previouslydiscussed it can be concluded that the optimized DFNN canassess screw performance degradation effectively
5 Conclusion
Screw performance degradation assessment based on QGAand DFNN is studied in this paper The experiment resultsclassified by the optimized DFNN show that our proposed
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
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Active and Passive Electronic Components
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VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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Electrical and Computer Engineering
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Navigation and Observation
International Journal of
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DistributedSensor Networks
International Journal of
Shock and Vibration 3
8704B100M1
INV1870
8765A250M5
Industrialcomputer
8704B100M1
Figure 1 Screw online monitoring system
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(a)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(b)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(c)
0 02 04 06 08 1minus5
0
5
Time (s)
Am
plitu
de (V
)
(d)
Figure 2 Vibrations of screw fixed end under different service life (a) vibration of 05-year-service screw (b) vibration of 2-year-servicescrew (c) vibration of 5-year-service screw and (d) vibration of 7-year-service screw
Before generating the first rule DFNN should set theinitialization parameters of the network Ten parametersof DFNN need to be initialized including membershipfunction width of the first rule 120590
0 overlap factor of the radial
based function 119896 width renewal factor 119896119908 rule threshold
119896err decay constant 120574 convergence constant 120573 maximumdebugging standard 120576maxminimumdebugging standard 120576minmaximumoutput error 119890max andminimumoutput error 119890minThe specific details of the ten initialization parameters areintroduced in [12ndash15]
DFNN will easily fall into local optimum due to therandom initialization of the network parameters Thereforethis paper applies QGA to obtain the optimal initializationparameters of DFNN
32 Quantum Genetic Algorithm The main ideas of QGAcan be expressed as follows according to the parametercharacteristics of DFNN chromosomal genes with quantumbit coding system are constructed and the population thatincludes several chromosomes is generated By adopting
4 Shock and Vibration
1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
30
35
40
Principal component
Prin
cipa
l com
pone
nt co
ntrib
utio
n (
)
Figure 3 The first ten principal component contributions
layer layer layer layer layer
x1
xr
y
w1
wj
wu
MFru Ru Nu
First Second Third Fourth Fifth
Figure 4 The structure of DFNN
quantum cross variation and quantum rotation gate theoptimal initialization parameters of DFNN can be obtainedFigure 5 shows the algorithm flowchart of QGA
321 Population Initialization Thepopulation size of the ini-tialized population Q(119905
0) = q1199050
1 q11990502 q1199050
119873 is 119873 By means
of the quantum bit coding system arbitrary chromosome q1199050119895
of the initialized populationQ(1199050) can be expressed as follows
q1199050119895=[
[
120572119905011
120573119905011
120572119905012
120573119905012
sdot sdot sdot
sdot sdot sdot
120572119905011198961
120573119905011198961
120572119905021
120573119905021
120572119905022
120573119905022
sdot sdot sdot
sdot sdot sdot
120572119905021198962
120573119905021198962
sdot sdot sdot
sdot sdot sdot
12057211990501198981
12057311990501198981
12057211990501198982
12057311990501198982
sdot sdot sdot
sdot sdot sdot
1205721199050119898119896119898
1205731199050119898119896119898
]
]
(7)
where 119898 is the number of the chromosomal genes and1198961 1198962 119896
119898represent the quantum bit number of each
chromosomal gene respectively q1199050119895is the 119895th chromosome
of the 1199050generation In this paper chromosome q1199050
119895includes
ten genes which are respectively corresponding to teninitialization parameters of DFNN Initialization probability
amplitude [120572 120573]119879 is [1radic2 1radic2]119879 so that each chromosomeexpresses the same state The fitness function is built asfollows [16 17]
119891 = 1minus 1119904
119904
sum
119901=1
1003816100381610038161003816100381610038161003816100381610038161003816
1199101015840
119901minus 119905119901
119905119901
1003816100381610038161003816100381610038161003816100381610038161003816
(8)
Shock and Vibration 5
Beginning
Population initialization
Individual measurement
Individual fitness evaluation
Quantum cross and variation
Renewal of population with quantum rotation gate
Recording optimal individual
Meetingtermination conditions
Bestindividual
Yes
No
QGA DFNN
Initializing DFNN
Generating the first rule
Obtaining initialization parameters
Calculating distance and searching the
Generating new rule
Calculating error decreased rate
Training end
Adjusting width
Adjusting the parameters
Yes
Yes
Yes
Yes
No
No
No
No
No
Yes
minimum value dmin
Calculating output error ei
Arbitrary data (Xi ti)(i gt 1)
dmin gt kd
ei gt ke ei gt ke
120578i lt kerr
Rejecting the ith rule
Figure 5 Algorithm flowchart of QGA
where 1199101015840119901is the predictive value of the imitating prediction
sample 119905119901is the true value of the imitating prediction sample
and 119904 is the number of the imitating prediction samplesFor DFNN training processing the predictive values
of the testing samples are prone to distortion though thepredictive values of the training samples are very good Toavoid having a seriously distorted prediction the fitnessfunction and imitating prediction samples can be used Thefitness function takes into account the fitting degree of the
training samples and the portability of optimized DFNNTherefore the prediction accuracy of the optimized DFNNis guaranteed
322 Quantum Cross and Variation In order to avoid fallinginto population local optimum quantum cross has been usedhere With the help of quantum cross new chromosomesare generated which means information exchange amongchromosomes is realized The cross processes are as follows
6 Shock and Vibration
Table 1 The adjustment strategy of the quantum rotating angle
119909119894119887119894
119891(119909) gt 119891(119887) Δ120579119894
119904(120572119894 120573119894)
120572119894120573119894gt 0 120572
119894120573119894lt 0 120572
119894= 0 120573
119894= 0
0 0 TRUEFALSE 0 0 0 0 00 1 FALSE 120596 +1 minus1 0 plusmn10 1 TRUE 120596 minus1 +1 plusmn1 01 0 FALSE 120596 minus1 +1 plusmn1 01 0 TRUE 120596 +1 minus1 0 plusmn11 1 TRUEFALSE 0 0 0 0 0
(1) Two chromosomes are randomly selected from thepopulation and whether cross operation should beconsidered is determined by cross probability
(2) If it is necessary to consider the cross operationexchanging the random cross position informationbetween two chromosomes is applied here
(3) Examining chromosome feasibility cross operation isfinished
By using quantum variation we can disturb the currentevolution direction of the chromosome to avoid early matu-rity so good global search capacity can be obtained
323 Quantum Rotation Gate Quantum gate is the actuatorof the evolution process for QGA The update process ofquantum rotation gate is as follows
[
1205721015840
1205731015840] = [
cos (120579) minus sin (120579)sin (120579) cos (120579)
] [
120572
120573
] (9)
where [120572 120573]119879 and [1205721015840 1205731015840]119879 represent quantum bit proba-
bility amplitudes before and after updating respectively 120579 isthe quantum rotating angle The adjustment strategy of thequantum rotating angle is shown in Table 1
Where 119909119894and 119887119894are the 119894th bit of the current chromosome
and the best chromosome respectively Δ120579119894is the adjusting
angle step and 119904(120572119894 120573119894) is the rotating angle direction This
paper adopts dynamic adjustment strategy based on expan-sion coefficient for quantum rotation gate [18ndash21] rotatingangle 120596 is defined as follows
120596 = 120596min + (120596max minus120596min) [1minus(119905119894
