research article prognostics and health management of an

Research ArticlePrognostics and Health Management of an AutomatedMachining Process

Cheng He,1,2 Jiaming Li,3 and George Vachtsevanos3

1School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China2School of Intelligent Manufacturing and Control Engineering, Shanghai Second Polytechnic University, Shanghai 201209, China3School of Electrical & Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250, USA

Correspondence should be addressed to George Vachtsevanos; [email protected]

Received 21 September 2015; Accepted 4 November 2015

Academic Editor: Uchechukwu E. Vincent

Copyright © 2015 Cheng He et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Machine failure modes are presenting a major burden to the operator, the plant, and the enterprise causing significant downtime,labor cost, and reduced revenue. New technologies are emerging over the past years to monitor the machine’s performance, detectand isolate incipient failures or faults, and take appropriate actions to mitigate such detrimental events. This paper addresses thedevelopment and application of novel Prognostics and Health Management (PHM) technologies to a prototype machining process(a screw-tightening machine). The enabling technologies are built upon a series of tasks starting with failure analysis, testing, anddata processing aimed to extract useful features or condition indicators from raw data, a symbolic regression modeling framework,and a Bayesian estimation method called particle filtering to predict the feature state estimate accurately. The detection schemedeclares the fault of a machine critical component with user specified accuracy or confidence and given false alarm rate while theprediction algorithm estimates accurately the remaining useful life of the failing component. Simulation results support the efficacyof the approach and match well the experimental data.

1. Introduction

Prognosis and Health Management (PHM) has emergedover recent years as significant technologies that are makingan impact on both military and commercial maintenancepractices. Automated machining processes are employedextensively inmanufacturing. Screw-tighteningmachines arecritical assets of an automated machining process. This studyfocuses on such a machining process with novel featuresfor automatic screw tightening in crucial manufacturing,assembly, and other operations. Figure 1 shows a pictureof the equipment. Screw tightening is usually carried outmanually resulting in wasted time, operator mistakes, andinconsistent applied torques. The automatic assembly linerequires, therefore, for improved performance an automaticscrew-tightening machine.

Themachine consists mainly of seven parts: feeder, screwfalling device, screw separating device, screwdriver, guidingdevice, 3-axis motion platform, and a clamping device. Thefunction of the feeder is to arrange the screws in a line.

The operator places thousands of screws in the center of thefeeder. The screws are arranged in a row along the track ofthe feeder via a vibration mechanism and arranged in a lineat the end of the track. The screws move along the track ofthe feeder and, via gravity, they drop into the pipe one byone and arranged in a line in the pipe. A screw separatingdevice picks one screw at a time and sent it to the head ofthe screwdriver.The 3-axis motion platformmoves the screwhole of the parts behind the head of the screwdriver.Then, thescrewdriver moves and tightens the screw.

2. Failure Analysis

Machine critical failure modes include the following: thescrews may pile up on the trail of the feeder, thus preventingthe screw separating device from separating the screws andarranging them one at a time. The 3-axis motion platformdoes not move to the precise location. The screwdriver isunable to tighten the screw. Among several other failure

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 651841, 10 pageshttp://dx.doi.org/10.1155/2015/651841

2 Mathematical Problems in Engineering

Figure 1: Automated screw-tightening machine.

modes, the 3-axis motive platform not moving to its preciselocation is the most serious one. In this case, the screwcannot be tightened in the screw hole and the parts cannot beconnected correctly. The major reason for the 3-axis motiveplatform not being able to move precisely is the presence of afault condition in bearings. Bearing fault/failure is deemed tobe critical, severe, and frequent and must be addressed if theautomated process will perform properly and expeditiously.

The overall architecture for the bearing health manage-ment system is shown in Figure 2.Wewill describe in the nextsection the function of each module of the architecture.

3. The Test Platform

In order to obtain test data, under normal and faultyconditions, for the targeted bearings a test platform wasdesigned and built. Accelerated life testing is performed ontwo rolling element bearings. The experimental data wasprocessed and appropriate features or condition indicators(Cis) were extracted. The processed data combined with asuitable model of the fault growth and a novel estimationalgorithm, called particle filtering, are used to implement thediagnostic and prognostic routines.

3.1. Test Platform Design. The test platform consists of asingle-axis servomotor-driven module and a data acquisitionand analysis system. Figure 3 is the single-axis servomotor-driven module. Figure 4 is the data acquisition system.

