Soft ComputDOI 10.1007/s00500-014-1326-5

METHODOLOGIES AND APPLICATION

Anfis model for vibration signals based on aging process in electricmotors

Duygu Bayram · Serhat Seker

© Springer-Verlag Berlin Heidelberg 2014

Abstract In this study, the aging process of an electricmotor is accomplished by adaptive neuro-fuzzy inferencesystem (ANFIS) using vibration signals. Different ANFISmodels are compared for representing the aging process inthe best possible way. An artificial aging experiment is per-formed and vibration data taken from the initial (healthy) andfinal (faulty) cases are used to identify the aging process.Four different ANFIS models are presented. Moving aver-age (MA) filters are applied to the input and output pairs fordifferent lagging factors to change the smoothness degree ofthe data and thus the performance of system identification.The success of the models is evaluated on three conditions;the performance of the ANFIS and the linear correlationbetween expected output (faulty case data) and aging modeloutput, in time and frequency domains.The study also evalu-ates the influence of preprocessing using MA filtering on theANFIS performance for vibration data which have stochasticcharacteristics.

Keywords ANFIS · Electric motor · Aging · Correlationcoefficient · Moving average · Spectral analysis

1 Introduction

Because of their rugged, reliable and simple structure, induc-tion motors are the most preferred electric machines by theindustry. So, they are constructed at various power levelsto get the industrial requirements (Siddique et al. 2005).

Communicated by V. Loia.

D. Bayram (B) · S. SekerElectrical Engineering Department, Istanbul Technical University,Maslak, Istanbul 34469, Turkeye-mail: bayramd@itu.edu.tr

Despite having high reliability, sometimes they might func-tion improperly and corrupt the continuity of the industrialprocesses (Nandi and Toliyat 1999). To provide the sustain-ability, condition monitoring and investigations about thelifetime of induction motors have vital importance. Condi-tion monitoring studies are used to observe the trends of theinduction motor parameters. These trends play an importantrole on determination of induction motor performance analy-sis and detection of failure potentials. In addition, some sur-veys and academic studies are executed on the lifetime ofinduction motors (Tavner 2008). Therefore, aging process isresearched extensively in the literature (Seker 2000; Weryn-ski et al. 2006). Aging process has a complicated structureand it contains a lot of unfamiliar components. For this rea-son, modeling of the aging processes is very difficult.

Different signal types can be used to investigate the agingprocess of an induction motor. Electrical signals carry hintsabout aging, whereas mechanical signals, like torque andvibration, directly show the aging effects. Hence, torque andvibration signals give the opportunity to define the agingdirectly. Therefore, vibration signals are the indispensableelements to realize a proper condition monitoring. Becauseof their nature they are convenient for the statistical studies;it is known that the statistical parameters of the data differwith aging and with other types of defects (Seker and Ayaz2003b; Yan and Gao 2011). Vibration signals can be investi-gated by various signal processing techniques to find out thedistinctive failure signatures. For example, spectral analysesof vibration signals are widely used in the literature becauselots of defects can be detected using spectral approaches(McCormick and Nandi 1999; Concari et al. 2008; Trajin etal. 2010; Bianchini et al. 2011; Frosini and Bassi 2010). Tofocus either specific bands of the spectra or the whole spec-tra, some transforms are used such as Fourier transforms,wavelet transforms and Hilbert transform (Seker and Ayaz

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2003a; Eren and Devaney 2004; Roy et al. 2005; Ayaz etal. 2006; Ruqiang and Gao 2006; Yan and Gao 2011). Andalso, it is pointed out that some frequency components canbe seen as the indication of specific faults. As an example,bearing damage can be observed above 2 kHz (Seker andAyaz 2003a; Ayaz et al. 2006; Trajin et al. 2010). Moreover,lots of soft computing techniques like artificial neural net-work and fuzzy logic are used to realize the fault detectionin the literature. In the related literature, ANFIS applicationsof induction motors and their aging studies are very rare. Inthis manner, one of them (Yilmaz and Ayaz 2009) introducesthe relation of the motor vibration and current during thetemperature shifts. And the other one is an hybrid approach,which combines wavelet transform and ANFIS, for diagnosisof electric motor (Sanz et al. 2010).