119905max)
120576
] (10)
where 120596min and 120596max are the minimum value and maximumvalue of the 120596 respectively 119905
119894is the number of the current
genetic generations 119905max is the number of the maximumgenetic generations and 120576 is the expansion coefficient
33 Screw Performance Degradation Model Sensor signalsare acquired by screw online monitoring system and highdimension features are extracted in both time domain andfrequency domain Then the feature vectors can be obtainedby PCA Feature vectors are sent to feature vectors librarytogether with the real-time working conditions Trainingsamples and imitating prediction samples are randomlyselected from the feature vectors library and used for training
DFNN and QGA After training testing samples selectedfrom the feature vectors library are used to test the optimizedand trained DFNN If the prediction accuracy falls onthe system error allowable range this DFNN can be usedas screw performance degradation model Otherwise theDFNN must be retrained by means of increasing samples ormodifying network parameters until the prediction accuracycan be guaranteed Flowchart of building screw performancedegradation model is showed in Figure 6
4 The Experiment Results
Screw vibration signals are not only determined by screwperformance degradation degree but also determined byworking conditions Feature vectors library which includesreal-time working conditions is accumulated with the help ofthe screw online monitoring system In this paper one ballscrew of CINCINNATIV5-3000 is used as the experimentobject Four class performance degradation samples of theball screw are randomly selected from the feature vectorslibrary together with their working conditions The lengthof each screw performance sample is 10 seconds while thesampling frequency is 256 kHz Four class screw perfor-mance samples include 05-year-service screw samples 2-year-service screw samples 5-year-service screw samplesand 7-year-service screw samples Training samples include400 samples (100 samples from each class) imitating pre-diction samples include 400 samples (100 samples from eachclass) and testing samples include 400 samples (100 samplesfrom each class)
A mapping method used for describing the output of thescrew performance degradation model is presented In thismethod different output intervals of the screw performancedegradation model show different kinds of screw perfor-mance Interval [0 02) indicates good performance Interval[02 04) indicates the performance degraded slightly Inter-val [04 06) indicates middle degraded performance whichcan still ensure the machining accuracy Interval [06 08)presents serious degraded performance which means thescrew is easy to go wrong Interval [08 1] means screwwith failure Combined with the field experiences the modeloutput of the 05-year-service screw samples 2-year-servicescrew samples 5-year-service screw samples and 7-year-service screw samples is 01 025 07 and 09
The QGA population scale and the number of theiterations should be based on comprehensive considerationof training samples and searching efficiency The parametersof the quantum cross variation and rotation gate can bedetermined by experiences on the premise of fast searchingoptimization The initialization parameters range of DFNNcan be obtained with multiple algorithm running tests [22ndash25] In this paper parameters of the QGA are selectedas follows [26 27] population scale is 40 the number ofthe iterations is 100 the initialization parameters intervalof DFNN is [0 3] cross probability is 03 while variationprobability is 01 maximum rotating angle 120596max is 015120587and minimum rotating angle 120596min is 001120587 and expansioncoefficient 120576 is 2
Shock and Vibration 7
Sensor signals
High dimension features
Featureextraction
Training samples Testing samples
QGA
Training DFNN
Optimal initialization parameters
Trained DFNNTest
Meet the requirements
Screw performancedegradation model
Yes
No
Increase samples
Modify network
parameters
PCA
Feature vectors libraryReal-time working
conditions
Imitating prediction samples
Figure 6 Flowchart of building screw performance degradation model
Table 2 The prediction accuracies of two DFNN
1205900
119896 119896119908
119896err 120574 120573 120576max 120576min 119890max 119890minAccuracy of training
samplesAccuracy of testing
samplesUnoptimizedDFNN 2 15 2 01 09 09 2 01 2 01 07350 06975
OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175
Table 2 shows the prediction accuracies of two DFNNCompared with the unoptimized DFNN the optimizedDFNN has higher prediction accuracies in both trainingsamples and testing samples From the prediction accuraciesof training samples and testing samples it is clear that theoptimized DFNNmaintains a stable prediction accuracy
Figures 7 and 8 show the confusion matrixes of unopti-mized DFNN It can be found that unoptimizedDFNN couldnot distinguish 5-year-service screw very well especially fortesting samples Figures 9 and 10 are the confusion matrixesof optimized DFNN It can be seen that optimized DFNNshows better prediction accuracies Figures 11 and 12 showthe training and testing accumulated errors of two DFNN
It is clear that optimized DFNN presents better predictionaccuracies
In order to validate the effect of the optimized DFNNbackpropagation (BP) neural network and radial basis func-tion (RBF) neural network are trained and tested with thesame samples Table 3 shows the prediction accuracies ofthree networks According to the results presented in Table 3prediction accuracy of the optimized DFNN is better thanthat of BP neural network and RBF neural network
Figures 13 and 14 are the confusion matrixes of BPneural network while Figures 15 and 16 are the confusionmatrixes of RBF neural network From Figure 13 to 16 it isfound that 2-year-service screw and 5-year-service screw are
8 Shock and Vibration
Table 3 The prediction accuracies of three networks
Optimized DFNN BP neural network RBF neural networkAccuracy of training samples 08225 06950 06925Accuracy of testing samples 08175 06375 06450
87
16
1
0
12
73
31
5
1
11
55
16
0
0
13
79
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 7 Unoptimized DFNN confusion matrix for training sam-ples
86
25
3
1
14
65
45
2
0
10
43
12
0
0
9
85
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 8 Unoptimized DFNN confusion matrix for testing sam-ples
difficult to distinguish both for BP neural network and forRBF neural network It is known that screw performancedegradation would obey the rule of bathtub curve 2-year-service screw and 5-year-service screw are in random failureperiodTherefore it is not easy to predict 2-year-service screwand 5-year-service screw Compared with Figures 9 and 10the optimizedDFNN shows better prediction accuracies thanBP neural network and RBF neural network
Figures 17 and 18 show the training and testing accu-mulated errors of three networks As seen in Figures 17 and
90
9
1
0
9
81
21
4
1
10
68
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 9 Optimized DFNN confusion matrix for training samples
87
11
1
0
12
79
18
2
1
10
71
8
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 10 Optimized DFNN confusion matrix for testing samples
18 the accumulated errors of BP network and RBF networkare larger than those of the optimized DFNN As previouslydiscussed it can be concluded that the optimized DFNN canassess screw performance degradation effectively
5 Conclusion
Screw performance degradation assessment based on QGAand DFNN is studied in this paper The experiment resultsclassified by the optimized DFNN show that our proposed
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
4 Shock and Vibration
1 2 3 4 5 6 7 8 9 100
5
10
15
20
25
30
35
40
Principal component
Prin
cipa
l com
pone
nt co
ntrib
utio
n (
)
Figure 3 The first ten principal component contributions
layer layer layer layer layer
x1
xr
y
w1
wj
wu
MFru Ru Nu
First Second Third Fourth Fifth
Figure 4 The structure of DFNN
quantum cross variation and quantum rotation gate theoptimal initialization parameters of DFNN can be obtainedFigure 5 shows the algorithm flowchart of QGA