3.1.1. Single-Axis Servomotor-Driven Module. The single-axisservomotor-driven module includes a 400w servo motor,a coupling device, two bearings, two bearing-bases, a ballscrew, and a suitable electrical control system. The servomo-tor is connected to the ball screw via the coupling. Both endsof the ball screw are installed in the bearings. The bearingsare fixed in the bearing-housing.

3.1.2. Data Acquisition System. The data acquisition systemis composed of a 16-channel dynamic signal data acquisitioninstrument (model: DH5902), a charge adapter, and two

Objects entered

Poor lubricant

Increase in friction

Fault (abrasion, crack)

Fault: abrasionOperating parameter

s

Bearing parameters

Vibration modeling

Feature extraction Fault size

Fault diagnosis

Failure prognosis

Bearing degradation

Fault: crack

Figure 2: Prognosis and health management architecture for bear-ing fault modes.

Figure 3: Single-axis servomotor-driven module.

vibration sensors (model: PCB356A32).The vibration sensorsare installed in a rack with a magnetic base. They acquirethe vibration signal and send it to the 16-channel dynamicsignal data acquisition instrument via the charge adapter.TheIndustrial Control Computer (IPC) receives the data from the16-channel dynamic signal data acquisition instrument viawireless transmission.

3.1.3. Experimental Parameters. The servomotor has threespeeds: 500 r/min, 1000 r/min, and 1500 r/min. The samplingfrequency is 2.5 Kz, and the sampling period is 10 seconds.Two bearings were tested. Each bearing is tested along the𝑍 direction resulting in two test points for each speed andeach test point providing three entries; that is, there are 6 dataentries for each speed setting.

3.2. Fault Analysis. Rolling bearings are typically damageddue to various causes, such as improper assembly, poor lubri-cation, and moisture. Corrosion and overload may also leadto premature bearing damage. If lubrication andmaintenance

Mathematical Problems in Engineering 3

Figure 4: Data acquisition system.

procedures are not performed regularly over time, fatiguespall and bearingwearmay occur.Themain failuremodes arefatigue spall, wear, plastic deformation, corrosion, fracture,gluing, cage damage, and so forth.

3.2.1. Fault Conditions. Among all the bearing faults, abra-sion is one of the most common. Abrasion implies thatmaterial is removed from themetal surface.The characteristicfeature for abrasion is a shallow trench, with a bright surface.It is produced in rolling contact surface or guide surface.Withabrasion present, the bearing clearance increases.

3.2.2. Root-Cause Analysis. Bearing abrasion is due primarilyto two causes: insufficient bearing lubrication and smallparticle penetration into the bearing resulting in materialremoval from themetallic surface via sliding friction. Surfacewear is the result of the relative motion between rollingtrack and rolling body when dust and other objects enterthe bearing surface resulting in increased bearing surfaceroughness and reduced motion accuracy. The motion accu-racy of the machine is also reduced increasing the machine’svibration and noise. For precision bearings, the amount ofwear determines the life of the bearing. On the other side,there is also a kind of wear with slight vibration.

3.3. Fault Injection. In testing, faults are injected periodicallyuntil the bearing reaches a failure condition and fault dataare recorded. The fault injection consists of the followingarrangement: a hole is drilled on the side of the bearing baseand a screw is tightened in the hole step by step. The screwgenerates friction with the bearing surface resulting in anabrasion fault mode.

4. Feature Extraction and Selection

As a bearing defect evolves, due to poor lubrication for exam-ple, the faultmode excites a specific frequency associatedwiththe particular type of defect.The amplitude and time durationof the defect frequency are generally good indicators of defectseverity.The increase of defect size usually increases the ratioof impulse force to operational noise. The increase of defectlength also increases the impulse force duration. If the defectarea is large along the raceway turning direction, harmonicsof the frequencywill also imply an indication of the severity of

0 2 4 6 8 10 12−15

−10

−5

0

5

10

15

×104

Figure 5: Section signals in time domain.

Table 1: Four special features in frequency domain. (66.25 Hz hasthe maximum energy.) [1].

50Hz 100Hz 150Hz 66.25HzAmplitude 𝑓

1𝑓3

𝑓5

𝑓7

Spectrum density 𝑓2

𝑓4

𝑓6

𝑓8

the defect present. Acquired vibration data are used to extractappropriate features.