In this study, the ANFIS is used to get the best possiblemodel in order to identify the aging process using vibrationsignals. However, each vibration signal is a proper mixtureof some frequency components and noises. By this point ofview, the existence of noises brings the signal in a stochasticstructure. Because of this, modeling and identifying the agingprocess with this stochastic content are very difficult. Simi-larly, some stochastic approaches are widely used for systemidentification and parameter estimation in different fields ofscience. For example, considering the nature of the system,Hodgkin–Huxley model, adaptive quadratic neuronal mod-els are employed in biology instead of neural networks, fuzzyinference system or adaptive neuro-fuzzy inference system(Jun et al. 2011; Lingfei et al. 2012).

Aging process of an induction motor is a complicatedprocess. It is well known that mechanical signals gener-ated by some faults (like bearing faults) have non-stationarynature because of the modulation of other mechanical com-ponents’ rotation (such as shaft and gears) (Wang and Jianu2010). According to our previous works, it is studied thatthere was bearing fault in that motor (Ayaz et al. 2006;Karatoprak et al. 2007; Seker and Ayaz 2003a,b; Seker etal. 2000). On such kind of artificial aging process, it is dif-ficult to identify non-stationarity and nonlinearity. However,it can be concluded that an aging model is a complicatedsystem identification problem. And also, an artificial agingprocess cannot be represented as an actual physical process.So its model is an ideational model instead of an actual phys-ical model. Because of this fact, using only mathematicalcharacterization is not satisfying. The model needs a fuzzyinterpretation also. It is known that artificial neural networklearns the behavior of each patterns using nonlinear relation-ships. Fuzzy logic uses a reasoning like a human using con-stant parameters to inference. ANFIS tunes the parametersof the rule base using neural network. In this manner, it con-solidates the learning skill of neural network and inferenceability of fuzzy logic. Considering its brilliance, ANFIS is agood choice to model complicated systems. In that manner,

the study becomes a suitable candidate for ANFIS modeling.The main goal of this study is modeling this complicatedprocess using a soft computing algorithm. To increase theANFIS success, MA filters are used to provide the smooth-ness. Hence, the most suitable model is investigated betweenmodels which have different degrees of smoothness depend-ing on the order of MA. The most suitable model is deter-mined considering three gauges. These are the success ofANFIS in terms of training and checking errors, the correla-tion coefficient calculated between outputs (expected outputand the aging model output) and the comparison of outputs’power spectra. As the contribution, the study shows that itis able to model such a complicated process with ANFIS.And also, the study evaluates the effect of MA filtering onthe ANFIS performance for such stochastic data.

This paper is organized as follows after the introduction;Sect. 2 gives the mathematical background of the study.Experimental study and measurement system are mentionedin Sect. 3. Section 4 explains the application of the performedanalysis. The simulation results are also given in this section.We conclude our work in the Sect. 5, by summarizing theachievements.

2 Mathematical background

In this study, power spectral density (PSD), correlation coef-ficient calculations, ANFIS and MA filtering are used. In thissection the aim of their employment is introduced.

2.1 Power spectral density estimation and correlationcoefficient

In this study, correlation coefficient is used to define the spec-tral similarities of two data. For this aim, the amplitudes ofPSDs are assumed as mathematical sequences independentfrom the frequencies. Then, correlation coefficient can becalculated between these new forms of PSDs. The expectedoutput for the model is the faulty case data. PSD is calculatedas Pfaulty( f ) on frequency domain for this data.

Preali ( fi ) = Pfaulty( f ) (1)

The Pfaulty( f ) contains two sequences; these are amplitudesequence (preali ) and frequency sequence ( fi ).

Preali ( fi ) = {preali | fi

}, i = 1, . . . , n (2)

The new set regarding the assumption can be realizedusing amplitude sequence only.

preal = {preal1 , preal2 , preal3 , . . . , prealn

}(3)

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The ANFIS output is compared with the expected output(faulty case data) by means of PSDs. In accordance with thispurpose, the PSD for the model output (Pfaulty′( f )) is alsodefined independent from frequencies.

Pmodeli ( fi ) = Pfaulty′( f ) (4)

Pmodeli ( fi ) = {pmodeli | fi

}, i = 1, . . . , n (5)

The second set regarding the assumption can be realizedusing amplitude sequence only.

pmodel = {pmodel1 , pmodel2, pmodel3, . . . , pmodeln

}(6)

Then, the correlation coefficient between these sequences canbe calculated by Eq. (7). As a result of Eq. (7), the similaritiesbetween PSDs can be interpreted.

