bearing damage assessment using jensen-rényi divergence...

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Mechanical Systems and Signal Processing

journal homepage: www.elsevier.com/locate/ymssp

Bearing damage assessment using Jensen-Rényi Divergence basedon EEMD

Jaskaran Singh, A.K. Darpe⁎, S.P. Singh

Vibration Research Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India

A R T I C L E I N F O

Keywords:Bearing damageEnsemble empirical mode decompositionRényi entropyJensen-Rényi divergenceConfidence value

A B S T R A C T

An Ensemble Empirical Mode Decomposition (EEMD) and Jensen Rényi divergence (JRD)based methodology is proposed for the degradation assessment of rolling element bearings usingvibration data. The EEMD decomposes vibration signals into a set of intrinsic mode functions(IMFs). A systematic methodology to select IMFs that are sensitive and closely related to thefault is proposed in the paper. The change in probability distribution of the energies of thesensitive IMFs is measured through JRD which acts as a damage identification parameter.Evaluation of JRD with sensitive IMFs makes it largely unaffected by change/fluctuations inoperating conditions. Further, an algorithm based on Chebyshev's inequality is applied to JRD toidentify exact points of change in bearing health and remove outliers. The identified changepoints are investigated for fault classification as possible locations where specific defect initiationcould have taken place. For fault classification, two new parameters are proposed: ‘α value’ andProbable Fault Index, which together classify the fault. To standardize the degradation process, aConfidence Value parameter is proposed to quantify the bearing degradation value in a range ofzero to unity. A simulation study is first carried out to demonstrate the robustness of theproposed JRD parameter under variable operating conditions of load and speed. The proposedmethodology is then validated on experimental data (seeded defect data and accelerated bearinglife test data). The first validation on two different vibration datasets (inner/outer) obtained fromseeded defect experiments demonstrate the effectiveness of JRD parameter in detecting a changein health state as the severity of fault changes. The second validation is on two accelerated lifetests. The results demonstrate the proposed approach as a potential tool for bearing performancedegradation assessment.

1. Introduction

Rolling element bearing forms an integral and vital part of any modern rotating machinery. Over a period of time due to varietyof reasons faults may develop in them that may cause overheating, friction torque, increased clearance leading to drop inperformance and if undetected can cause breakdown. Based on vibration data, a number of signal processing techniques in timedomain, frequency domain and time-frequency domain have been proposed in the past for an early and accurate fault detection [1].However, the traditional methods can have some drawbacks and limitations that hinder the development of a robust online bearing

http://dx.doi.org/10.1016/j.ymssp.2016.10.028Received 16 April 2016; Received in revised form 28 July 2016; Accepted 29 October 2016

⁎ Correspondence to: Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India.E-mail addresses: Jaskaran.Singh@mech.iitd.ac.in (J. Singh), akdarpe@mech.iitd.ac.in (A.K. Darpe), singhsp@mech.iitd.ac.in (S.P. Singh).

Abbreviations: BDF, Ball Defect Frequency; CV, Confidence Value; EMD, Empirical Mode decomposition; EEMD, Ensemble Empirical Mode Decomposition; FFT,Fast Fourier Transform; IMFs, Intrinsic Mode Function; IRDF, Inner Race Defect Frequency; JRD, Jensen-Rényi divergence; ORDF, Outer Race Defect Frequency;PFI, Probable Fault Index; SNR, Signal to Noise Ratio; WPD, Wavelet Packet Decomposition

Mechanical Systems and Signal Processing 87 (2017) 307–339

degradation assessment tool. For example, in practice whenever data is acquired over the entire life span of a bearing, the signals areusually exposed to interference by the effect of background noise, presence of outliers, unexpected variation in operating parameterssuch as load variation and speed fluctuation. It can become challenging to accurately assess the bearing health status over its lifetimeand timely forewarning of failure. The accurate estimation of current health status may reduce economic losses, decrease productiondowntime and improve efficiency.

Many researchers have attempted to address this problem in the past. Enough literature on variety of fault features is available inthe field of bearing degradation assessment. Different features are sensitive to different faults and degradation severity [2]. Statisticalmoments such as RMS and kurtosis have been frequently used in many works as features for machine health condition monitoring[3,4]. Qiu et al. [5] and Peter et al. [6] showed that the sensitivity of the RMS feature, in terms of identifying an incipient defect, isvery low. Gebraeel et al. [7] chose the average of the amplitudes of the defective frequency and its first six harmonics, as thedegradation index over the full cycle life of a bearing. However, it is difficult to detect and track the weak signals at an early stageusing only time domain and frequency domain parameters [8].

