Motor shaft misalignment detection using multiscale entropy with wavelet denoising

Expert Systems with Applications 37 (2010) 7200–7204

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Expert Systems with Applications

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Motor shaft misalignment detection using multiscale entropywith wavelet denoising

Jun-Lin Lin a, Julie Yu-Chih Liu a,*, Chih-Wen Li a, Li-Feng Tsai b, Hsin-Yi Chung b

a Department of Information Management, Yuan Ze University, 135 Yuan-Tung Road, Chung-Li 32003, Taiwanb Energy and Environment Research Laboratories, Industrial Technology Research Institute, Hsinchu 310, Taiwan

a r t i c l e i n f o

Keywords:Multiscale entropyWavelet transformInduction motorFault detection

0957-4174/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.eswa.2010.04.009

* Corresponding author.E-mail addresses: [email protected] (J.-L.

edu.tw (J.Y.-C. Liu), [email protected] (C.-WTsai), [email protected] (H.-Y. Chung).

a b s t r a c t

Misalignment of motor shaft (also manifesting as static eccentricity) is a common motor fault resultingfrom improper installation or damage of the machine components and their support structure. Spectrumanalysis is generally used for online detection of such faults. This study presents a novel approach to dis-cover features that distinguish the vibration signals of a normal motor from those of a misaligned one.These features are obtained from the difference of multiscale entropy of a signal, before and after the sig-nal is denoised using wavelet transform. Experimental results show that classifiers based on these fea-tures obtain better and more stable accuracy rates than those based on frequency-related features.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Induction motors are vital components of various industrialapplications. Although they are robust and reliable, they may de-velop motor faults in harsh working environments or undesiredstress. Various motor faults have been studied in the literature,including winding faults, unbalanced stator and rotor, broken rotorbars, air-gap eccentricity and bearing faults (Benbouzid, 2000;Siddique, Yadava, & Singh, 2005; Tavner, Ran, Penman, & Sedding,2008; Thorsen & Dalva, 1995). Motor faults cause motors to workineffectively, resulting in inefficient energy consumption and evenfailures.

The working condition of an indiction motor should be regularlyor even continuously monitored to ensure that it is working effec-tively and efficiently. Condition monitoring adopts a variety of sen-sors to collect measurements from an online motor, and thenanalyzes the collected measurements to identify possible motorfaults (Tavner et al., 2008). Common measurements include statorvoltage and current (Schoen, Habetler, Kamran, & Bartfield, 1995;Thomson, Rankin, & Dorrell, 1999; Thomson & Fenger, 2001), air-gap and external magnetic flux densities (Thollon, Jammal, &Grellet, 1993), rotor position and speed (Piotrowski, 2006), outputtorque, internal and external temperature (Tavner et al., 2008),vibration (Eisenmann & Eisenmann, 1997; Finley, Hodowanec, &Holter, 2000) and acoustics (Li & Mechefske, 2006; Tímár, 1989).

ll rights reserved.

Lin), [email protected].. Li), [email protected] (L.-F.

This study considers the problem of detecting motor shaft mis-alignment. Possible causes of misalignment include improperinstallation, wearing of the machine components and damage ofthe installed bases due to vibration from machines or earthquakes.Poor alignment can result in bearing failures, bearing housingdamage, bent rotors or crankshafts and coupling wear (Eisenmann& Eisenmann, 1997). Therefore, proper alignment must be main-tained to ensure safe and reliable operation. Shaft alignment isthe most common form of alignment performed on rotating ma-chines. Laser tools are commonly used now for improved align-ment measurements and accuracy (Piotrowski, 2006). However,they are usually used during installation and routine checkup,and are not suitable for continuous monitoring.

As an effective means of analyzing the regularity of a time seriesfrom multiple scales, multiscale entropy (MSE) analysis has beensuccessfully adopted to analyze electrocardiogram signals (Angeliniet al., 2007; Bornas et al., 2006; Costa, Goldberger, & Peng, 2002a,2002b, 2005; Costa et al., 2006; Costa & Healey, 2003; Norris, Stein,& Morris, 2007; Thuraisingham & Gottwald, 2006). Intuitively, amotor in a machine is analogous to a heart in a person. Thisanalogy motivates the use of MSE on motor signals in this currentwork. Specifically, this work proposes a method for detectingmotor shaft misalignment by measuring the motor vibration. Theproposed method calculates the difference between the MSE ofthe original vibration signal and that of the signal after the signalis denoised by wavelet transform. Experimental results show thatthis difference can be used to distinguish effectively betweenaligned and misaligned motors.