ρa,b = cov[preal, pmodel]√var[preal]var[pmodel] = cov[preal, pmodel]

σprealσpmodel

(7)

2.2 Moving average

Moving average can be interpreted as a special low-pass filterin signal processing. It is employed to smoothen the data bydecreasing the fluctuations. For a set {xi } elements, an L-moving average is a new set {x ′

i } calculated from {xi }, bycomputing the arithmetic mean of the subsets composed byL terms (Alessio et al. 2002; Yongzhen et al. 2007). Movingaveraged data can be created using Eq. (8).

{x ′

i

} = 1

L

i+L−1∑

j=1

x j (8)

The frequency response of a moving average filter can becalculated as Eq. (9).

H(ω) =(

1

L

)(1 − e− jωL)/(1 − e− jω) (9)

It is well known that cutoff frequency of a low-pass filteris accepted as the frequency where the power is half ofmaximum power. In other words ωcutoff is angular cut offfrequency, where | H(ωcutoff)| = 0.707.

2.3 Adaptive neuro-fuzzy inference system (ANFIS)

Artificial neural network (ANN) recognizes patterns andlearns the behavior of each pattern using nonlinear relation-ships which are defined between input and output. Fuzzylogic (FL) utilizes a knowledge base, to reach a conclusionon the basis of reasoning like a human. However, it uses con-stant parameters to inference and its knowledge base is builtby if-then rules.

Layer 1(Adaptive

Nodes)Assigning MF

Layer 2(Fixed Nodes)Combination

Layer

Layer 3(Fixed Nodes)Normalization

Layer

Layer 4(Adaptive

Nodes)Inference Layer

Layer 5(Fixed Nodes)

Summation Layer

1

2

1

2

Fig. 1 ANFIS structure

ANFIS defines rule base and tunes the parameters of therule base using neural network. In this manner, it incorporatesthe learning ability of neural network and inference power offuzzy logic. ANFIS is a good choice to model nonlinear andcomplicated systems because of its intelligence.

Figure 1 shows the basic ANFIS structure as a multi-layerfeedback network. The network has adaptive and fixed nodes.The adaptive nodes serve to minimize the error by tuningrelevant parameters. The structure given in Fig. 1 has twoinputs (x, y) and one output f (Jang 1993a).

Layer1 includes adaptive nodes with their membershipfunctions (MF). The parameters of membership function arenamed as premise parameters which can change its shape.Then, nodes located at this layer become adaptive by thischange. Layer 2 combines the input signals to produce anactivation (firing) strength. Nodes at this layer are the fixednodes which multiply its inputs and defining a rule. Layer 3,which contains fixed nodes, is used to normalize the activa-tion (firing) strengths. Layer 4 includes adaptive nodes whichcompute the consequent parameters. This layer representsthe inference ability of the algorithm. Layer 5 is formed by afixed node which calculates the output of the ANFIS as thesum of all incoming signals (Jang 1993b; Sanz et al. 2010).

3 Experiment and data acquisition system

In this study, an artificial aging process is applied to an induc-tion motor. The process is composed by 7 cycles. During eachcycle (step), two types of aging techniques are applied to themotor. These are electrical discharge machining (EDM) andthe thermal and chemical aging actions, respectively. Dur-ing the nominal operation of an induction motor (IM), anunexpected voltage is induced on the shaft because of theexistence of magnetic field and rotation movement. The dis-charge of this voltage may cause breaking down of the rollingelements and bearings. EDM is an imitation of shaft voltagedischarge. To simulate the discharge, 30 V is applied to theshaft from an external source. And 27 A current is providedthrough the bearings.

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Signal Conditioner

Data from faulty case

Data from healthy case

Signal Conditioner

INITIAL (Healthy Case) FINAL (Faulty Case)

Seven Cycles for Aging Process

Chemical and Thermal Aging &

Electrical Discharge Machining

Fig. 2 Experimental setup and data acquisition system

#1#2#3&4

#5#6

Fig. 3 Orientation of the accelerometers

Chemical and thermal aging actions are also applied tothe motor in order to accelerate the process after EDM. Themotor is sunk to a water tank and then placed into oven andheated up to 140 ◦C. The corrosion and thermal aging isprovided by these chemical and thermal actions.

