research article screw performance degradation assessment...

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


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)


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


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


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


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

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

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

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


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


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

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

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

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

Figure 16 RBF neural network confusion matrix for testing sam-ples


0

10

20

30

40

50


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


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


[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


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



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)


8704B100M1

INV1870

8765A250M5

Industrialcomputer

8704B100M1


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)









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 (

)



x1

xr

y

w1

wj

wu

MFru Ru Nu





0) = q1199050

1 q11990502 q1199050

119873 is 119873 By means



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)





119895includes



119891 = 1minus 1119904

119904

sum

119901=1

1003816100381610038161003816100381610038161003816100381610038161003816

1199101015840

119901minus 119905119901

119905119901

1003816100381610038161003816100381610038161003816100381610038161003816

(8)


Beginning








Bestindividual

Yes

No

QGA DFNN

Initializing DFNN




Generating new rule


Training end

Adjusting width


Yes

Yes

Yes

Yes

No

No

No

No

No

Yes

minimum value dmin



dmin gt kd

ei gt ke ei gt ke

120578i lt kerr











119909119894119887119894

119891(119909) gt 119891(119887) Δ120579119894

119904(120572119894 120573119894)

120572119894120573119894gt 0 120572

119894120573119894lt 0 120572

119894= 0 120573

119894= 0







[

1205721015840

1205731015840] = [


] [

120572

120573

] (9)








119905max)

120576

] (10)











Sensor signals


Featureextraction


QGA

Training DFNN


Trained DFNNTest



Yes

No

Increase samples

Modify network

parameters

PCA


conditions




1205900

119896 119896119908




OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175









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


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




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


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



5 Conclusion



0

5

10

15

20

25

30

35


Accu

mul

ated

erro

r



0

5

10

15

20

25

30

40

35

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r



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


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


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


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



0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










8704B100M1

INV1870

8765A250M5

Industrialcomputer

8704B100M1


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)









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 (

)



x1

xr

y

w1

wj

wu

MFru Ru Nu





0) = q1199050

1 q11990502 q1199050

119873 is 119873 By means



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)





119895includes



119891 = 1minus 1119904

119904

sum

119901=1

1003816100381610038161003816100381610038161003816100381610038161003816

1199101015840

119901minus 119905119901

119905119901

1003816100381610038161003816100381610038161003816100381610038161003816

(8)


Beginning








Bestindividual

Yes

No

QGA DFNN

Initializing DFNN




Generating new rule


Training end

Adjusting width


Yes

Yes

Yes

Yes

No

No

No

No

No

Yes

minimum value dmin



dmin gt kd

ei gt ke ei gt ke

120578i lt kerr











119909119894119887119894

119891(119909) gt 119891(119887) Δ120579119894

119904(120572119894 120573119894)

120572119894120573119894gt 0 120572

119894120573119894lt 0 120572

119894= 0 120573

119894= 0







[

1205721015840

1205731015840] = [


] [

120572

120573

] (9)








119905max)

120576

] (10)











Sensor signals


Featureextraction


QGA

Training DFNN


Trained DFNNTest



Yes

No

Increase samples

Modify network

parameters

PCA


conditions




1205900

119896 119896119908




OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175









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


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




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


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



5 Conclusion



0

5

10

15

20

25

30

35


Accu

mul

ated

erro

r



0

5

10

15

20

25

30

40

35

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r



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


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


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


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



0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










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 (

)



x1

xr

y

w1

wj

wu

MFru Ru Nu





0) = q1199050

1 q11990502 q1199050

119873 is 119873 By means



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)





119895includes



119891 = 1minus 1119904

119904

sum

119901=1

1003816100381610038161003816100381610038161003816100381610038161003816

1199101015840

119901minus 119905119901

119905119901

1003816100381610038161003816100381610038161003816100381610038161003816

(8)


Beginning








Bestindividual

Yes

No

QGA DFNN

Initializing DFNN




Generating new rule


Training end

Adjusting width


Yes

Yes

Yes

Yes

No

No

No

No

No

Yes

minimum value dmin



dmin gt kd

ei gt ke ei gt ke

120578i lt kerr











119909119894119887119894

119891(119909) gt 119891(119887) Δ120579119894

119904(120572119894 120573119894)

120572119894120573119894gt 0 120572

119894120573119894lt 0 120572

119894= 0 120573

119894= 0







[

1205721015840

1205731015840] = [


] [

120572

120573

] (9)








119905max)

120576

] (10)











Sensor signals


Featureextraction


QGA

Training DFNN


Trained DFNNTest



Yes

No

Increase samples

Modify network

parameters

PCA


conditions




1205900

119896 119896119908




OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175









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


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




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


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



5 Conclusion



0

5

10

15

20

25

30

35


Accu

mul

ated

erro

r



0

5

10

15

20

25

30

40

35

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r



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


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


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


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



0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Beginning








Bestindividual

Yes

No

QGA DFNN

Initializing DFNN




Generating new rule


Training end

Adjusting width


Yes

Yes

Yes

Yes

No

No

No

No

No

Yes

minimum value dmin



dmin gt kd

ei gt ke ei gt ke

120578i lt kerr











119909119894119887119894

119891(119909) gt 119891(119887) Δ120579119894

119904(120572119894 120573119894)

120572119894120573119894gt 0 120572

119894120573119894lt 0 120572

119894= 0 120573

119894= 0







[

1205721015840

1205731015840] = [


] [

120572

120573

] (9)








119905max)

120576

] (10)











Sensor signals


Featureextraction


QGA

Training DFNN


Trained DFNNTest



Yes

No

Increase samples

Modify network

parameters

PCA


conditions




1205900

119896 119896119908




OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175









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


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




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


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



5 Conclusion



0

5

10

15

20

25

30

35


Accu

mul

ated

erro

r



0

5

10

15

20

25

30

40

35

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r



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


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


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


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



0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119909119894119887119894

119891(119909) gt 119891(119887) Δ120579119894

119904(120572119894 120573119894)

120572119894120573119894gt 0 120572

119894120573119894lt 0 120572

119894= 0 120573

119894= 0







[

1205721015840

1205731015840] = [


] [

120572

120573

] (9)








119905max)

120576

] (10)











Sensor signals


Featureextraction


QGA

Training DFNN


Trained DFNNTest



Yes

No

Increase samples

Modify network

parameters

PCA


conditions




1205900

119896 119896119908




OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175









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


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




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


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



5 Conclusion



0

5

10

15

20

25

30

35


Accu

mul

ated

erro

r



0

5

10

15

20

25

30

40

35

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r



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


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


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


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



0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Sensor signals


Featureextraction


QGA

Training DFNN


Trained DFNNTest



Yes

No

Increase samples

Modify network

parameters

PCA


conditions




1205900

119896 119896119908




OptimizedDFNN 23896 10065 20226 00036 07432 01840 16578 03766 23861 05571 08225 08175









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


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




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


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



5 Conclusion



0

5

10

15

20

25

30

35


Accu

mul

ated

erro

r



0

5

10

15

20

25

30

40

35

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r



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


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


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


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



0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












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


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




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


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



5 Conclusion



0

5

10

15

20

25

30

35


Accu

mul

ated

erro

r



0

5

10

15

20

25

30

40

35

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r



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


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


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


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



0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

10

15

20

25

30

35


Accu

mul

ated

erro

r



0

5

10

15

20

25

30

40

35

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r



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


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


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


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



0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

10

20

30

40

50


Accu

mul

ated

erro

r



50

0

10

20

30

40

60

0 50 100 150 200 250 300 350 400Testing samples

Accu

mul

ated

erro

r










Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article screw performance degradation assessment...

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