321 Population Initialization Thepopulation size of the ini-tialized population Q(119905
0) = q1199050
1 q11990502 q1199050
119873 is 119873 By means
of the quantum bit coding system arbitrary chromosome q1199050119895
of the initialized populationQ(1199050) can be expressed as follows
q1199050119895=[
[
120572119905011
120573119905011
120572119905012
120573119905012
sdot sdot sdot
sdot sdot sdot
120572119905011198961
120573119905011198961
120572119905021
120573119905021
120572119905022
120573119905022
sdot sdot sdot
sdot sdot sdot
120572119905021198962
120573119905021198962
sdot sdot sdot
sdot sdot sdot
12057211990501198981
12057311990501198981
12057211990501198982
12057311990501198982
sdot sdot sdot
sdot sdot sdot
1205721199050119898119896119898
1205731199050119898119896119898
]
]
(7)
where 119898 is the number of the chromosomal genes and1198961 1198962 119896
119898represent the quantum bit number of each
chromosomal gene respectively q1199050119895is the 119895th chromosome
of the 1199050generation In this paper chromosome q1199050
119895includes
ten genes which are respectively corresponding to teninitialization parameters of DFNN Initialization probability
amplitude [120572 120573]119879 is [1radic2 1radic2]119879 so that each chromosomeexpresses the same state The fitness function is built asfollows [16 17]
119891 = 1minus 1119904
119904
sum
119901=1
1003816100381610038161003816100381610038161003816100381610038161003816
1199101015840
119901minus 119905119901
119905119901
1003816100381610038161003816100381610038161003816100381610038161003816
(8)
Shock and Vibration 5
Beginning
Population initialization
Individual measurement
Individual fitness evaluation
Quantum cross and variation
Renewal of population with quantum rotation gate
Recording optimal individual
Meetingtermination conditions
Bestindividual
Yes
No
QGA DFNN
Initializing DFNN
Generating the first rule
Obtaining initialization parameters
Calculating distance and searching the
Generating new rule
Calculating error decreased rate
Training end
Adjusting width
Adjusting the parameters
Yes
Yes
Yes
Yes
No
No
No
No
No
Yes
minimum value dmin
Calculating output error ei
Arbitrary data (Xi ti)(i gt 1)
dmin gt kd
ei gt ke ei gt ke
120578i lt kerr
Rejecting the ith rule
Figure 5 Algorithm flowchart of QGA
where 1199101015840119901is the predictive value of the imitating prediction
sample 119905119901is the true value of the imitating prediction sample
and 119904 is the number of the imitating prediction samplesFor DFNN training processing the predictive values
of the testing samples are prone to distortion though thepredictive values of the training samples are very good Toavoid having a seriously distorted prediction the fitnessfunction and imitating prediction samples can be used Thefitness function takes into account the fitting degree of the
training samples and the portability of optimized DFNNTherefore the prediction accuracy of the optimized DFNNis guaranteed
322 Quantum Cross and Variation In order to avoid fallinginto population local optimum quantum cross has been usedhere With the help of quantum cross new chromosomesare generated which means information exchange amongchromosomes is realized The cross processes are as follows
6 Shock and Vibration
Table 1 The adjustment strategy of the quantum rotating angle
119909119894119887119894
119891(119909) gt 119891(119887) Δ120579119894
119904(120572119894 120573119894)
120572119894120573119894gt 0 120572
119894120573119894lt 0 120572
119894= 0 120573
119894= 0
0 0 TRUEFALSE 0 0 0 0 00 1 FALSE 120596 +1 minus1 0 plusmn10 1 TRUE 120596 minus1 +1 plusmn1 01 0 FALSE 120596 minus1 +1 plusmn1 01 0 TRUE 120596 +1 minus1 0 plusmn11 1 TRUEFALSE 0 0 0 0 0
(1) Two chromosomes are randomly selected from thepopulation and whether cross operation should beconsidered is determined by cross probability
(2) If it is necessary to consider the cross operationexchanging the random cross position informationbetween two chromosomes is applied here
(3) Examining chromosome feasibility cross operation isfinished
By using quantum variation we can disturb the currentevolution direction of the chromosome to avoid early matu-rity so good global search capacity can be obtained
323 Quantum Rotation Gate Quantum gate is the actuatorof the evolution process for QGA The update process ofquantum rotation gate is as follows
[
1205721015840
1205731015840] = [
cos (120579) minus sin (120579)sin (120579) cos (120579)
] [
120572
120573
] (9)
where [120572 120573]119879 and [1205721015840 1205731015840]119879 represent quantum bit proba-
bility amplitudes before and after updating respectively 120579 isthe quantum rotating angle The adjustment strategy of thequantum rotating angle is shown in Table 1
Where 119909119894and 119887119894are the 119894th bit of the current chromosome
and the best chromosome respectively Δ120579119894is the adjusting
angle step and 119904(120572119894 120573119894) is the rotating angle direction This
paper adopts dynamic adjustment strategy based on expan-sion coefficient for quantum rotation gate [18ndash21] rotatingangle 120596 is defined as follows
120596 = 120596min + (120596max minus120596min) [1minus(119905119894
119905max)
120576
] (10)
where 120596min and 120596max are the minimum value and maximumvalue of the 120596 respectively 119905
119894is the number of the current
genetic generations 119905max is the number of the maximumgenetic generations and 120576 is the expansion coefficient
33 Screw Performance Degradation Model Sensor signalsare acquired by screw online monitoring system and highdimension features are extracted in both time domain andfrequency domain Then the feature vectors can be obtainedby PCA Feature vectors are sent to feature vectors librarytogether with the real-time working conditions Trainingsamples and imitating prediction samples are randomlyselected from the feature vectors library and used for training
DFNN and QGA After training testing samples selectedfrom the feature vectors library are used to test the optimizedand trained DFNN If the prediction accuracy falls onthe system error allowable range this DFNN can be usedas screw performance degradation model Otherwise theDFNN must be retrained by means of increasing samples ormodifying network parameters until the prediction accuracycan be guaranteed Flowchart of building screw performancedegradation model is showed in Figure 6
4 The Experiment Results
Screw vibration signals are not only determined by screwperformance degradation degree but also determined byworking conditions Feature vectors library which includesreal-time working conditions is accumulated with the help ofthe screw online monitoring system In this paper one ballscrew of CINCINNATIV5-3000 is used as the experimentobject Four class performance degradation samples of theball screw are randomly selected from the feature vectorslibrary together with their working conditions The lengthof each screw performance sample is 10 seconds while thesampling frequency is 256 kHz Four class screw perfor-mance samples include 05-year-service screw samples 2-year-service screw samples 5-year-service screw samplesand 7-year-service screw samples Training samples include400 samples (100 samples from each class) imitating pre-diction samples include 400 samples (100 samples from eachclass) and testing samples include 400 samples (100 samplesfrom each class)
A mapping method used for describing the output of thescrew performance degradation model is presented In thismethod different output intervals of the screw performancedegradation model show different kinds of screw perfor-mance Interval [0 02) indicates good performance Interval[02 04) indicates the performance degraded slightly Inter-val [04 06) indicates middle degraded performance whichcan still ensure the machining accuracy Interval [06 08)presents serious degraded performance which means thescrew is easy to go wrong Interval [08 1] means screwwith failure Combined with the field experiences the modeloutput of the 05-year-service screw samples 2-year-servicescrew samples 5-year-service screw samples and 7-year-service screw samples is 01 025 07 and 09