Qiu et al. [5] developed a robust degradation assessment method based on optimal wavelet filter and self-organizing map (SOM).Huang et al. [9] further predicted the degradation condition using SOM and back propagation neural network on the basis of themethodology given by Qiu et al. [5]. Pan et al. [10] proposed a methodology for bearing performance assessment based on animproved wavelet packet-support vector data description. Suggesting further improvements in the past work, Pan et al. [2] proposeda new health assessment index based on lifting wavelet packet decomposition and fuzzy c-means. Pan et al. [11] proposed spectralentropy as a health index and the results of both simulations and experiments showed that spectral entropy effectively reflects thebearing degradation process. Yu [12,13] proposed dimension reduction and feature extraction approach based on locally preservingprojections for bearing degradation assessment, and further quantified the performance of bearings by the integration of theexponential weighted moving average statistic and the negative log likelihood probability based on Gaussian mixture model. Heproposed a hybrid-learning-based feature selection method for fault diagnosis and machine health assessment [14]. Mi et al. [15]proposed a method to achieve multi-step bearing degradation prediction based on an improved back propagation neural networkmodel using features extracted by principle component analysis. Wang [16] trained the features extracted from Empirical ModeDecomposition (EMD) using SVM and further used Mahalanobis distance as a fault indicator. Li et al. [17] used autoregressivemodel to separate the original vibration signal into random parts and deterministic parts and used the energy ratio between therandom parts and the original signal as a fault indicator. Hong et al. [18] combined wavelet packet and EMD for feature extractionand derived a confidence value through SOM to assess bearing health states. Shakya et al. [19] applied Chebyshev׳s inequality to theMahalanobis distance for online monitoring and damage stage detection for naturally progressing defect. Ali et al. [20] combinedtraditional statistical features and EMD energy entropy and estimated the degradation condition with the back propagation neural

Nomenclature

a Scaling parameter to evaluate confidence valuea(t) Envelope signalAm Amplitude of the mth harmonic of rotational

speed in healthy signalci(t) ith IMF of a signaldo Magnitude of the impulse or amplitude level of

defectd(t) Impulse functionDJRα

ω Jensen-Rényi divergenceE Total signal energyEi Energy of ith IMFf Frequencyfinner Characteristic inner race defect frequencyfouter Characteristic outer race defect frequencyfs Shaft rotational frequencyH[.] Hilbert transform of a signalK Number of standard deviations to be considered in

Chebyshev's inequalityM Number of points to be considered to evaluate

mean for removing outlier in Z-statisticsn(t) White Gaussian Noisep Probability distributionpi percent of energy of ith IMFqinner Applied load on the shaft in case of inner race

defectqmean Applied mean radial load on the shaftqouter Applied load on the shaft in case of outer race

defectqo(t) Applied radial load on the shaftqunbalance Unbalance force on the shaftqv Random variation of the loadQ Consecutive data points to be considered to de-

clare change in health of a bearing in Z-statisticsrn(t) Residual function of EEMDR(r,k) Time deviation from the expected period of im-

pulse repetitionRα(p) Rényi entropyTd reciprocal of corresponding bearing defect fre-

quencyTdo Modified Td to account for speed variationx(t) vibration signal in time domainxH(t) simulated healthy vibration signal in time domainz(t) analytic signalα Rényi entropy exponentα value parameter extracted from EEMD envelope spec-

trum of IMFβn Sensitivity index of IMFsδ(t) Dirac delta functionε load distribution factorσ Standard Deviationμ Mean of a distributionψn Pearson's correlation coefficient between original

signal and nth IMFπ π π, ... . n1 2 weights assigned to distributions in Jensen-

Rényi divergenceθmax angle limiting the load zone

J. Singh et al. Mechanical Systems and Signal Processing 87 (2017) 307–339

network for online bearing fault diagnosis. Hu et al. [21] used Mahalanobis–Taguchi system and SOM network to track the dynamicdegradation trend of the bearing from real-time vibration data.

Many a times the fault information in vibration signals of the bearings is weak due to strong background noise. For such signalsthe time–frequency methods are considered to be an effective way for extracting the features from the noisy data. In recent years,EMD which is a widely used time-frequency domain analysis technique has been successfully used to decompose a signal into a set ofintrinsic mode functions (IMFs) for fault diagnosis using the concept of energy entropy [8,22–24]. Boškoski and Juričić [25,26]further extended the concept of energy entropy to evaluate an information index known as Jensen-Rényi Divergence (JRD) based onRényi entropy. JRD evaluated the relative change in the energy distribution of coefficients derived from wavelet packet transform ofa defective signal with reference to a base distribution in order to quantify mechanical faults. But it is well established that diagnosisapproach based on EMD energy entropy identifies roller bearing fault patterns effectively and is superior to that based on waveletpacket decomposition and reconstruction [22]. In addition in all the above studies the appropriate IMFs to be selected for evaluatingentropy have been chosen randomly or based on visual inspection. The choice of appropriate IMFs is crucial not only to monitor thehealth of the bearing but also for fault classification.

Studies reveal that though the importance of bearing degradation assessment has prompted many researches in this field, yetthere are challenges in accurately assessing the health status of a bearing.

1) The first major challenge is to devise a robust and a stable condition monitoring parameter that can be used to detect incipientdamage for any degradation mode. The parameter should be sensitive enough to detect any change in the level of degradationduring early part of damage propagation rather than showing changes close to the complete failure to raise an alarm. Most of theproposed methods use SOM, ANN, SVM etc. which rely on prior knowledge of the domain wherein training data from all classesof specific bearing defects is required during the training phase. These methods provide reasonably good results for thoseparticular defects only. For practical bearing health assessment, it may be quite difficult to have a complete prior knowledgeabout the type of failure mode. A large amount of training data is also needed for accurate modelling. Moreover a change in theoperating parameters or bearing type will change the vibration characteristics, hence the machine learning operator needs to betrained for the new set of conditions.