4.1. Feature Extraction. The vibration signal is convertedfrom the time to the frequency domain. Analysis showsthat the signal changes rapidly between 1700Hz and 1900Hzwith features extracted in this area. Several vibration signalsfrom bearings with different fault conditions are illustratedin Figure 5. For each data set we cut the period with signal asshown in Figure 5, the section between these two lines.

Frequency domain studies indicate when a bearing defectexists with the defect exhibiting a signature in the frequencyspectra of the vibration signals. The signal is digitized ina frequency region around the resonances of the structureand such features as the energy, amplitude, and so forth areextracted. The frequency spectra are shown in Figure 6.

We choose four frequency domain features, as is shownin Table 1.

Time domain features include mean value (𝑓9) and stan-

dard deviation (𝑓10). We calculate the correlation coefficient

for each feature. Table 2 shows the results.

4.2. Feature Fusion. Within an automated health manage-ment system, there are many areas where fusion technologiesplay a contributing role. At the lowest level, data fusion canbe used to combine information from a multisensory dataarray to validate signals and create features. At a higher level,fusion may be used to combine features in intelligent ways soas to obtain the best possible diagnosis information. Finally,knowledge fusion is used to incorporate experience-basedinformation such as legacy failure rates or physical modelpredictions with signal-based information.


50

40

30

20

10

0

0

−10

−20

−30

−40

−500 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5

×104 ×104

15

10

5

−5

−10

−15

−20

−25

−30

Healthy bearing Fault bearing

Figure 6: Bearing vibration signals in frequency domain.

Table 2: Correlation coefficient.

𝑓1

𝑓2

𝑓3

𝑓4

𝑓5

𝑓6

𝑓7

𝑓8

𝑓9

𝑓10

CC 0.7972 0.3797 0.7867 0.5902 0.2729 0.0327 0.0097 0.2957 0.2368 0.9347Three features with the highest correlation coefficient are picked up: 𝑓1, 𝑓3, 𝑓10.

Table 3: Correlation coefficient.

Feature 𝑓1

𝑓3

𝑓10

𝑓combined

CC 0.79 0.78 0.93 0.95The combined feature has the best highest coefficient and performs betterthan any individual feature.

Thus, we combine the features and get the combinedfeature:

𝐹combined = 𝑓0.29

1⋅ 𝑓0.18

3⋅ 𝑓2.01

10. (1)

The combined correlation coefficient is 0.95. The combinedfeature performance is shown in Figure 7.

4.3. Performance Comparison. We apply correlation coeffi-cient as the performance metric and come up with Table 3.

5. Modeling

Reliable, high-fidelity fault growth models form the founda-tion for accurate and robust detection and failure prediction.A suitable modeling framework assists in the development,testing, and evaluation of detection and prediction algo-rithms. It may be employed to generate data for data-drivenmethods to diagnostics/prognostics and test and validateroutines for data processing tool development, among others.The flexibility provided by a simulation platform, housingappropriate detection and progression models, is a uniqueattribute in the study of how fault processes are initiated and

Com

bine

d fe

atur

e val

ue

Ground truth

5

4.8

4.6

4.4

4.2

4

3.8

3.6

3.4

3.20 5 10 15 20 25 30

Figure 7: Combined feature performance.

propagating so that corrective action can be taken beforea catastrophic event occurs. The objective of the modelingeffort is to develop, test, and evaluate novel fault initiationand progression models that will assist in the design andimplementation of “smart” sensors and sensing modalitiesfor critical machine systems.

5.1. Modeling-Symbolic Regression. Fault detection and pre-diction algorithms rely on data, a model of the degradationprocess and an estimation method that, given the current


Motor box

CouplingsSevromotor Ball screw

Platform

Bearing

Bearing

Bearing Box

Bearing box

Accelerometer

Accelerometer

Figure 8: Structure model of the platform.

state of the system, predicts its evolution over the next timestep. Such models are typically based on first principles whileothers are built on the basis of data. We exploit in this efforta modeling framework called symbolic regression. It is a typeof regression analysis that searches the space of mathematicalexpressions to find the model that best fits a given dataset, interms of both accuracy and simplicity. No particular model isprovided as a starting point to the algorithm. Instead, initialexpressions are formed by randomly combining mathemati-cal building blocks such as mathematical operators, analyticfunctions, constants, and state variables. (Usually, a subsetof these primitives will be specified by the operator, butthat is not a requirement of the technique.) New equationsare then formed by combining previous ones, using geneticprogramming. In linear regression, the dependent variable isa linear combination of the parameters (but need not be linearin the independent variables). Nonlinear symbolic regressionand other regression techniques incorporating uncertaintyare based on similar principles. The structure model of theplatform is shown in Figure 8.