The QGA population scale and the number of theiterations should be based on comprehensive considerationof training samples and searching efficiency The parametersof the quantum cross variation and rotation gate can bedetermined by experiences on the premise of fast searchingoptimization The initialization parameters range of DFNNcan be obtained with multiple algorithm running tests [22ndash25] In this paper parameters of the QGA are selectedas follows [26 27] population scale is 40 the number ofthe iterations is 100 the initialization parameters intervalof DFNN is [0 3] cross probability is 03 while variationprobability is 01 maximum rotating angle 120596max is 015120587and minimum rotating angle 120596min is 001120587 and expansioncoefficient 120576 is 2
Shock and Vibration 7
Sensor signals
High dimension features
Featureextraction
Training samples Testing samples
QGA
Training DFNN
Optimal initialization parameters
Trained DFNNTest
Meet the requirements
Screw performancedegradation model
Yes
No
Increase samples
Modify network
parameters
PCA
Feature vectors libraryReal-time working
conditions
Imitating prediction samples
Figure 6 Flowchart of building screw performance degradation model
Table 2 The prediction accuracies of two DFNN
1205900
119896 119896119908
119896err 120574 120573 120576max 120576min 119890max 119890minAccuracy of training
samplesAccuracy of testing
samplesUnoptimizedDFNN 2 15 2 01 09 09 2 01 2 01 07350 06975
OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175
Table 2 shows the prediction accuracies of two DFNNCompared with the unoptimized DFNN the optimizedDFNN has higher prediction accuracies in both trainingsamples and testing samples From the prediction accuraciesof training samples and testing samples it is clear that theoptimized DFNNmaintains a stable prediction accuracy
Figures 7 and 8 show the confusion matrixes of unopti-mized DFNN It can be found that unoptimizedDFNN couldnot distinguish 5-year-service screw very well especially fortesting samples Figures 9 and 10 are the confusion matrixesof optimized DFNN It can be seen that optimized DFNNshows better prediction accuracies Figures 11 and 12 showthe training and testing accumulated errors of two DFNN
It is clear that optimized DFNN presents better predictionaccuracies
In order to validate the effect of the optimized DFNNbackpropagation (BP) neural network and radial basis func-tion (RBF) neural network are trained and tested with thesame samples Table 3 shows the prediction accuracies ofthree networks According to the results presented in Table 3prediction accuracy of the optimized DFNN is better thanthat of BP neural network and RBF neural network
Figures 13 and 14 are the confusion matrixes of BPneural network while Figures 15 and 16 are the confusionmatrixes of RBF neural network From Figure 13 to 16 it isfound that 2-year-service screw and 5-year-service screw are
8 Shock and Vibration
Table 3 The prediction accuracies of three networks
Optimized DFNN BP neural network RBF neural networkAccuracy of training samples 08225 06950 06925Accuracy of testing samples 08175 06375 06450
87
16
1
0
12
73
31
5
1
11
55
16
0
0
13
79
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 7 Unoptimized DFNN confusion matrix for training sam-ples
86
25
3
1
14
65
45
2
0
10
43
12
0
0
9
85
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 8 Unoptimized DFNN confusion matrix for testing sam-ples
difficult to distinguish both for BP neural network and forRBF neural network It is known that screw performancedegradation would obey the rule of bathtub curve 2-year-service screw and 5-year-service screw are in random failureperiodTherefore it is not easy to predict 2-year-service screwand 5-year-service screw Compared with Figures 9 and 10the optimizedDFNN shows better prediction accuracies thanBP neural network and RBF neural network
Figures 17 and 18 show the training and testing accu-mulated errors of three networks As seen in Figures 17 and
90
9
1
0
9
81
21
4
1
10
68
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 9 Optimized DFNN confusion matrix for training samples
87
11
1
0
12
79
18
2
1
10
71
8
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 10 Optimized DFNN confusion matrix for testing samples
18 the accumulated errors of BP network and RBF networkare larger than those of the optimized DFNN As previouslydiscussed it can be concluded that the optimized DFNN canassess screw performance degradation effectively
5 Conclusion
Screw performance degradation assessment based on QGAand DFNN is studied in this paper The experiment resultsclassified by the optimized DFNN show that our proposed
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 5
Beginning
Population initialization
Individual measurement
Individual fitness evaluation
Quantum cross and variation
Renewal of population with quantum rotation gate
Recording optimal individual
Meetingtermination conditions
Bestindividual
Yes
No
QGA DFNN
Initializing DFNN
Generating the first rule
Obtaining initialization parameters
Calculating distance and searching the
Generating new rule
Calculating error decreased rate
Training end
Adjusting width
Adjusting the parameters
Yes
Yes
Yes
Yes
No
No
No
No
No
Yes
minimum value dmin
Calculating output error ei
Arbitrary data (Xi ti)(i gt 1)
dmin gt kd
ei gt ke ei gt ke
120578i lt kerr
Rejecting the ith rule
Figure 5 Algorithm flowchart of QGA
where 1199101015840119901is the predictive value of the imitating prediction
sample 119905119901is the true value of the imitating prediction sample
and 119904 is the number of the imitating prediction samplesFor DFNN training processing the predictive values
of the testing samples are prone to distortion though thepredictive values of the training samples are very good Toavoid having a seriously distorted prediction the fitnessfunction and imitating prediction samples can be used Thefitness function takes into account the fitting degree of the
training samples and the portability of optimized DFNNTherefore the prediction accuracy of the optimized DFNNis guaranteed
322 Quantum Cross and Variation In order to avoid fallinginto population local optimum quantum cross has been usedhere With the help of quantum cross new chromosomesare generated which means information exchange amongchromosomes is realized The cross processes are as follows
6 Shock and Vibration
Table 1 The adjustment strategy of the quantum rotating angle
119909119894119887119894
119891(119909) gt 119891(119887) Δ120579119894
119904(120572119894 120573119894)
120572119894120573119894gt 0 120572
119894120573119894lt 0 120572
119894= 0 120573
119894= 0
0 0 TRUEFALSE 0 0 0 0 00 1 FALSE 120596 +1 minus1 0 plusmn10 1 TRUE 120596 minus1 +1 plusmn1 01 0 FALSE 120596 minus1 +1 plusmn1 01 0 TRUE 120596 +1 minus1 0 plusmn11 1 TRUEFALSE 0 0 0 0 0
(1) Two chromosomes are randomly selected from thepopulation and whether cross operation should beconsidered is determined by cross probability
(2) If it is necessary to consider the cross operationexchanging the random cross position informationbetween two chromosomes is applied here
(3) Examining chromosome feasibility cross operation isfinished
By using quantum variation we can disturb the currentevolution direction of the chromosome to avoid early matu-rity so good global search capacity can be obtained
323 Quantum Rotation Gate Quantum gate is the actuatorof the evolution process for QGA The update process ofquantum rotation gate is as follows
[
1205721015840
1205731015840] = [
cos (120579) minus sin (120579)sin (120579) cos (120579)
] [
120572
120573
] (9)
where [120572 120573]119879 and [1205721015840 1205731015840]119879 represent quantum bit proba-
bility amplitudes before and after updating respectively 120579 isthe quantum rotating angle The adjustment strategy of thequantum rotating angle is shown in Table 1
Where 119909119894and 119887119894are the 119894th bit of the current chromosome
and the best chromosome respectively Δ120579119894is the adjusting