2) Whenever data is acquired over the entire life cycle of the bearing, the measured vibration signals are often disturbed byuncertain impulsive changes and random fluctuations. The overall effect of such changes is a confusing trend of the conditionmonitoring parameter involving false positives. Such trends have been observed from the bearing life test data reported byShakya et al. [19]. It is necessary to filter out the effects of these disturbances as they can cause false indication of abrupt rise inthe value of condition monitoring parameter.

3) A generalized health indicator is necessary that allows to judge the health of different bearings, having different defect types on acommon platform. The performance degradation assessment methodology should be independent of the physical characteristicsof the bearing or the operating conditions, for it to be more general.

4) The method should be capable of accurately classifying the type of defect as soon as it develops. Identifying the point of defectinitiation is essential for accurate prognosis of bearing.

5) In order to automate the degradation assessment methodology, the approach should be non-parametric in nature.6) The condition monitoring parameter should be insensitive to background noise and temporal variability in operating conditions

during the full life cycle of the in-service bearing.

Fig. 1. Flowchart showing the components of bearing degradation assessment methodology.

To address all these issues for better bearing degradation assessment, a divergence (Jensen Rényi divergence) based feature as acondition monitoring parameter is implemented in this work. Ensemble Empirical Mode Decomposition (EEMD) is employed todecompose the signal into a set of IMFs. A new sensitive IMF selection methodology is proposed where IMFs are clustered into twogroups of sensitive and redundant (not-so-sensitive) IMFs. Using the selected IMFs a probability distribution of their energies isevaluated. Presence of any kind of defect in a rolling element bearing is expected to alter the probability distribution. Jensen Rényidivergence (JRD) measures and quantifies the deviation between probability distributions and is used here as an indicator of changeof bearing condition. The presence of outliers in the trended JRD parameter is detected and removed with the help of an algorithmbased on Chebyshev's inequality. Finally a Confidence value (CV) which will act as a generalized quantification index to assesscurrent health state of the bearing is proposed.

The paper is organised as follows. Section 2 introduces the components of the proposed methodology based on EEMD, aprocedure for selecting the sensitive IMFs, Rényi entropy, Jensen Rényi divergence, Chebyshev's inequality and fault classificationmethodology. Section 3 explains the proposed methodology. Section 4 discusses verification of the methodology as applied onsimulated vibration signals and experimental data. Experimental data consists of seeded defect data measured on an industrial testsetup and run-to-failure bearing life data sourced from Prognostics Centre of Excellence through prognostic data repositorycontributed by Intelligent Maintenance System (IMS), University of Cincinnati [27].

2. Degradation assessment framework

The proposed methodology for bearing degradation assessment is subdivided into two broad parts: 1. Monitoring the bearinghealth and 2. Fault identification. The subcomponents of these two parts are summarized in the flowchart given in Fig. 1.

Monitoring the bearing health uses an integral approach that uses EEMD for IMF generation followed by an automatic selectionof sensitive IMFs. The EEMD will help to achieve higher degree of damage detection and particularly enhance the fault typeidentification when used for degradation assessment of rolling element bearings. The sensitive IMF selection methodology selectsIMFs those do not include low frequency information typically spanning first few harmonics of the characteristic defect frequenciesof the bearing, making degradation assessment largely independent of the geometric parameters of the bearing as well as lower orderharmonics and shaft rotational frequency. This can make the divergence based feature broadly immune to the effects of commonrotor faults (such as rotor unbalance) and to reasonable variations in load and speed. Using the selected IMFs, the JRD is evaluatedwhich will act as an indicator of change in bearing health. Calculation of the JRD parameter is based on the probability distributionsof the IMF energies generated by EEMD.

As long as the monitoring process does not indicate change in bearing health condition, the JRD parameter is used to monitor theoverall condition of bearings. However as and when the change in health condition is detected, detailed fault identification processtakes over. The Fault identification part is further subdivided into fault detection and fault classification (see Fig. 1). For faultdetection, a methodology based on Chebyshev's inequality is implemented for detecting any deviation in health of the bearing.Chebyshev's inequality based criteria is used to identify outliers as well as change in state of health. The methodology may help toidentify the probable location in time at which defect initiation would have taken place. If presence of a defect type is recognized atany of the points found by Chebyshev's inequality, that point will be declared as defect initiation point.

In the current study, the sensitive IMF cluster (a set of sensitive IMFs) will not only be used for degradation assessment but alsoused further for fault classification. Envelope spectrum of an automatically selected appropriate IMF will be evaluated for faultclassification. Two new indices extracted from the envelope spectrum are proposed, which will aid in accurate fault typeidentification.

Finally, a quantification index that helps in assessing working health state of the bearing on a common platform (i.e. as aparticular value of condition monitoring parameter for one bearing for a given defect severity/state may correspond to a differentstate for another bearing,). A general valued quantification index will provide a valuable input to adjust the maintenance scheduleand minimize downtime.