The functionalmodel of the platform is shown in Figure 9.During real time operation, model parameters are tuned

as new data is streaming in and an error between theestimated state and the detected state is exploited in anoptimization scheme to arrive at the “best” model for furtherprediction purposes. Eureqa is a useful tool to implement thesymbolic regression routine. Exploiting the test data, Eureqasearches to find the model (both model structure and modelparameters) that best fit a given data set. We arrive at thefollowing parametric model:

Feature = 8.11 × 103 + 0.262𝑥3. (2)

𝑥 implies cycle times; here we use 𝑥 as time, 𝑡.Figure 10(a) shows the result from the application of

Eureqa. Figure 10(b) shows a plot of (8.11 × 103 + 0.262𝑥3)and the error as the process proceeds. Figure 10(c) shows theaccuracy versus complexity plot. By trading off accuracy forcomplexity, the best model from the list generated by Eureqais (8.11 × 103 + 0.262𝑥3).

A sufficient data set is obtained by using the followingformula to enrich the data:

Feature = 𝑔 (𝑥 [𝑘]) + 𝑛 (0, 𝑆) , (3)

where 𝛿(𝑥) is the model fitted by regression, 𝑆 is the standarddeviation,𝑁 is the number of samples, and 𝑥 is a variable:

𝑆 =√∑𝑁

𝑖=1[1/𝑖 − 𝛿 (𝑥

𝑖)]2

𝑁 − 1.

(4)

6. The Particle Filtering Framework for FaultDiagnosis and Failure Prognosis

Particle filtering is an emerging and powerful methodologyfor sequential signal processing based on the concepts ofBayesian theory and Sequential Importance Sampling (SIS).Particle filtering is very suitable for nonlinear systems or inthe presence of non-Gaussian process/observation noise. Forthis approach, both diagnosis and prognosis rely upon esti-mating the current value of a fault/degradation dimension, aswell as other important parameters, and use a set of observa-tions (or measurements) for this purpose.This research teamhas pioneered the introduction of particle filtering techniquesinto fault diagnosis and failure prognosis [1, 2]. The team hasalso demonstrated how these techniques can be combinedwith traditional artificial intelligencemethods in a synergisticway [3]. The success of this novel model-based approachhas been demonstrated in a number of diverse applicationdomains from rotorcraft critical components to electricalsystems, environmental control systems, and high poweramplifiers [4]. Figure 11 depicts the flow of the componentmodules comprising the health management architecture.

The underlying principle of the methodology is theapproximation of the conditional state probability distribu-tion 𝑝(𝑧

𝑘/𝑥𝑘) using a swarm of points called particles and a

set of weights associated with them representing the discreteprobabilitymasses. Particles can be generated and recursivelyupdated easily given a nonlinear process model (whichdescribes the evolution in time of the system under analysis),a measurement model, a set of available measurements 𝑧

1,𝑘=

(𝑧1, . . . , 𝑧

𝑘), and an initial estimation for the state PDF 𝑝(𝑥

0),

as shown in the following equations:

𝑥𝑘= 𝑓𝑘(𝑥𝑘−1, 𝜔𝑘) ←→ 𝑝 (𝑥

𝑘| 𝑥𝑘−1) ,

𝑧𝑘= ℎ𝑘(𝑥𝑘, V𝑘) ←→ 𝑝 (𝑧

𝑘| 𝑥𝑘) .

(5)

As in every Bayesian estimation problem, the estimation pro-cess can be achieved into two steps, namely, prediction andfiltering. On the one hand, prediction uses both knowledgeof the previous state estimation and the process model togenerate the a priori state PDF estimation for the next timeinstant, as is shown in the following expression:

𝑝 (𝑥𝑘| 𝑧1:𝑘−1)

= ∫𝑝 (𝑥𝑘| 𝑥𝑘−1) 𝑝 (𝑥

𝑘−1| 𝑧1:𝑘−1) 𝑑𝑥𝑘−1.

(6)


Test Place

Place Support

Provide ChangeTransferthe motion motion motion type

Place

Test

Motorbox

CouplingsSevromotor Ball screw

Platform

Bearing

Bearing

Bearing box

Bearing box

Accelerometer

Accelerometer

Figure 9: Functional model of the platform.