angle step and 119904(120572119894 120573119894) is the rotating angle direction This
paper adopts dynamic adjustment strategy based on expan-sion coefficient for quantum rotation gate [18ndash21] rotatingangle 120596 is defined as follows
120596 = 120596min + (120596max minus120596min) [1minus(119905119894
119905max)
120576
] (10)
where 120596min and 120596max are the minimum value and maximumvalue of the 120596 respectively 119905
119894is the number of the current
genetic generations 119905max is the number of the maximumgenetic generations and 120576 is the expansion coefficient
33 Screw Performance Degradation Model Sensor signalsare acquired by screw online monitoring system and highdimension features are extracted in both time domain andfrequency domain Then the feature vectors can be obtainedby PCA Feature vectors are sent to feature vectors librarytogether with the real-time working conditions Trainingsamples and imitating prediction samples are randomlyselected from the feature vectors library and used for training
DFNN and QGA After training testing samples selectedfrom the feature vectors library are used to test the optimizedand trained DFNN If the prediction accuracy falls onthe system error allowable range this DFNN can be usedas screw performance degradation model Otherwise theDFNN must be retrained by means of increasing samples ormodifying network parameters until the prediction accuracycan be guaranteed Flowchart of building screw performancedegradation model is showed in Figure 6
4 The Experiment Results
Screw vibration signals are not only determined by screwperformance degradation degree but also determined byworking conditions Feature vectors library which includesreal-time working conditions is accumulated with the help ofthe screw online monitoring system In this paper one ballscrew of CINCINNATIV5-3000 is used as the experimentobject Four class performance degradation samples of theball screw are randomly selected from the feature vectorslibrary together with their working conditions The lengthof each screw performance sample is 10 seconds while thesampling frequency is 256 kHz Four class screw perfor-mance samples include 05-year-service screw samples 2-year-service screw samples 5-year-service screw samplesand 7-year-service screw samples Training samples include400 samples (100 samples from each class) imitating pre-diction samples include 400 samples (100 samples from eachclass) and testing samples include 400 samples (100 samplesfrom each class)
A mapping method used for describing the output of thescrew performance degradation model is presented In thismethod different output intervals of the screw performancedegradation model show different kinds of screw perfor-mance Interval [0 02) indicates good performance Interval[02 04) indicates the performance degraded slightly Inter-val [04 06) indicates middle degraded performance whichcan still ensure the machining accuracy Interval [06 08)presents serious degraded performance which means thescrew is easy to go wrong Interval [08 1] means screwwith failure Combined with the field experiences the modeloutput of the 05-year-service screw samples 2-year-servicescrew samples 5-year-service screw samples and 7-year-service screw samples is 01 025 07 and 09
The QGA population scale and the number of theiterations should be based on comprehensive considerationof training samples and searching efficiency The parametersof the quantum cross variation and rotation gate can bedetermined by experiences on the premise of fast searchingoptimization The initialization parameters range of DFNNcan be obtained with multiple algorithm running tests [22ndash25] In this paper parameters of the QGA are selectedas follows [26 27] population scale is 40 the number ofthe iterations is 100 the initialization parameters intervalof DFNN is [0 3] cross probability is 03 while variationprobability is 01 maximum rotating angle 120596max is 015120587and minimum rotating angle 120596min is 001120587 and expansioncoefficient 120576 is 2
Shock and Vibration 7
Sensor signals
High dimension features
Featureextraction
Training samples Testing samples
QGA
Training DFNN
Optimal initialization parameters
Trained DFNNTest
Meet the requirements
Screw performancedegradation model
Yes
No
Increase samples
Modify network
parameters
PCA
Feature vectors libraryReal-time working
conditions
Imitating prediction samples
Figure 6 Flowchart of building screw performance degradation model
Table 2 The prediction accuracies of two DFNN
1205900
119896 119896119908
119896err 120574 120573 120576max 120576min 119890max 119890minAccuracy of training
samplesAccuracy of testing
samplesUnoptimizedDFNN 2 15 2 01 09 09 2 01 2 01 07350 06975
OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175
Table 2 shows the prediction accuracies of two DFNNCompared with the unoptimized DFNN the optimizedDFNN has higher prediction accuracies in both trainingsamples and testing samples From the prediction accuraciesof training samples and testing samples it is clear that theoptimized DFNNmaintains a stable prediction accuracy
Figures 7 and 8 show the confusion matrixes of unopti-mized DFNN It can be found that unoptimizedDFNN couldnot distinguish 5-year-service screw very well especially fortesting samples Figures 9 and 10 are the confusion matrixesof optimized DFNN It can be seen that optimized DFNNshows better prediction accuracies Figures 11 and 12 showthe training and testing accumulated errors of two DFNN
It is clear that optimized DFNN presents better predictionaccuracies
In order to validate the effect of the optimized DFNNbackpropagation (BP) neural network and radial basis func-tion (RBF) neural network are trained and tested with thesame samples Table 3 shows the prediction accuracies ofthree networks According to the results presented in Table 3prediction accuracy of the optimized DFNN is better thanthat of BP neural network and RBF neural network
Figures 13 and 14 are the confusion matrixes of BPneural network while Figures 15 and 16 are the confusionmatrixes of RBF neural network From Figure 13 to 16 it isfound that 2-year-service screw and 5-year-service screw are
8 Shock and Vibration
Table 3 The prediction accuracies of three networks
Optimized DFNN BP neural network RBF neural networkAccuracy of training samples 08225 06950 06925Accuracy of testing samples 08175 06375 06450
87
16
1
0
12
73
31
5
1
11
55
16
0
0
13
79
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 7 Unoptimized DFNN confusion matrix for training sam-ples
86
25
3
1
14
65
45
2
0
10
43
12
0
0
9
85
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 8 Unoptimized DFNN confusion matrix for testing sam-ples
difficult to distinguish both for BP neural network and forRBF neural network It is known that screw performancedegradation would obey the rule of bathtub curve 2-year-service screw and 5-year-service screw are in random failureperiodTherefore it is not easy to predict 2-year-service screwand 5-year-service screw Compared with Figures 9 and 10the optimizedDFNN shows better prediction accuracies thanBP neural network and RBF neural network
Figures 17 and 18 show the training and testing accu-mulated errors of three networks As seen in Figures 17 and
90
9
1
0
9
81
21
4
1
10
68
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 9 Optimized DFNN confusion matrix for training samples
87
11
1
0
12
79
18
2
1
10
71
8
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 10 Optimized DFNN confusion matrix for testing samples
18 the accumulated errors of BP network and RBF networkare larger than those of the optimized DFNN As previouslydiscussed it can be concluded that the optimized DFNN canassess screw performance degradation effectively
5 Conclusion
Screw performance degradation assessment based on QGAand DFNN is studied in this paper The experiment resultsclassified by the optimized DFNN show that our proposed
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
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VLSI Design
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Shock and Vibration