Electrical, thermal and chemical aging actions comprisethe procedure of one aging cycle. After 7 aging cycles, theexperiment is terminated considering the condition of themotor. The details of the experiment can be found in the Ph.D.thesis of Erbay (1999) and in some other studies (Seker et al.2000; Ayaz et al. 2009a,b; Seker and Ayaz 2003a,b; Bayramet al. 2012, 2014; Bayram and Seker 2013).

In this paper, first (initial) and last cycle’s vibration dataare used to model the aging process.

Six identical accelerometers are used for this experiment.Accelerometer 5 is on the fan. Accelerometers 3, 4 and 5are placed on the fan end, recording axial, vertical and hor-izontal vibrations. Accelerometer 6 is on the front carcass.Accelerometer 1 and 2 are located at the process end, sym-metrically. The orientation of accelerometers can be seen inFig. 3. The vibration record taken from the accelerometer 2is used in this study.

The sampling frequency of the recorded data is 12 kHz.Besides, in order to avoid from the high frequency noiseinterference, an anti-aliasing filter with cut off frequency at4 kHz is used. The type of the motor is an induction motorof 5 HP, three-phase, four-poles, designed for 60 Hz supplyfrequency and with the nominal speed 1,742 rpm (rotationper minute). Measurement and data acquisition system canbe seen in the Figs. 2 and 3.

Seven aging cycles are applied to the motor. The timedomain and frequency domain representations can be seen

0 5 10-5

0

5initial case

0 5 10-5

0

51. case

0 5 10-5

0

52. case

0 5 10-5

0

53. case

0 5 10-5

0

54. case

0 5 10-5

0

55. case

0 5 10-5

0

56. case

0 5 10-5

0

57. case

0 2000 4000 60000

2

PSD of initial case

0 2000 4000 60000

2

PSD of 1. case

0 2000 4000 60000

2

PSD of 2. case

0 2000 4000 60000

2

PSD of 3. case

0 2000 4000 60000

2

PSD of 4. case

0 2000 4000 60000

2

PSD of 5. case

0 2000 4000 60000

2

PSD of 6. case

0 2000 4000 60000

2

PSD of 7. case

Fig. 4 Time domain and frequency domain representations of agingcycles

Table 1 Basic statistical properties of aging cycles

Aging cycles Mean Standard deviation Variance

Initial 0.0016 0.1135 0.0129

1. Cycle 0.0014 0.1553 0.0241

2. Cycle 0.0012 0.2082 0.0433

3. Cycle 0.0013 0.2894 0.0837

4. Cycle 0.0009 0.3275 0.1073

5. Cycle 0.0010 0.3548 0.1259

6. Cycle 0.0005 0.4147 0.1720

7. Cycle 0.0030 0.6040 0.3648

in Fig. 4. Table 1 shows the basic statistical properties of eachcycle.

4 Aging models and performance evaluation

Modeling of an aging process is impossible using fuzzy infer-ence system (FIS), because defining a rule base is very dif-ficult for such a stochastic data (Jang et al. 1997). Because

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Anfis model for vibration signals

Aging Models

Investigation for the most suitable model

ANFIS Success

Correlation with expected result

Healthy Case(with or without

moving

Faulty Case(with or without moving average)

Fig. 5 The ideational flow of the study

Selecting 3 input variables

Pool of delayed data from healthy and

faulty cases

ANFIS Model

ANFIS output: Estimation for faulty

case

Inputs

Sequential search algorithm to select

3 inputs

Searching for the minimum training and checking

errors from the all possible combinations

Fig. 6 The schematic of the aging model

of the aforementioned reasons, ANFIS is employed in thisstudy.

The complex systems, which contain lots of unfamiliarcomponents like various frequency components and noises,are in the need of being smoothed to increase the modelsuccess. For this reason, moving average filters are used inthis study. The success of ANFIS is investigated for differentmoving averaged input–output pairs. The schematic aboutthe ideational flow can be seen in the Fig. 5.

Modeling and identification of a complex system usingANFIS can be done employing some techniques like select-ing input variable by sequential search algorithm. For thisreason a pool, which consists of ten delayed input or outputdata, is created (Jang et al. 1997). Three input variables areselected from this pool.