On the other hand, the filtering step considers the currentobservation 𝑧

𝑘and the a priori state PDF to generate the a

posteriori state PDF by using Bayes’ formula:

𝑝 (𝑥𝑘| 𝑧1:𝑘) =𝑝 (𝑧𝑘| 𝑥𝑘) 𝑝 (𝑥

𝑘| 𝑧1:𝑘−1)

𝑝 (𝑧𝑘| 𝑧1:𝑘−1)

. (7)

The actual distributions then would be approximated by aset of samples and the corresponding normalized importanceweights 𝑤𝑖

𝑘= 𝑤𝑘(𝑥𝑖

0:𝑘) for the 𝑖th sample:

𝑝 (𝑥𝑘| 𝑧1:𝑘) ≈

𝑁

∑

𝑖=1

𝑤𝑘(𝑥𝑖

0:𝑘) 𝛿 (𝑥

0:𝑘− 𝑥𝑖

0:𝑘) , (8)

where the update for the importance weights is given by

𝑤𝑘= 𝑤𝑘−1

𝑝 (𝑧𝑘| 𝑥𝑘) 𝑃 (𝑥

𝑘| 𝑥𝑘−1)

𝑃 (𝑥𝑘| 𝑥0:𝑘−1, 𝑧1:𝑘). (9)

Fault Diagnosis. The proposed particle-filter-based diagnosisframework aims to accomplish the tasks of fault detection andidentification, under general assumptions of non-Gaussiannoise structures and nonlinearities in process dynamic mod-els, using a reduced particle population to represent thestate pdf [5]. A compromise between model-based and data-driven techniques is accomplished by the use of a particlefilter-based module built upon the nonlinear dynamic statemodel:

𝑥𝑑(𝑡 + 1) = 𝑓

𝑏(𝑥𝑑(𝑡) , 𝑛 (𝑡)) ,

𝑥𝑐(𝑡 + 1) = 𝑓

𝑡(𝑥𝑑(𝑡) , 𝑥𝑐(𝑡) , 𝑤 (𝑡)) ,

Features (𝑡) = ℎ𝑡(𝑥𝑑(𝑡) , 𝑥𝑐(𝑡) , V (𝑡)) ,

(10)

where 𝑓𝑏, 𝑓𝑡and ℎ

𝑡are nonlinear mappings, 𝑥

𝑑(𝑡) is a

collection of Boolean states associated with the presenceof a particular operating condition in the system (normaloperation, fault type #1, #2, etc.), 𝑥

𝑐(𝑡) is a set of continuous-

valued states that describe the evolution of the system given

those operating conditions, and 𝑤(𝑡) and V(𝑡) are non-Gaussian distributions that characterize the process andfeature noise signals, respectively. At any given instant oftime, this framework provides an estimate of the probabilitymasses associated with each fault mode, as well as a pdfestimate for meaningful physical variables in the system.Once this information is available within the diagnosticmodule, it is conveniently processed to generate proper faultalarms and to inform about the statistical confidence of thedetection routine. Customer specifications are translated intoacceptable margins for types I and II errors in the detectionroutine. The algorithm itself will indicate when type II error(false negatives) has decreased to the desired level. Typicalresults of the diagnostic algorithm are shown in Figure 12.

Failure Prognosis.The evolution in time of the fault dimensionmay be described through the state equation:

𝑥1(𝑡 + 1) = 𝑥

1(𝑡) + 𝑥

2(𝑡) ⋅ 𝐹 (𝑥 (𝑡) , 𝑡, 𝑈) , 𝑤

1(𝑡) ,

𝑥2(𝑡 + 1) = 𝑥

2(𝑡) + 𝑤

2(𝑡) ,

(11)

where 𝑥1(𝑡) is a state representing the fault dimension under

analysis, 𝑥2(𝑡) is a state associated with an unknown model

parameter, 𝑈 are external inputs to the system (load profile,etc.), 𝐹(𝑥(𝑡), 𝑡, 𝑈) is a general time-varying nonlinear func-tion, and 𝑤

1(𝑡) and 𝑤

2(𝑡) are white noises (not necessarily

Gaussian) [5].The nonlinear functionmay represent a modelbased on first principles, a neural network, or even a fuzzysystem. Long term predictions are generated on the basis ofthe current state pdf estimate, and using kernel functions toreconstruct the state pdf estimate for future time instants,