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Civil EngineeringAdvances in
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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
6 Shock and Vibration
Table 1 The adjustment strategy of the quantum rotating angle
119909119894119887119894
119891(119909) gt 119891(119887) Δ120579119894
119904(120572119894 120573119894)
120572119894120573119894gt 0 120572
119894120573119894lt 0 120572
119894= 0 120573
119894= 0
0 0 TRUEFALSE 0 0 0 0 00 1 FALSE 120596 +1 minus1 0 plusmn10 1 TRUE 120596 minus1 +1 plusmn1 01 0 FALSE 120596 minus1 +1 plusmn1 01 0 TRUE 120596 +1 minus1 0 plusmn11 1 TRUEFALSE 0 0 0 0 0
(1) Two chromosomes are randomly selected from thepopulation and whether cross operation should beconsidered is determined by cross probability
(2) If it is necessary to consider the cross operationexchanging the random cross position informationbetween two chromosomes is applied here
(3) Examining chromosome feasibility cross operation isfinished
By using quantum variation we can disturb the currentevolution direction of the chromosome to avoid early matu-rity so good global search capacity can be obtained
323 Quantum Rotation Gate Quantum gate is the actuatorof the evolution process for QGA The update process ofquantum rotation gate is as follows
[
1205721015840
1205731015840] = [
cos (120579) minus sin (120579)sin (120579) cos (120579)
] [
120572
120573
] (9)
where [120572 120573]119879 and [1205721015840 1205731015840]119879 represent quantum bit proba-
bility amplitudes before and after updating respectively 120579 isthe quantum rotating angle The adjustment strategy of thequantum rotating angle is shown in Table 1
Where 119909119894and 119887119894are the 119894th bit of the current chromosome
and the best chromosome respectively Δ120579119894is the adjusting
angle step and 119904(120572119894 120573119894) is the rotating angle direction This
paper adopts dynamic adjustment strategy based on expan-sion coefficient for quantum rotation gate [18ndash21] rotatingangle 120596 is defined as follows
120596 = 120596min + (120596max minus120596min) [1minus(119905119894
119905max)
120576
] (10)
where 120596min and 120596max are the minimum value and maximumvalue of the 120596 respectively 119905
119894is the number of the current
genetic generations 119905max is the number of the maximumgenetic generations and 120576 is the expansion coefficient
33 Screw Performance Degradation Model Sensor signalsare acquired by screw online monitoring system and highdimension features are extracted in both time domain andfrequency domain Then the feature vectors can be obtainedby PCA Feature vectors are sent to feature vectors librarytogether with the real-time working conditions Trainingsamples and imitating prediction samples are randomlyselected from the feature vectors library and used for training
DFNN and QGA After training testing samples selectedfrom the feature vectors library are used to test the optimizedand trained DFNN If the prediction accuracy falls onthe system error allowable range this DFNN can be usedas screw performance degradation model Otherwise theDFNN must be retrained by means of increasing samples ormodifying network parameters until the prediction accuracycan be guaranteed Flowchart of building screw performancedegradation model is showed in Figure 6
4 The Experiment Results
Screw vibration signals are not only determined by screwperformance degradation degree but also determined byworking conditions Feature vectors library which includesreal-time working conditions is accumulated with the help ofthe screw online monitoring system In this paper one ballscrew of CINCINNATIV5-3000 is used as the experimentobject Four class performance degradation samples of theball screw are randomly selected from the feature vectorslibrary together with their working conditions The lengthof each screw performance sample is 10 seconds while thesampling frequency is 256 kHz Four class screw perfor-mance samples include 05-year-service screw samples 2-year-service screw samples 5-year-service screw samplesand 7-year-service screw samples Training samples include400 samples (100 samples from each class) imitating pre-diction samples include 400 samples (100 samples from eachclass) and testing samples include 400 samples (100 samplesfrom each class)
A mapping method used for describing the output of thescrew performance degradation model is presented In thismethod different output intervals of the screw performancedegradation model show different kinds of screw perfor-mance Interval [0 02) indicates good performance Interval[02 04) indicates the performance degraded slightly Inter-val [04 06) indicates middle degraded performance whichcan still ensure the machining accuracy Interval [06 08)presents serious degraded performance which means thescrew is easy to go wrong Interval [08 1] means screwwith failure Combined with the field experiences the modeloutput of the 05-year-service screw samples 2-year-servicescrew samples 5-year-service screw samples and 7-year-service screw samples is 01 025 07 and 09
The QGA population scale and the number of theiterations should be based on comprehensive considerationof training samples and searching efficiency The parametersof the quantum cross variation and rotation gate can bedetermined by experiences on the premise of fast searchingoptimization The initialization parameters range of DFNNcan be obtained with multiple algorithm running tests [22ndash25] In this paper parameters of the QGA are selectedas follows [26 27] population scale is 40 the number ofthe iterations is 100 the initialization parameters intervalof DFNN is [0 3] cross probability is 03 while variationprobability is 01 maximum rotating angle 120596max is 015120587and minimum rotating angle 120596min is 001120587 and expansioncoefficient 120576 is 2
Shock and Vibration 7
Sensor signals
High dimension features
Featureextraction
Training samples Testing samples
QGA
Training DFNN
Optimal initialization parameters
Trained DFNNTest
Meet the requirements
Screw performancedegradation model
Yes
No
Increase samples
Modify network
parameters
PCA
Feature vectors libraryReal-time working
conditions
Imitating prediction samples
Figure 6 Flowchart of building screw performance degradation model
Table 2 The prediction accuracies of two DFNN
1205900
119896 119896119908
119896err 120574 120573 120576max 120576min 119890max 119890minAccuracy of training
samplesAccuracy of testing
samplesUnoptimizedDFNN 2 15 2 01 09 09 2 01 2 01 07350 06975
OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175
Table 2 shows the prediction accuracies of two DFNNCompared with the unoptimized DFNN the optimizedDFNN has higher prediction accuracies in both trainingsamples and testing samples From the prediction accuraciesof training samples and testing samples it is clear that theoptimized DFNNmaintains a stable prediction accuracy
Figures 7 and 8 show the confusion matrixes of unopti-mized DFNN It can be found that unoptimizedDFNN couldnot distinguish 5-year-service screw very well especially fortesting samples Figures 9 and 10 are the confusion matrixesof optimized DFNN It can be seen that optimized DFNNshows better prediction accuracies Figures 11 and 12 showthe training and testing accumulated errors of two DFNN
It is clear that optimized DFNN presents better predictionaccuracies
In order to validate the effect of the optimized DFNNbackpropagation (BP) neural network and radial basis func-tion (RBF) neural network are trained and tested with thesame samples Table 3 shows the prediction accuracies ofthree networks According to the results presented in Table 3prediction accuracy of the optimized DFNN is better thanthat of BP neural network and RBF neural network
Figures 13 and 14 are the confusion matrixes of BPneural network while Figures 15 and 16 are the confusionmatrixes of RBF neural network From Figure 13 to 16 it isfound that 2-year-service screw and 5-year-service screw are
8 Shock and Vibration
Table 3 The prediction accuracies of three networks