The rest of this paper is organized as follows. Section 2describes the concept of MSE. Section 3 presents the proposed

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J.-L. Lin et al. / Expert Systems with Applications 37 (2010) 7200–7204 7201

method for detecting motor shaft misalignment. Section 4 de-scribes the experimental setup and the performance results. Final-ly, Section 5 concludes this paper.

0 5 10 15 201

1.5

2

2.5

Scale Factor

Sam

ple

Ent

ropy

white noise1/f noise

Fig. 1. Sample entropy as a function of the scale factor for coarse-grained timeseries of white and 1

f noises (Costa et al., 2002a).

2. Preliminaries

Finding regularity in a time series is an important issue for bothclassifying time series and predicting future values in time series.For short, noisy time series, Pincus (1991, 1995) proposed a statis-tical measure, called approximate entropy (ApEn), to quantify theregularity of time series. ApEn is closely related to the Kolmogo-rov–Sinai entropy (Young, 2003, chap. 16), which is more suitablefor longer time series. Given a time series and a tolerance r foraccepting matches, any two segments of equal length in the timeseries are matched if for each pair of corresponding points in bothsegments, the difference between them is no larger than r timesthe standard deviation of the time series. Let N denote the lengthof the time series. ApEn (m,r,N) approximately equals the negativenatural logarithm of the conditional probability that any two seg-ments (not necessary at different position in the time series), eachwith length m + 1, in the time series that are matched for the firstm points remain matched for the next point, all within a tolerancer. The calculation of ApEn takes a template-wise approach as fol-lows. Let the segment of length m (and m + 1) starting at positioni in the time series be a template, and let nm

i and nmþ1i

� �be the

number of segments of length m (and m + 1) in the time seriesmatching the template, including self-matching. Then, ApEn(m,r,N) can be calculated by the equation:

ApEnðm; r;NÞ ¼ 1N �m

XN�m

i¼1

� lnnmþ1

i

nmi

� �: ð1Þ

ApEn measures the time series for similar segments, and a largenumber of such segments yields a small value of ApEn. By includ-ing self matching in both nmþ1

i and nmi , Eq. (1) prevents the occur-

rences of lnð0Þ and division by zero in the numerator anddenominator, respectively. However, this also causes the value ofApEn reporting more similarity than is present in the time series.Richman and Moorman (2000) indicated that including self-matchingmakes ApEn heavily dependent on the length of time series.Specifically, ApEn is uniformly smaller than expected for shortertime series. Additionally, ApEn does not always show consistentresults for different tested conditions (i.e., different values of mand r). To remedy this problem, Richman and Moorman (2000) pro-posed a new statistical measure called sample entropy (SampEn),which excludes self-matches. Specifically, given a time series oflength N, SampEn (m,r,N) equals the negative average natural log-arithm of the conditional probability that any two segments lo-cated at two different positions in the time series that are similarfor m points remain similar for the next point, all within a toler-ance r. Unlike ApEn, SampEn excludes self-matching when count-ing nm

i and nmþ1i . SampEn (m,r,N) is computed using the equation:

SampEnðm; r;NÞ ¼ � lnPN�m

i¼1 nmþ1iPN�m

i¼1 nmi

!: ð2Þ

Notably, in both ApEn and SampEn, the tolerance is commonly ex-pressed as a fraction of the standard deviation of the time series tomake both ApEn and SampEn scale-invariant. Both ApEn and Sam-pEn have been applied to noisy time series of physiological signals(Lake, Richman, Griffin, & Moorman, 2002; Pincus & Viscarello,1992).

Regularity in a time series is sometimes presented at a coarsegranularity. Therefore, time series need to be explored from vari-ous scales. Costa et al. (2002a) proposed multiscale entropy (MSE),which considers SampEn at multiple scales. MSE has since been

successfully used to analyze physiological signals (Angelini et al.,2007; Bornas et al., 2006; Costa et al., 2002b, 2005, 2006; Costa& Healey, 2003; Costa, Peng, Goldberger, & Hausdorff, 2003; Norriset al., 2007; Thuraisingham & Gottwald, 2006). Given a time series,{x1, . . . ,xN}, a coarse-grained time series in MSE is built by

yðsÞj ¼1s

Xjs

i¼ðj�1Þsþ1

xi; ð3Þ

where s is called the scale factor, and 1 6 j 6 Ns. For s = 1, the coarse-

grained time series is the original time series. As s increases, thelength of the resulting coarse-grained time series decreases. Costaet al. (2002a) showed that the SampEn of a white noise falls quicklyas the scale factor rises (Fig. 1). Conversely, the SampEn of a 1

f noiseremains fairly stable as the scale factor rises. Therefore, white noiseis more regular than 1

f noise.