The following sections briefly outlines the theoretical background of various processes involved in the method.

2.1. Monitoring bearing health

As shown in Fig. 1, the bearing condition is monitored through JRD parameter applied on the IMFs extracted through theprocess of EEMD. This section discusses in brief the following processes a) Ensemble Empirical Mode Decomposition, b) Selection ofsensitive IMFs and c) Jensen-Rényi Divergence and Rényi entropy.

2.1.1. Ensemble Empirical Mode Decomposition (EEMD)EMD is a powerful time-frequency domain analysis technique to decompose a nonlinear and non-stationary time series into a set

of orthogonal components named as intrinsic mode functions (IMFs) [28]. EMD is self-adaptive in nature, meaning that it does notuse any predefined basis function to process the signal and rather constructs a basis directly on the information contained in thesignal. EMD has a problem of mode mixing, which is alleviated through a process of ensemble empirical mode decomposition(EEMD) [29]. EEMD is a noise-assisted data analysis method and by adding finite white noise to the signal, the EEMD method caneliminate the problem of mode mixing automatically to improve EMD. The principle of the EEMD algorithm is the following: a whitenoise signal consists of components of different frequency scales. When this uniformly distributed white noise of constant standarddeviation is added to the signal under consideration, components in different scales of original signal will get projected onto proper

scales of reference. The white noise will make the different scale signals reside in the corresponding IMFs. The EMD thereforeproduces very noisy decomposition results for this combined signal. Therefore a large number of trials need to be carried out for theentire process, where every trial will produce noisy decompositions but the noise in every trial will be different. An ensemble of thetrials will therefore decrease or completely cancel out the effects of noise. This is so because a collection of white noise signals willcancel each other out in an ensemble mean; therefore, only the perfect signal will survive and persist in the final noise-added signalensemble mean. In the EEMD process, if the amplitude of the added noise is too small relative to the original signal, the noise maynot affect the extrema that the EMD method uses for extraction process. As a result, no effect on mode mixing prevention can beachieved [30]. On the other hand, if the amplitude of the added noise is too large, it would result in a large number of redundantIMFs. In general when the data is dominated by high-frequency signals, the noise amplitude may be smaller; and when the data isdominated by low-frequency signals, the noise amplitude may be increased [31]. An amplitude of about 0.2 times the standarddeviation of that of the data may suffice in most situations (Wu and Hang [29]) and the same has been used in this work.

The original signal x(t) is decomposed into n-IMFs using EEMD as follows:

∑x t c t r t( ) = ( ) + ( )i

i n=1 (1)

where x t( ) is the original time series,r t( )n is the residual function and c t( )i are the IMFs of different frequency content ranging fromhigh to low.

EEMD decomposes a signal on the basis of its frequency content and variation [32]. Therefore the decomposed IMFs havedifferent energy due to different frequency content in them. Under the operating life of a bearing as it degrades, the distribution ofenergy content of the acquired signal across the frequency range changes. The energies of different IMFs can characterise the signal.The energies of ith IMF is as follows:

∫E c dt= (i = 1, 2 … ….N)i i−∞

where N are the total number of data points in the signal.These evaluated energies can be converted into a set of probability distribution as follows:

∑ ∑p EE

E E p= , where = ⇒ = 1ii

i=1 =1 (3)

where pi is the percent of the energy of ith IMF (ci(t)) in the total signal energy E or probability of energy Ei in the total signal energyE, for one particular signal. For a new acquired signal from the given bearing a different set of probabilities may be present. It hasbeen observed from the past measured data [33] that the energy distribution changes as the bearing degrades over time. The changein probability distribution could be used to monitor damage progression. The divergence of the probability distribution is computedusing JRD that is discussed later in this section.

2.1.2. Selection of sensitive IMFsAfter performing EEMD on a signal, a series of IMFs are obtained. Most of the studies conducted so far ignored systematic

selection of most effective IMFs for bearing diagnosis. Only a selected few IMFs are expected to contain the bearing fault relatedinformation, and the remaining IMFs may be excluded in the degradation analysis. To improve the sensitivity of the diagnosisparameter which in our case is derived out of probability distribution, it is important that we select the useful IMFs. The eliminationof redundant IMFs from the probability distribution can make bearing degradation assessment parameter relatively insensitive tooperating conditions.

In this paper a new method for the selection of IMFs is proposed, which divides the IMFs into clusters of sensitive and not sosensitive IMFs. The method for selecting sensitive IMFs is as follows:

• Calculate the Pearson's correlation coefficient ψn (n=1, 2…N) between the nth IMF of the signal x(t) and the signal x(t), where Nis the total number of IMFs of the signal.

• Calculate the sensitivity index βn of the IMFs using the Min-Max Normalization technique where the [min, max] limits are set to[0,1]. Hence the IMF with maximum correlation value will be normalized to a value of 1 and the IMF with the least correlation isnormalized to a value of 0. The sensitivity index βn is thus:

βψ ψ

ψ ψ=

− min( )max( ) − min( )n

n⎛⎝⎜

⎞⎠⎟ (4)

• Rank the sensitivity index of the IMFs in descending order.