Optimized DFNN BP neural network RBF neural networkAccuracy of training samples 08225 06950 06925Accuracy of testing samples 08175 06375 06450
87
16
1
0
12
73
31
5
1
11
55
16
0
0
13
79
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 7 Unoptimized DFNN confusion matrix for training sam-ples
86
25
3
1
14
65
45
2
0
10
43
12
0
0
9
85
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 8 Unoptimized DFNN confusion matrix for testing sam-ples
difficult to distinguish both for BP neural network and forRBF neural network It is known that screw performancedegradation would obey the rule of bathtub curve 2-year-service screw and 5-year-service screw are in random failureperiodTherefore it is not easy to predict 2-year-service screwand 5-year-service screw Compared with Figures 9 and 10the optimizedDFNN shows better prediction accuracies thanBP neural network and RBF neural network
Figures 17 and 18 show the training and testing accu-mulated errors of three networks As seen in Figures 17 and
90
9
1
0
9
81
21
4
1
10
68
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 9 Optimized DFNN confusion matrix for training samples
87
11
1
0
12
79
18
2
1
10
71
8
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 10 Optimized DFNN confusion matrix for testing samples
18 the accumulated errors of BP network and RBF networkare larger than those of the optimized DFNN As previouslydiscussed it can be concluded that the optimized DFNN canassess screw performance degradation effectively
5 Conclusion
Screw performance degradation assessment based on QGAand DFNN is studied in this paper The experiment resultsclassified by the optimized DFNN show that our proposed
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 7
Sensor signals
High dimension features
Featureextraction
Training samples Testing samples
QGA
Training DFNN
Optimal initialization parameters
Trained DFNNTest
Meet the requirements
Screw performancedegradation model
Yes
No
Increase samples
Modify network
parameters
PCA
Feature vectors libraryReal-time working
conditions
Imitating prediction samples
Figure 6 Flowchart of building screw performance degradation model
Table 2 The prediction accuracies of two DFNN
1205900
119896 119896119908
119896err 120574 120573 120576max 120576min 119890max 119890minAccuracy of training
samplesAccuracy of testing
samplesUnoptimizedDFNN 2 15 2 01 09 09 2 01 2 01 07350 06975
OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175
Table 2 shows the prediction accuracies of two DFNNCompared with the unoptimized DFNN the optimizedDFNN has higher prediction accuracies in both trainingsamples and testing samples From the prediction accuraciesof training samples and testing samples it is clear that theoptimized DFNNmaintains a stable prediction accuracy
Figures 7 and 8 show the confusion matrixes of unopti-mized DFNN It can be found that unoptimizedDFNN couldnot distinguish 5-year-service screw very well especially fortesting samples Figures 9 and 10 are the confusion matrixesof optimized DFNN It can be seen that optimized DFNNshows better prediction accuracies Figures 11 and 12 showthe training and testing accumulated errors of two DFNN
It is clear that optimized DFNN presents better predictionaccuracies
In order to validate the effect of the optimized DFNNbackpropagation (BP) neural network and radial basis func-tion (RBF) neural network are trained and tested with thesame samples Table 3 shows the prediction accuracies ofthree networks According to the results presented in Table 3prediction accuracy of the optimized DFNN is better thanthat of BP neural network and RBF neural network
Figures 13 and 14 are the confusion matrixes of BPneural network while Figures 15 and 16 are the confusionmatrixes of RBF neural network From Figure 13 to 16 it isfound that 2-year-service screw and 5-year-service screw are
8 Shock and Vibration
Table 3 The prediction accuracies of three networks
Optimized DFNN BP neural network RBF neural networkAccuracy of training samples 08225 06950 06925Accuracy of testing samples 08175 06375 06450
87
16
1
0
12
73
31
5
1
11
55
16
0
0
13
79
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 7 Unoptimized DFNN confusion matrix for training sam-ples
86
25
3
1
14
65
45
2
0
10
43
12
0
0
9
85
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 8 Unoptimized DFNN confusion matrix for testing sam-ples
difficult to distinguish both for BP neural network and forRBF neural network It is known that screw performancedegradation would obey the rule of bathtub curve 2-year-service screw and 5-year-service screw are in random failureperiodTherefore it is not easy to predict 2-year-service screwand 5-year-service screw Compared with Figures 9 and 10the optimizedDFNN shows better prediction accuracies thanBP neural network and RBF neural network
Figures 17 and 18 show the training and testing accu-mulated errors of three networks As seen in Figures 17 and
90
9
1
0
9
81
21
4
1
10
68
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 9 Optimized DFNN confusion matrix for training samples
87
11
1
0
12
79
18
2
1
10
71
8
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 10 Optimized DFNN confusion matrix for testing samples
18 the accumulated errors of BP network and RBF networkare larger than those of the optimized DFNN As previouslydiscussed it can be concluded that the optimized DFNN canassess screw performance degradation effectively
5 Conclusion
Screw performance degradation assessment based on QGAand DFNN is studied in this paper The experiment resultsclassified by the optimized DFNN show that our proposed
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
8 Shock and Vibration
Table 3 The prediction accuracies of three networks
Optimized DFNN BP neural network RBF neural networkAccuracy of training samples 08225 06950 06925Accuracy of testing samples 08175 06375 06450
87
16
1
0
12
73
31
5
1
11
55
16
0
0
13
79
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 7 Unoptimized DFNN confusion matrix for training sam-ples
86
25
3
1
14
65
45
2
0
10
43
12
0
0
9
85
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 8 Unoptimized DFNN confusion matrix for testing sam-ples
difficult to distinguish both for BP neural network and forRBF neural network It is known that screw performancedegradation would obey the rule of bathtub curve 2-year-service screw and 5-year-service screw are in random failureperiodTherefore it is not easy to predict 2-year-service screwand 5-year-service screw Compared with Figures 9 and 10the optimizedDFNN shows better prediction accuracies thanBP neural network and RBF neural network
Figures 17 and 18 show the training and testing accu-mulated errors of three networks As seen in Figures 17 and
90
9
1
0
9
81
21
4
1
10
68
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 9 Optimized DFNN confusion matrix for training samples
87
11
1
0
12
79
18
2
1
10
71
8
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 10 Optimized DFNN confusion matrix for testing samples
18 the accumulated errors of BP network and RBF networkare larger than those of the optimized DFNN As previouslydiscussed it can be concluded that the optimized DFNN canassess screw performance degradation effectively
5 Conclusion
Screw performance degradation assessment based on QGAand DFNN is studied in this paper The experiment resultsclassified by the optimized DFNN show that our proposed
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 9
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 11 Training accumulated errors of two DFNN
0
5
10
15
20
25
30
40
35
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of the unoptimized DFNN
Figure 12 Testing accumulated errors of two DFNN
70
20
1
0
28
63
34
6
2
17
55
4
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 13 BPneural network confusionmatrix for training samples
71
27
4
1
29
54
46
3
0
19
40
6
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 14 BP neural network confusion matrix for testing samples
83
9
1
0
17
78
63
9
0
13
26
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 15 RBF neural network confusion matrix for trainingsamples