3. Proposed method

Tavner et al. (2008) concluded that the key for diagnosing mo-tor faults in vibration monitoring is analyzing the frequency spec-trum of the received vibration signal. Important frequenciesrelated to misalignment of motor shaft include the 1�, 2�, 3�and 4� harmonic components of the rotating speed of a motor.However, effectively detecting motor shaft misalignment usingthese harmonic components is not trivial. In Section 4, the vibra-tion signals of a motor rotating at various speeds (900–1800 rpm) are collected under normal or misaligned conditions,and then the energy spectral densities at harmonic componentsfrom 0.5� to 12� of each collected signal are calculated. A decisiontree classifier is built using these energy spectral densities as input,and results in performance that is worse than that of randomguesses (see Test 1 in Section 4).

Additionally, direct use of MSE does not work well when detect-ing motor shaft misalignment. Fig. 2 shows the mean and standarddeviation of SampEn of the above vibration signals at differentscale factors. At each scale factor, the range of SampEn of the nor-mal motor overlaps widely with that of a misaligned motor, mak-ing normal and misaligned motors difficult to distinguish.

Vibration signals are generally noisy, while wavelet transform isa widely adopted method for removing noise from signals. How-ever, the effect of wavelet denoising depends on the signal. Fig. 3shows the MSE curves calculated from the raw vibration signalsand the denoised signals of a normal motor and a misaligned mo-tor, all rotating at 1500 rpm. Overall, denoising has a similar effect

0 5 10 15 20

1.4

1.6

1.8

2

2.2

2.4

Scale Factor

Sam

ple

Ent

ropy

normalmisaligned

Fig. 2. Mean and standard deviation of sample entropy at different scale factors ofnormal and misaligned motors.

0 5 10 15 200

0.5

1

1.5

2

2.5

3

Scale Factor

Sam

ple

Ent

ropy

normalnormal after denoisingmisalignedmisaligned after denoising

Fig. 3. Sample entropy at different scale factors of normal and misaligned motors at1500 rpm before and after denoising.

7202 J.-L. Lin et al. / Expert Systems with Applications 37 (2010) 7200–7204

on both normal signals and misaligned signals. It reduces SampEnwhen the scale factor is small, and increases SampEn when thescale factor is large. However, the effects of denoising to normalsignals and to misaligned signals vary subtly: the difference be-tween the SampEn before and after denoising is larger for normalsignals than for misaligned signals when the scale factor is large.This observation motivates the idea of using the SampEn differenceto differentiate normal signals from misaligned ones.

A method for detecting motor shaft misalignment based onvibration measurement of a motor is presented as follows. The dif-ference between the SampEn of the original vibration signals and

Fig. 4. Experime

the SampEn of the vibration signals after denoising by wavelettransform is calculated, for a scale factor from 1 to 20. These differ-ences (called MSE-related features) are then used as input to a clas-sification algorithm (such as decision trees or neural networks) tobuild a classifier for detecting misaligned signals. The performancecomparison of the classifiers, based on either these MSE-related ortraditional frequency-related features, is studied next.

4. Experimental results

4.1. Experiment setup

To conduct the experiment, a three-phase induction motor (Ta-tung Co. TKKE high efficiency series, 5HP) was installed on a fixedplatform, as shown in Fig. 4. An accelerometer (IMI SENSORS, series660, TO-5, measurement range 20 g) was installed above the bearingon the right hand side to collect vibration signals (see the dash-linecircle in Fig. 4). To generate the misaligned situations, the supportstructure of the bearing was moved (see the solid-line circle inFig. 4) by adjusting its position on the platform, as shown in Fig. 5.

Four sets of vibration signals were collected in this experiment.The first set of normal data (denoted by N1) was collected with themotor running without misalignment. The motor was then misa-ligned by the process described above, and the first set of misa-ligned data (denoted by M1) was collected. Subsequently, themotor was adjusted back to its form without misalignment, andthe second set of normal data (denoted by N2) was collected. Final-ly, the motor was misaligned again to collect the second set of mis-aligned data (denoted by M2). Each set of data contained 31records, recording the vibration signals at 31 different speeds(from 900 rpm to 1800 rpm with an increment of 30 rpm).