• The relative change in the sensitivity index is evaluated.

• A significant relative change in sensitivity index is used to identify the threshold for selection of sensitive IMFs. Based on thisthreshold, the IMFs are grouped in “sensitive” and “not sensitive” clusters.

The EMD decomposition generates some redundant IMFs (residuals or trends) along with IMF's containing useful information.Only first 10 IMFs from the decomposition are considered in this study as the remaining IMFs are typically residual or trends and do

not contain bearing related fault information. Among the considered IMFs, selection procedure of sensitive IMFs is based on thePearson coefficient, which is used to measure the correlation between the original signal and the individual IMFs. In bearings,whenever a rolling element passes over a localized defect it generates periodic impulses, which often excites one or more resonancemodes of the bearing. Frequencies of these resonant modes are very high in comparison to the characteristic bearing defectfrequencies and in general vibration energy of these resonant frequencies dominates the signal. In the IMF decomposition processthe IMF with higher frequency content contains these resonant frequencies. These IMFs have high correlation coefficient values withthe original signal x(t). On the other hand the bearing fault characteristic frequencies are very low and are present in the lowfrequency IMF and mixed with shaft frequency and its harmonics. These IMFs may have lower correlation with the original signalx(t). Hence, for the lower IMFs that contain the lower order harmonics not related to fault, the correlation value drops significantly.The value of the Pearson's coefficient is high for IMFs having higher fault information (resonance excited by impulses) and decreaseswith the increasing IMF number, due to the lack of fault information in those IMFs.

In the proposed approach, the Pearson's coefficient values are normalized in a range of 0–1 and the normalized coefficients aretermed as sensitivity indices, with 1 indicating maximum correlation and 0 indicating least correlation. The relative change in thesensitivity indices is β β β( − )/reference , where βreference=1, the maximum normalized Pearson Coefficient. The relative change is used toselect the IMF threshold criteria for partitioning the IMFs in sensitive and not-so-sensitive groups. The cluster of sensitive IMFs isused to evaluate the probability distribution to ascertain bearing damage.

2.1.3. Jensen-Rényi Divergence and Rényi entropyIn recent years, Rényi entropy of a time frequency distribution has been used for estimating the content of information in a signal

[34]. Tao et al. [35] proposed a new time domain index based on Rényi entropy for condition monitoring of rolling element bearingsand established that it is better in comparison with kurtosis and Honarvar third moment trend as the defect progresses. Boškoskiand Juričić [25] proposed a novel approach for the diagnosis of gearboxes using information indices based on the Renyi entropyderived from coefficients of the wavelet packet transform of measured vibration records. Boškoski et.al [26] used Rényi entropybased features for prognosis of rolling element bearings.

Let k N∈ and X x x x= { , .... }k1 2 be a finite set with a probability distribution p p p p= ( , .... )k1 2 i.e. p∑ = 1jk

j=1 and p P x= ( ) ≥ 0j j

where P (.) denotes the probability. Rényi entropy is defined as [34,36]:

∑R pα

p α α( ) = 11 −

log( ), > 0 and ≠ 1αj

=1 (5)

In the case of distributions where we have small randomness, most of the probability values will be approximately zero and veryfew values will be close to one. In this case the overall contribution will be low (R p( ) → 0α ), because the argument of the logarithmtends to one. On the other hand in case of distributions where the randomness is large, probabilities will be distributed uniformlyp j N→ , ∀ = 1, 2....j N

1 . Thus the entropy value will be higher in this case, because the argument of the logarithm tends to N α1− ,therefore R p N( ) → logα . Hence the main idea is that the Rényi entropy yields larger values when all pj's are almost equal to eachother, and yields smaller values when only a few pj's are large and most of the others are very small in comparison.

The parameter α in Rényi entropy can be used to make it more or less sensitive to particular segments of the probabilitydistributions. The exponent α helps to provide flexibility by highlighting the values closer to the edges of the probability distribution[37]. α→0 causes the Rényi entropy to become highly sensitive to changes in the tails of the distribution and for α→1, it reduces toShannon entropy and hence the Rényi entropy becomes more sensitive in the regions where the bulk of the probability mass islocated [25,26].

Some of the past studies have established that keeping α=0.5 gives ideal results [25,26,37,38]. Hero et al. [37] suggested anoptimal choice of α=0.5 for the case of Jensen Rényi divergence. Markel et al. [38] used α=0.5 for a novel multimodalitysegmentation algorithm using the Jensen-Rényi divergence. Later Boškoski et al. [25,26] have implemented Rényi entropy and JRDbased features for machinery fault diagnosis and achieved significant results by choosing α=0.5.

Jensen-Rényi divergence DJRαω between n probability distributions p p p p= ( , .... )n1 2 with the corresponding weights π π π, ... . n1 2

Fig. 2. (a) 10 Gaussian distributions having constant mean and different variances. (b) Jensen-Rényi divergence for the given Gaussian distributions.