82
7
2
0
18
79
81
9
0
14
7
1
0
0
10
90
Predictive value
True
val
ue
05-year 2-year 5-year 7-year
05-year
2-year
5-year
7-year
Figure 16 RBF neural network confusion matrix for testing sam-ples
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
10 Shock and Vibration
0
10
20
30
40
50
0 50 100 150 200 250 300 350 400Training samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 17 Training accumulated errors of three networks
50
0
10
20
30
40
60
0 50 100 150 200 250 300 350 400Testing samples
Accu
mul
ated
erro
r
Accumulated error of the optimized DFNNAccumulated error of BP networkAccumulated error of RBF network
Figure 18 Testing accumulated errors of three networks
method has the best performance compared to other threemodels
(1) Screw online monitoring system is applied toCINCINNATIV5-3000 machining center Consid-ering that the machining center always workson changeable working conditions the real-timeworking conditions are also stored as an importantpart of the feature vectors library
(2) To solve the prediction stability problem of usingDFNN model an optimization algorithm based onQGA and imitating prediction samples is presentedin this paper Compared to the unoptimized DFNNthe optimized DFNN maintains a good predictionaccuracy
(3) Screw feature vectors of different service life areapplied to test the model performance in the exper-iment from the discussion among three network
models the conclusion can be reached that theoptimized DFNN presents better prediction accuracythan BP and RBF network and is suitable for screwperformance assessment
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors would like to extend their thanks to the jointfinancial support by National Natural Science Fund of China(51275426)
References
[1] C-H Lee M-Y Yang C-W Oh T-W Gim and J-Y Ha ldquoAnintegrated prediction model including the cutting process forvirtual product development of machine toolsrdquo InternationalJournal of Machine Tools and Manufacture vol 90 pp 29ndash432015
[2] R Perez A Molina and M Ramırez-Cadena ldquoDevelopmentof an integrated approach to the design of reconfigurablemicromesoscale cnc machine toolsrdquo Journal of ManufacturingScience and Engineering vol 136 no 3 Article ID 031003 10pages 2014
[3] A Gok C Gologlu and H I Demirci ldquoCutting parameter andtool path style effects on cutting force and tool deflection inmachining of convex and concave inclined surfacesrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 69no 5ndash8 pp 1063ndash1078 2013
[4] A Deshpande ldquoAn empirical study to evaluate machine toolproduction readiness and performancerdquo International Journalof Advanced Manufacturing Technology vol 64 no 9ndash12 pp1285ndash1296 2013
[5] P C Tsai C C Cheng and Y C Hwang ldquoBall screw preloadloss detection using ball pass frequencyrdquo Mechanical Systemsand Signal Processing vol 48 no 1-2 pp 77ndash91 2014
[6] Z H Li K G Fan J G Yang and Y Zhang ldquoTime-varying positioning error modeling and compensation for ballscrew systems based on simulation and experimental analysisrdquoInternational Journal of Advanced Manufacturing Technologyvol 73 no 5ndash8 pp 773ndash782 2014
[7] Y Pan M J Er X Li H Yu and R Gouriveau ldquoMachinehealth condition prediction via online dynamic fuzzy neuralnetworksrdquo Engineering Applications of Artificial Intelligence vol35 no 1 pp 105ndash113 2014
[8] JMateo AM Torres andMAGarcıa ldquoDynamic fuzzy neuralnetwork based learning algorithms for ocular artefact reductionin EEG recordingsrdquo Neural Processing Letters vol 39 no 1 pp45ndash67 2014
[9] C-F Juang ldquoA TSK-type recurrent fuzzy network for dynamicsystems processing by neural network and genetic algorithmsrdquoIEEE Transactions on Fuzzy Systems vol 10 no 2 pp 155ndash1702002
[10] C-H Lee and C-C Teng ldquoIdentification and control ofdynamic systems using recurrent fuzzy neural networksrdquo IEEETransactions on Fuzzy Systems vol 8 no 4 pp 349ndash366 2000
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
Shock and Vibration 11
[11] R-JWai andP-CChen ldquoRobust neural-fuzzy-network controlfor robot manipulator including actuator dynamicsrdquo IEEETransactions on Industrial Electronics vol 53 no 4 pp 1328ndash1349 2006
[12] A Subasi ldquoAutomatic detection of epileptic seizure usingdynamic fuzzy neural networksrdquo Expert Systems with Applica-tions vol 31 no 2 pp 320ndash328 2006
[13] S Q Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001
[14] H Adeli and X M Jiang ldquoDynamic fuzzy wavelet neuralnetwork model for structural system identificationrdquo Journal ofStructural Engineering vol 132 no 1 pp 102ndash111 2006
[15] C-F Juang and C-D Hsieh ldquoA locally recurrent fuzzy neuralnetwork with support vector regression for dynamic-systemmodelingrdquo IEEE Transactions on Fuzzy Systems vol 18 no 2pp 261ndash273 2010
[16] CGHuangG Li Z X Xu and L P Chang ldquoDesign of optimaldigital lattice filter structures based on genetic algorithmrdquoSignal Processing vol 92 no 4 pp 989ndash998 2012
[17] L Liu L-H Guo H Xiao J-J Wang and G-G WangldquoSoftware reliability growth model based on SAA-DFNNrdquoJournal of Jilin University vol 42 no 5 pp 1225ndash1230 2012
[18] X C Zhang H L Gao H F Huang L Guo and S D XiaoldquoOptimization design of mathematical morphology filter basedon quantum genetic algorithmrdquo Journal of Southwest JiaotongUniversity vol 49 no 3 pp 462ndash469 2014
[19] K-H Han and J-H Kim ldquoQuantum-inspired evolutionaryalgorithm for a class of combinatorial optimizationrdquo IEEETransactions on Evolutionary Computation vol 6 no 6 pp580ndash593 2002
[20] J Zhang H Z Li Z G Tang Q P Lu X O Zheng and JL Zhou ldquoAn improved quantum-inspired genetic algorithmfor image multilevel thresholding segmentationrdquoMathematicalProblems in Engineering vol 2014 Article ID 295402 12 pages2014
[21] S E-O Bahlous M Neifar S El-Borgi and H SmaouildquoAmbient vibration based damage diagnosis using statisticalmodal filtering and genetic algorithm a bridge case studyrdquoShock and Vibration vol 20 no 1 pp 181ndash188 2013
[22] AMontazeri and J Poshtan ldquoOptimizing amulti-channel ANCsystem for broadband noise cancellation in a telephone kioskusing genetic algorithmsrdquo Shock and Vibration vol 16 no 3pp 241ndash260 2009
[23] A Lin and J Phillips ldquoOptimization of random diffractiongratings in thin-film solar cells using genetic algorithmsrdquo SolarEnergy Materials and Solar Cells vol 92 no 12 pp 1689ndash16962008
[24] J-C Lee W-M Lin G-C Liao and T-P Tsao ldquoQuantumgenetic algorithm for dynamic economic dispatch with valve-point effects and including wind power systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 33 no 2 pp189ndash197 2011
[25] M J Er F Liu and M B Li ldquoChannel equalization usingdynamic fuzzy neural networksrdquo International Journal of FuzzySystems vol 11 no 1 pp 10ndash19 2009
[26] A SaiToh R Rahimi and M Nakahara ldquoA quantum geneticalgorithm with quantum crossover and mutation operationsrdquoQuantum Information Processing vol 13 no 3 pp 737ndash7552014
[27] JWGuM Z Gu CWCao andX S Gu ldquoA novel competitiveco-evolutionary quantum genetic algorithm for stochastic jobshop scheduling problemrdquo Computers amp Operations Researchvol 37 no 5 pp 927ndash937 2010
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
International Journal of
AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Active and Passive Electronic Components
Control Scienceand Engineering
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
RotatingMachinery
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation httpwwwhindawicom
Journal ofEngineeringVolume 2014
Submit your manuscripts athttpwwwhindawicom
VLSI Design
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Shock and Vibration
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawi Publishing Corporation httpwwwhindawicom
Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
SensorsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
DistributedSensor Networks
International Journal of
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