Each record was a time series containing 16384 signal values,collected by the accelerometer at 10 kHz. For each record, twotypes of features were derived. Frequency-related features in-cluded 24 energy spectral densities at harmonic components from0.5� to 12� of the signal, calculated using Fast Fourier Transform.MSE-related features included the difference in SampEn at eachscale (from 1 to 20) before and after denoising. Denosing was per-formed using the Daubechies wavelet transform, which was imple-mented with Matlab wavelet function with the parameter settings(tptr = ‘‘rigrsure”; sorh = ‘‘s”; scal = ‘‘mln”; n = ‘‘4”; wav = ‘‘db4”).

4.2. Performance results

Four tests were performed in this experiment. Test 1 used theset N1 [M1 as the training set, and the set N2 [M2 as the testset. Test 2 swapped the training and the test sets adopted in Test1. Test 3 used all records collected while the rotating speed of

nt platform.

Fig. 5. Moving the support structure to generate misalignment.

Table 1Prediction accuracy on the test set for Test 1 (i.e., training set = N1 [M1, testset = N2 [M2).

Freq-related features (%) MSE-related features (%)

Decision tree 43.5 75.8Neural network 50.0 82.3SVM 50.0 85.5

Table 2Prediction accuracy on the test set for Test 2 (i.e., training set = N2 [M2, testset = N1 [M1).



Table 3Prediction accuracy on the test set for Test 3 (i.e., training set 61350 rpm, test setP1380 rpm).



Table 4Prediction accuracy on the test set for Test 4 (i.e., training set P1380 rpm, test set61350 rpm).



J.-L. Lin et al. / Expert Systems with Applications 37 (2010) 7200–7204 7203

the motor was less than or equal to 1350 rpm as the training set,and all records collected while the rotating speed of the motorwas greater than or equal to 1380 rpm as the test set. Test 4swapped the training and the test sets adopted in Test 3. In eachtest, three classification algorithms (decision tree, neural networkand SVM implemented in Weka (Witten & Frank, 2005)) wererun to compare the performances of using either the 24 fre-quency-related features or the 20 MSE-related features, describedearlier in Section 4.1.

The results in Tables 1 and 2 show that using MSE-relatedfeatures leads to better prediction accuracy in Tests 1 and 2 thanusing frequency-related features. With frequency-related features,the prediction accuracy on the test set in Test 1 for all threeclassification algorithms is not better than random guessing. Test2 had better prediction accuracy than Test 1, possibly becausethe training set provided a better coverage of patterns for thecorresponding test set in Test 2 than in Test 1. However, usingMSE-related features still achieved an accuracy of 75.8–85.5%, evenin Test 1.

Test 3 (Test 4) built a classifier from the signals collected at low-er (higher) rotating speeds, and tested the classifier against the sig-nals collected at higher (lower) rotating speeds. The results, shownin Tables 3 and 4, indicate that using the MSE-related featuresachieves more stable and mostly better prediction accuracy thanusing the frequency-related features. Overall, these MSE-relatedfeatures captured the patterns of motor shaft misalignment betterthan those frequency-related features.

5. Conclusions

Multiscale entropy analysis of electrocardiogram signals (Costaet al., 2005; Costa & Healey, 2003) has shown that sample entropyat large scale factor is higher for healthy persons than for thosewith congestive heart failure, although the difference is smallwhen the scale factor is low. However, this finding cannot be di-rectly applied to vibration signals of motors to distinguish a normalmotor from a misaligned one, owing to the high overlap amongthese two types of signals. This study presents a novel use of themultiscale entropy technique by comparing the difference of sam-ple entropy of a signal before and after the signal is denoised usingwavelet transform. The differences at some scale factors appearlarger for normal motors than for misaligned motors and, there-fore, can be used to build effective classifiers for detecting mis-alignment of motor shaft. This approach is now being extendedto detect other motor faults.

Acknowledgements

This research was partially supported by the Bureau of Energy,Ministry of Economic Affairs, Taiwan, under the project of KeyTechnology Development for Energy Saving Network System.

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Motor shaft misalignment detection using multiscale entropy with wavelet denoising