The schematic of the aging model can be seen in Fig. 6.The input candidates are chosen from a pool of delayed ver-sions for healthy case h(t) and faulty case data f (t). Sequen-tial search algorithm and investigating training-checkingerrors for all possible input combinations give three inputsfrom ten input candidates. The expected output of the ANFISis always faulty case data. In this study, there are four differentANFIS models. Their input–output pairs preprocessed usingMA filters for various lagging factors and their performanceare evaluated.

The vibration data achieved from first and final agingcycles are used in this study. It can be seen obviously thatthe amplitude of the vibration increases with aging in Figs. 4and 7.

Another identifier of aging is the change of their PSDs. ThePSDs of the signals can be seen in Fig. 8. As it is well known,aging manipulates the frequency content of a vibration signal

0 2 4 6-3

-2

-1

0

1

2

3Healthy case vibration signal

Time [s]

Am

plitu

de [g

]

0 2 4 6-3

-2

-1

0

1

2

3Faulty case vibration signal

Time [s]

Am

plitu

de [g

]

(a) (b)

Fig. 7 The vibration signals of the electric motor. a Healthy case bFaulty case

0 2000 4000 60000

0.5

1

1.5

2

2.5

3

3.5

PSD of healthy case

Frequency [Hz]

PS

D [g

2 /H

z]

0 2000 4000 60000

1

2

3

4

5

6

7

8

9

PSD of faulty case

Frequency [Hz]

PS

D [g

2 /H

z]

Fig. 8 PSDs of the signals

as seen in Fig. 4. Either defining a threshold in time domainor searching for fault signatures in frequency domain are verybasic ways of recognizing the faulty operation. However, theaim of the study is not detecting or recognizing fault signa-tures. The goal is modeling the aging of an induction motorwhich is a complex process. Although aging is a physicalevent, the aging model is an ideational model which outputsthe faulty case to the healthy case input (Fig. 5).

Forming an aging model using ANFIS does not providereasonable training and checking errors. That is why smooth-ing is needed in order to increase the model success. Dif-ferent ANFISs are designed for different moving averageddata pairs. The models are named after their moving averagelagging parameters. The highest lagging parameter providesthe smoothest data.

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D. Bayram, S. Seker

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Frequency responses of MA filters

omega

H

H5

H10H15

0 200 400 600 800 1000 1200 1400 1600 1800 20000

0.5

1

1.5

2

2.5

3

3.5PSD of healthy case with cutoff frequencies of MA filters

Frequency [Hz]

PS

D [g

2 /H

z]

healthy case's PSD

fcutoff for MA5

fcutoff for MA10

fcutoff for MA15

(a)

(b)

Fig. 9 a Bode plot of MA filters b cutoff frequencies on healthy casePSD

The choice of the lagging parameters, in other words cut-off frequency of MA filters, are tuned considering the signals’nature. It is obvious that lots of aging frequencies can be mon-itored at frequencies higher than 2,000 Hz. In the previousstudies, it is shown that these high-frequency components arehigher order harmonics of some pre-existing faults (Bayramand Seker 2013). That is why, it is focused on low-frequencyregion considering the healthy case PSD. The most notice-

able frequencies on healthy case are seen around 1,015 and375 Hz. MA filters’ cut off frequencies are tuned, assum-ing these frequencies as upper and lower limits. Consideringthese limits, the lagging parameters are set to 5, 10 and 15corresponding to 1,081, 534 and 355 Hz, respectively.

The frequency responses of these moving average filterscan be seen in Fig. 9a. The cutoff frequencies are markedwith diamonds on the plot considering |H(ωcutoff)| = 0.707.These cut off frequencies are also marked with dashed lineson the PSD of healthy (initial) case in Fig. 9b.

In this study, a Sugeno’s type ANFIS is used, which has3 inputs and 1 output with 2 bell-shaped membership func-tions for each input, to model the aging process. In otherwords, ANFIS produces 8 rules, 18 premise parameters and32 consequent parameters.

As seen on the Table 2, models’ training and checkingerrors decrease, whereas the model order increases. This isan expected fact because the smoothness increases with themoving average order, and then modeling the data becomeseasier.