𝑝 (𝑥𝑡+𝑘| 𝑥𝑡+𝑘−1)

≈

𝑁

∑

𝑖=1

𝑤(𝑖)

𝑡+𝑘−1𝐾(𝑥𝑡+𝑘− 𝐸 [𝑥

(𝑖)

𝑡+𝑘| 𝑥(𝑖)

𝑡+𝑘−1]) ,

(12)

where 𝐾(⋅) is a kernel density function, which may cor-respond to the process noise pdf, a Gaussian kernel, or arescaled version of the Epanechnikov kernel.


Size Fit Solution1.000

0.748

0.998

0.721

0.707

0.676

0.653

0.649

0.584

0.449

0.399

0.390

0.390

Feature = 7.81e3 + 6.4x2

Feature = 8.11e3 + 0.262x3

Feature = 8.2e3 + 0.0108x4

Feature = 8.27e3 + 0.000415x5

Feature = 7.01e3 + 159x − 1.15e3 sin(175x)Feature = 7.13e3 + 139x + 84.4x cos(144x)

Feature = 7.15e3 + 131x + 5.54x2 cos(144x)

Feature = 7.98e3 + 4.37x2 + 5.25x2 cos(144x)

Feature = 7.97e3 + x + 4.35x2 + 5.27x2 cos(144x)

1

5

3

6

7

9

11

13

14

16

18

20

22

Feature =4.46e5

62.8 − x

Feature = 8.89e3

Feature = 6.54e3 + 198x

Feature = 8.8e3 + x

(a)

14000

13000

12000

11000

10000

9000

8000

7000

Feat

ure

0 5 10 15 20 25

Feature (train)Size 9

(b)

Feature (validation)Feature (train)Size 9

150014001300120011001000900800700600500400

0 5 10 15 20 25 30 35 40 45

(c)

Figure 10: Symbolic regression using Eureka.

Data

Extractfeature Feature.mat cftool ffmapping.

mat

Data synthesis

Synthfault.mat

Diagnostics

Diagnosticresult.mat

Prognostics

Data file

Code

Figure 11: The health management architecture.


Particlefilter

4.5

4

3.5

350 100 150 200 250

50 100 150 200 250

1

0.5

0

4

2

02.5 3 3.5 4 4.5

×10−3

xd(t + 1) = fb[xd(t) + n(t)]

xc(t) = ft[xd(t), xc(t), 𝜔(t)]

Features(t) = ht[xd(t), xc(t), v(t)]

Figure 12: Typical results of the diagnostic algorithm.

Bearing platform

Vibration sensor

Signal process

Feature extraction

Algorithm development

Schedule required

maintenance

Figure 13: An integrated approach for fault diagnosis and failure prognosis.

7. Results

Using the machinery data, we determine its health status andhence its current fault/failure condition. The main modulesof an integrated approach to fault diagnosis and failureprognosis are shown in Figure 13. It includes experimentdesign, fault classification, data collection, signal process,feature extraction, algorithm development, and schedulesrequired maintenance.

The resulting predicted state pdf contains critical infor-mation about the evolution of the fault dimension over time.This information is condensed through the computation ofstatistics (expectations, 90% confidence intervals), the Time-of-Failure (ToF), or the Remaining Useful Life (RUL) ofthe faulty system. Figure 16 depicts a typical prognosticconfiguration.

Data from simulation as well as the experiments wereused to implement and evaluate the fault diagnosis and failureprognosis routines. Performance metrics were applied at alllevels of the architecture (data analysis/feature extraction,diagnosis, and prognosis).

7.1. Fault Predict. Using Eureka software and the model, wefitted a curve shown in Figure 14. The points represent 27features extracted in 27 cycles.The red line is the model fitted

14000

13000

12000

11000

10000

9000

8000

7000

Feat

ure

0 5 10 15 20 25

Feature (train)Size 9

Figure 14: Feature extraction curve fitting.

by the feature. According to the deviation of the data itself,the model was enriched and data were generated with noiseinjected into the model. The data is shown in Figure 15. Thered line is the model and the blue curve is the generated data.

Figures 16 and 17 show the results obtained when theproposed approach is applied to the problem of fault detec-tion/prediction due to degradation of the bearing lubrication.