(such that π∑ = 1in

i=1 and π0 ≤ ≤ 1i ) is defined as [39]:

∑ ∑D p p p R π p π R p[ , .... ] = − ( )JR n αi

i α i1 2=1 =1

⎛⎝⎜⎜

⎞⎠⎟⎟

where R p( )α is the Rényi entropy.Key mathematical properties of DJRα

ω are [40]:

1. Jensen inequality implies that: D p p p[ , .... ] ≥ 0JR n1 2αω with D p p p[ , .... ] = 0JR n1 2α

ω if p p p= = ....= )n1 22. DJRα

ω is symmetric in its arguments p p p, ... . n1 2 , i.e. DJRαω is invariant for any permutation of its arguments p p p, ... . n1 2 .

One of the major features of JRD is that different weights can be assigned to the involved probability distributions according totheir importance. This allows flexibility to adjust the measurement sensitivity of the probability densities according to the concernedproblem at hand. Before implementing the methodology, through some simulations, the authors noted that altering the weights ofthe two dimensional JRD has no significant effect on the qualitative nature of results. The nonuniform weights only alter the absolutevalue of JRD. The case of uniform weights resulted in better sensitivity for any change in defect severity. In some previousinvestigations, uniform weights have been selected while implementing the JRD. Markel et al. [38] used uniform weights for a novelmultimodality segmentation algorithm using the JRD. He et al. [41] established the optimality of the uniform weights for imageregistration in the context of the JRD. Dolenc et al. [42] established that with the selection of uniform weights, JRD reachesmaximum value. In the present work α=0.5 and π1=π2=0.5 are considered. Another added advantage of JRD is that it is anonparametric approach that makes no assumptions about the underlying distribution [38].

A simple simulation example in Fig. 2 demonstrates the concept of JRD. In Fig. 2(a) 10 Gaussian distribution curves with samemean and different variance values have been stacked together. Fig. 2(a) simulates abrupt change in probability distributions for 10distributions. Taking the first Gaussian distribution (i=1) as the base distribution, JRD is evaluated for all the distributions (i=1, 2,3…10). It can be seen in Fig. 2(b) that as the 1st PDF is similar to itself the divergence value is zero. The divergence value is also zerofor the last distribution as it is identical to the base distribution (i=1). However as the distribution number 3, 4, etc. are significantlydifferent from that of the base distribution (i=1), the divergence value is higher and proportional to the variation with respect to thebase distribution.

In order to assess the degradation of the bearing, two probability distributions are considered. The first probability distributioncorresponds to a healthy bearing (pHealty) calculated based on the vibration data collected on new, healthy bearing. The seconddistribution is calculated based on the new signals acquired from the bearing (pNew). Initially, when the bearing condition is healthy,no significant difference between the two distributions (pHealthy and pNew) is expected and the divergence value will be close to zero.As the condition of the bearing starts to deteriorate, the JRD between the two distributions (pHealthy, pNew) is expected to increaseand can be used to monitor the health.

2.2. Fault identification

The JRD parameter identifies a change in health condition of the bearing by making use a methodology based on Chebyshev'sinequality. After a change is detected fault classification is carried out. This section discusses in brief the following processes a)Chebyshev's Inequality and b) Fault classification.

2.2.1. Chebyshev's inequalityLet X be a random variable from a data with a finite mean μ and variance σ. If this data set is normally distributed then it will

have fixed values for the spread of the data relative to the number of standard deviations from the mean (i.e. 68.2%, 95.4% and99.73% within the first, second and third standard deviation from the mean respectively). But if the assumption of normaldistribution is not valid, then the above values will be unknown. Chebyshev's inequality helps to provide insight into the segment ofdata that lies within ‘K’ standard deviations from the mean for any data. Therefore it estimates the percentage of the data clusteredaround the mean for any probability distribution. Based on Chebyshev's inequality, no more than 1/K2 data points of a distribution'svalues lie beyond ‘K’ standard deviations away from the mean [43]. It can be expressed mathematically in the following form:

P x μ K σK

K{ − ≥ } ≤ for any > 02

where P(.) represents the probability of the event. As σ will always be positive, therefore the above equation can be rearranged as

P x μσ

− ≥ ≤ 12

⎧⎨⎩⎫⎬⎭ (8)

The expression x μσ

( − ) is known as Z statistic and is a standard statistical term. Therefore the previous expression can be rewrittenas

P Z KK

{ ≥ } ≤ 12 (9)

In the present work K is taken as 2, which means that the probability of any data point for any probability distribution fallingoutside of the 2σ distance from the mean is ½2. Thus unless there is actually some physical change in the bearing condition, theparameter ‘x’ changes significantly, enough to shift beyond the 2σ limit and outside of the present distribution of the data. The valueof Z-Statistics thus indicates deviation of current value of the parameter from its existing distribution. However, in practicalmeasured data such fresh data value or parameter can be a chance data rather than a genuine shift in the condition of the bearing.Hence before processing the current data further a method of ascertaining if this data set is an outlier is implemented. This involveschecking the Z-statistic for ‘Q’ consecutive data points. If ‘Q’ consecutive Z-statistic values are greater than 2, then it indicates achange in health state of the bearing. Therefore to detect a genuine change in the health state of a bearing the Z-statistic should bemore than 2 for ‘Q’ consecutive data points (in the present work, ‘Q’ is taken as 5). If not, these points are treated as outliers. Theoutlier data point is normalized the mean of previous ‘M’ data points (in the present work, ‘M’ is taken as 5).