The elapsed times are measured for each model. They arevery close to each other. To measure the accurate computationtime, every ANFIS is run for 100 times in one trial. Then, thecomputation time is recorded for 4 trials. The average of these4 trials is assumed as the accurate computation time. It shouldbe noted that the sequential search for the input selection,training and checking times are also included. It is noticedthat the computation time is decreasing with smoothing asexpected. The average elapsed times can be seen on Table 3.

However, training and checking error investigation are notenough to identify the most suitable model. And also, thecomputation times do not provide a great advantage betweenmodels. In these circumstances, the correlation coefficient

Table 3 Averaged computation times for models

Model Averaged computation time [s]

M0 3.0025

M5 2.9574

M10 2.9492

M15 2.9300

Table 2 Training and checkingerrors of the proposed models Model Moving average parameters (lagging) Errors

Training error Checking error

M0 0 (without moving average) 0.49043 0.48159

M5 5 0.1945 0.19669

M10 10 0.10187 0.10414

M15 15 0.06663 0.073

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Anfis model for vibration signals

Table 4 The correlation coefficient between the model outputs andexpected outputs

Model Correlation coefficient between outputs

M0 0.5583

M5 0.6527

M10 0.7319

M15 0.6395

Table 5 The correlation coefficient between PSD amplitude sequencesof expected outputs and model outputs

Model Correlation coeffi-cient between PSDs’amplitude sequences

M0 0.8392

M5 0.9605

M10 0.9504

M15 0.7740

which is calculated between model output and expected out-put must be considered too. The output of aging model isexpected to be a faulty case response which is a result of anaging process. However, the model cannot achieve to pro-duce an accurate faulty case data. Table 4 shows the corre-lation coefficients calculated between the model outputs andexpected outputs (faulty case data) for each model. M10 pro-vides the highest correlation coefficient, whereas M0 is theworst model without any smoothing operation.

And also, the similarity between PSDs is also an evalua-tion criterion. Because the third gauge of the success is iden-tified as the producing ability of the high-frequency compo-nents occurred at high-frequency region, which can be seen atthe Fig. 8. In that manner, the correlation between the PSDamplitude sequences of expected output and model outputmust be examined also. The maximum correlation coeffi-cient is defined as another indication for the most suitablemodel. The correlation coefficient between PSD amplitudesequences can be seen on the Table 5.

As seen on the Table 5, the last model (M15) is the worstANFIS model with low correlation coefficient on spectraldomain which is an indication of information loss.

To define the most suitable model, Fig. 10 can be usedconsidering all of these gauges. It can be interpreted that anymodel defined between M5 and M10 can be accepted as asuitable model.

5 Conclusion

In this study, aging of an induction motor is considered as anexample of highly complicated system. The modeling and

Fig. 10 Investigation for the most suitable model

system identification of the aging process are aimed. It isrealized by ANFIS using the vibration signals for healthy(initial) and faulty cases of the same induction motor. Toobtain the data, an artificial aging experiment is implemented.The amplitudes and the spectral densities are distinctive prop-erties between healthy and faulty cases.

To change smoothness of the data, moving average methodis used for different lagging parameters. The success of therealized models is discussed with three criteria. These arethe training and checking errors of ANFIS, the correlationcoefficient calculated between model output and expectedoutput and the consistency between PSDs of these outputs.As a result of these observations, it is noticed that increas-ing in the moving average order causes the disappearance ofspectral details which characterize the aging. Although thehighest order moving average operation provides the low-est training and checking error, it cannot be accepted as asuccessful aging model because of the information loss.

Figure 10 shows that any cutoff frequency tuned between1,081 and 534 Hz (corresponding M5 and M10) providesa successful MA filtering operation for a suitable model ofaging process. As a result of this study, it can be concludedthat low ANFIS error levels cannot be the only one suc-cess criterion for such complicated systems. To decide themost reasonable model, it must consider the other criterialike frequency and time domain properties of the system.In this sense, this study shows an interesting application ofANFIS modeling on the motor aging studies. The study con-tributes that ANFIS is capable of modeling such a compli-cated process with some supporting analyses.

Acknowledgments The simpler version of this study is presented onThe 10th International FLINS Conference on Uncertainty Modelingin Knowledge Engineering and Decision Making (FLINS 2012). Theauthors would present their special thanks to Prof. B.R. Upadhyayafrom the Maintenance and Reliability Center and Nuclear EngineeringDepartment of University of Tennessee Knoxville, USA, for permissionto the use of experimental data.

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