4.5

4

3.5

0 500 1000 1500 2000 2500

Wea

r

Time (hour)

Figure 15: Enrich feature extraction curve fitting.

10.80.60.40.200 500 1000 1500 2000 2500

Prob

abili

ty

Time (hour)

Figure 16: Trending of the selected feature.

15

10

5

0

Obs

erve

d

3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

(ppm)

Figure 17: Baseline versus current distributions.

In Figure 19, the feature value is depicted as a function of time.It exhibits the fault growth (green line) and the set threshold,that is, the fault value at a predetermined level (red line).One hundred points in each time window are selected. Theblue histogram represents the normal pdf. The blue line isselected as the threshold. 5% of the normal pdf is on the rightof the threshold implying that type I error is 5%. The redhistogram represents the current pdf. 6% of the current pdfis on the left of the threshold. So, type II error is 6%. Thus,the corresponding confidence in the declaration of the faultcondition is 90% meaning that after 998 cycles, there is 94%possibility that the test platform is experiencing a fault.

7.2. Failure Prognosis. For prediction purposes the model istuned first, as shown in Figure 18.The distance of the bearingrun in miles corresponds to time in this case. 5000 particlesare used for resampling purposes. The red line correspondsto the measurement data. The blue dot line represents theestimated data.

In Figure 19, the red “line” is the threshold value. Thethreshold or hazard zone is actually a probability densityfunction (pdf) set by the user and representing the latter’sconception from past experiences of the fault dimension afailure event is imminent and must be corrected. Multiplehazard zones may be specified. The histogram along thetime/mileage axis (approximate pdf) represents the timeor miles traveled to failure. Statistics, such as the meanand standard deviation, are computed to provide the userwith useful information, that is, when action should betaken to repair the failing component (earlier or later thanthe mean time depending on the risk the user is willingto take under the prevailing circumstances). Appropriate

Model tuning result15

10

5

00 500 1000 1500 2000 2500 3000

Measured dataEstimated data

Mileage

Figure 18: Model tuning.

76.56

5.55

4.54

3.530 500 1000 1500 2000 2500 3000 3500 4000

0 500 1000 1500 2000 2500 3000 3500 4000

Wea

rTime (hour)

7006005004003002001000

Failure time (prognose time + RUL)

Figure 19: Failure prognosis.

performancemetrics are defined and employed relating to theprediction accuracy [1].

8. Conclusions

Prognosis and health management is an important subjectworthy of study for automated machining processes. Thispaper introduces a framework for the process, fault type,and assessment and testing of a critical component froman automated machining process based on novel particlefiltering algorithms. Fault diagnosis has been shown to resultin detection and isolation of a faulty machine componentwith user specified accuracy (confidence) and given falsealarm rate. The prognostic approach, based on streamingdata, an appropriate feature vector, a data-driven symbolicregression model, and a Bayesian estimation process-particlefiltering, has been demonstrate to provide accurate results forthe test case under consideration. As a result, the maintaineris provided with useful information as to when correctiveaction is required considering risk issues. The applicationexample employs real fault/failure data derived from a seededfault test in a bearing of the automated machining pro-cess. It provides excellent insight about the effect of modelinaccuracies and customer specifications in the algorithmperformance.


Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

References

[1] G. Vachtsevanos, F. L. Lewis,M. Roemer, A. Hess, and B. Q.Wu,Intelligent Fault Diagnosis and Prognosis for Engineering System,Wiley, New York, NY, USA, 2006.

[2] M. E. Orchard and G. J. Vachtsevanos, “A particle-filteringapproach for on-line fault diagnosis and failure prognosis,”Transactions of the Institute of Measurement and Control, vol.31, no. 3-4, pp. 221–246, 2009.

[3] Narasimhan, “A conceptual model of the alignment-perform-ance link in PSM,” 2005.

[4] X. Qi, J. Qi, D. Theilliol et al., “A review on fault diagnosis andfault tolerant control methods for single-rotor aerial vehicles,”Journal of Intelligent & Robotic Systems, vol. 73, no. 1–4, pp. 535–555, 2014.

[5] M. Orchard, G. Kacprzynski, K. Goebel, B. Saha, and G. Vacht-sevanos, “Advances in uncertainty representation and manage-ment for particle filtering applied to prognostics,” in Proceedingsof the International Conference on Prognostics and HealthManagement (PHM ’08), pp. 1–6, IEEE, Denver, Colo, USA,October 2008.

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