The values of K, M and Q depend on factors such as noise present in the signals, sensitivity of sensors and the frequency of dataacquisition interval. If a large value of ‘K’ is considered then chances are that outlier data points may fall within the specified Z-statistic value and will not be removed. On the other hand if a very small/strict value for ‘K’ is considered, though noise in the trendwill be suppressed but there will be false detection of change in health states.

If a very small value of ‘Q’ is chosen then many data points which are actually outliers will be misclassified as a change of stateand will not be removed. On the other hand if the value of ‘Q’ is chosen to be large then though error in declaring a change of statewill be low, but small changes in the health state of a bearing will not be detected early.

2.2.2. Fault classificationIt is critical to assess the damage severity of rolling element bearings and it is equally important to identify the defect type in

order to investigate the cause of bearing failure. A concept of ‘α value’ and Probable Fault Index (PFI) is proposed here.It is well known that the defect frequencies modulate structural resonance frequency. Demodulating the structural vibration

signal in the high frequency resonance region, interference of the background noise and other low frequency components can beeliminated [44]. In the conventional demodulation technique, the signal to be processed first needs to be band-pass filtered toenhance the bearing-fault frequency. The central frequency of the band pass filter should match the structural resonance frequencyin order to get appropriate envelope signal. Therefore; the choice of central frequency greatly influences the analysis results [45,46].Some studies combined EMD with envelope analysis to extract the modulation characteristics of roller bearing fault vibration signals[46–51]. However they invariably extracted information based on first or second IMF. However, for signals with low SNR, the choiceof first /second IMF may provide incorrect diagnosis parameter. For an automated diagnosis a statistical index based selection is abetter approach to select proper IMF. Yang et al. [46] used the amplitude ratio of defect frequencies as a fault feature for automaticfault type identification. With this approach it may be difficult to identify the presence of multiple faults. Application of themethodology in [46] for automatic fault identification requires prior information for every defect type to be trained with the SupportVector machine (SVM) model. Thus a large number of experiments need to be carried out to gather the required amplitude ratios.Tsao et al. [49,50] identified the appropriate resonant frequency band by carrying out a sweep excitation through running up a rotarymachine. However, it may not be always possible to carry out a swept sine excitation for every set-up. Fernandez et al. [51] selectedthe appropriate resonant band using a sensitivity test that relies on input from a trained SVM. But the SVM model depends on theparameters like bearing type, operating conditions etc. So a change in any of these parameters will not be accommodated by thetrained SVM model, and it may affect the accuracy of selection of appropriate IMF. Moreover the model will depend on the featuresthat are used to train the model i.e. if parameters which are not sensitive to the defect are included to train the model, they maydecrease the accuracy of the model.

In light of those shortcomings, a new automatic fault type identification methodology based on the envelope of the suitable IMFobtained from EEMD is proposed here.

Apply Hilbert transform H[x(t)] to the IMFs of signal x(t):

∫H c tπ

c τt τ

dτ[ ( )] = 1 ( )−ii

where H[.] denotes Hilbert transform operation. The analytic signal z(t) can thus be expressed as -:

z t c t iH c t( ) = ( ) + [ ( )]i i (11)

Hence, envelope of an IMF cj(t) can be expressed as

a t c t H c t( ) = ( ) + [ ( )]i i2 2 (12)

The proposed method for fault identification is described as follows:

• Decompose the vibration signal using EEMD into a number of IMF components. As discussed earlier in Section 2.1.1 pre-processing the signal with noise in the EEMD process overcomes the mode mixing problem and increases the decompositionprecision of vibration signals

• Evaluate the sensitivity indices for the evaluated IMFs as per the methodology discussed in Section 2.1.2. The IMF selectionmethodology highlighted that the selected IMF is independent of the operating conditions, level of noise, bearing characteristicsand does not require any prior knowledge for training purposes. Considering the IMFs of the sensitive IMF cluster, evaluate the

kurtosis of the IMFs of this cluster. The IMF with the maximum kurtosis value is expected to contain the maximum faultinformation.

• Find frequency spectrum of the envelope of the selected IMF.

• In order to extract the fault features from the Fourier spectrum, a Probable Fault Index for a given defect is defined as:

PFIA f

( )( )i

Fault Signal

Healthy Signal (13)

where i=ORDF/IRDF/BDF and A indicates mean value of amplitude of fi based on healthy bearing vibration spectrum. Thus theprobable fault index for outer race defect can be calculated using amplitude A f( )ORDF Fault Signal extracted from the envelope spectrumof selected IMF corresponding to outer race defect frequency and mean of the amplitudes at this frequency extracted from healthyvibration database, A f( )ORDF Healhy Signal as follows:

PFIA f

( )ORDFORDF Fault Signal

ORDF Healthy Signal (14)

In presence of a defect, the PFIBPFO ratios are expected to be very high. The PFI for an inner race and ball defect are also definedsimilarly.

In practice, the mathematically evaluated characteristic defect frequencies may vary slightly from the experimental value due toslipping of rolling elements or variation in the operating speed. Hence a bandwidth is assumed around the mathematical values ofthe characteristic defect frequencies and the value of maximum amplitude is selected from the given bandwidth.

• In case of a noisy data with strong noise floor in the spectrum the PFI alone may not give reliable judgement. This is so because ifthere is an overall increase in the noise floor and even if there is no defect, the PFI value will be high. Therefore an additionalcriteria to examine presence of faults is proposed:

α valueA f

mean A f A f=

[ ( )]( ( − 10), ( + 10))

i i measured on fault signal (15)

Thus the amplitude is now normalized by mean of the amplitudes in the frequency bandwidth of 20 Hz around the defectfrequency. For this study the threshold for α is set to 2.5. It implies that if the mean value of the noise floor around the defectfrequency is less than 40% of the amplitude of the defect frequency amplitude, then it verifies the presence of an actual defect. Thechosen values of bandwidth (20 Hz) and threshold (40%) are user dependent and can be changed according to the problem at hand.

• In order to automate the fault detection process, it is rational to assume a threshold (PFI > 2) to conclude the presence of theactual defect type. It will not only confirm the presence of a fault but will also eliminate the case of the false alarm. The advantageof this scheme is that it not only applies to single fault but is also suitable for multiple fault cases.

As an example, consider a vibration signal of an outer race defect from a rolling element bearing as shown in Fig. 3(a). Thefrequency spectrum in Fig. 3(b) does show the characteristic outer race defect frequency (149 Hz), however the energy associatedwith the frequency is low and comparable with other frequencies in the range.

The vibration signal is now decomposed using EEMD and the corresponding IMFs are shown in Fig. 4. The first five IMFs formthe sensitive IMF cluster (based on the method discussed in Section 2.1.2). The third IMF is found to have the highest kurtosis andhence is considered for further analysis. This highlights the fact that in case of low defect severity coupled with low SNR signals (low

Fig. 3. (a) Time domain vibration signal of an outer race defect, (b) Frequency spectrum of the outer race defect.

signal to noise ratio), it may not be necessary that the first IMF would contain the maximum fault information. Hence IMF 3 isselected for envelope analysis and the corresponding envelope spectrum is shown in Fig. 5(b). Compared to the spectra in Fig. 3(b),the envelope spectra in Fig. 5(b) shows better clarity on fault information.

3. Proposed methodology

The flowchart explaining the complete methodology is given in Fig. 6(a) and (b). Initially at the start of the acquisition process,EEMD will be applied on the raw time domain vibration data to decompose the signal into a set of IMFs. Thereafter, sensitive IMFcluster will be identified, which will be used to construct the probability distribution. For any new acquired signal, Jensen Rényidivergence is evaluated by calculating the distance between the probability distribution of healthy and the new signal. In practicalsituations, while acquiring data over the entire lifespan of the bearing, sharp rises (outliers) and random fluctuations can be seen inthe values of the condition monitoring parameter. This poses challenge in identification of the change in health state of a bearing. Inorder to assess the true current status, it is important to benchmark the healthy working state of the bearing. Therefore a referencedata set is obtained from the initial operation of the bearing after commissioning of the fresh bearing. The mean and standarddeviation of this reference data set is evaluated, against which the Z value for any subsequent measured data is calculated andcompared against a predefined threshold value (K value).

If the Z-statistic value is less than the predefined threshold the acquired data point belongs to the existing health condition stage.For this case the reference data set will be updated with the addition of the new acquired dataset.

If the Z-statistic value is more than the predefined threshold, the acquired data point is either an outlier or it is no longer a part ofthe chosen reference dataset depending upon the trend of the previous 5 data points. The criteria of 5 consecutive points is set toaddress the issue of false alarm of state change in the presence of noise and outliers.

Fig. 4. EEMD decomposition results of a bearing vibration signal with an outer race defect.

Fig. 5. Envelope spectrum for the considered outer race defect vibration signal (a) IMF 1 (b) IMF 3.

a) If the Z value is more than the predefined value for five consecutive data points, a change in damage state is declared. In this casea new reference data set will be generated consisting of these 5 data points.

b) If the Z value is more than the predefined value but not for 5 consecutive points, then these points are declared as outliers and arenormalized by the average of the JRD value of the previous 5 data points.

After this step, the trended JRD plot will be free of outliers. Abrupt change in Z-value indicates likely event location where achange of health state is identified. These time locations become probable moments where initiation of defect would have takenplace. ‘α value’ and PFI's are evaluated at these points and checked if any of the αouter, αinner, and αball exceed the set threshold(αthreshold=2.5). The values of αi (where i=outer/inner/ball) beyond the threshold indicates the presence of a defect. PFI's areevaluated only when the ‘α value’ exceeds the threshold and again checked if any of them (PFIouter, PFIinner or PFIball) lie beyond theset threshold (2). To minimize the issue of false alarm for bearing degradation, PFI values of ‘P’ consecutive data points need toexceed the threshold limit. If the value of ‘P’ is chosen to be very large the error of raising a false alarm will be reduced but theknowledge of initiation of bearing deterioration will be delayed. On the other hand selecting a small value of ‘P’may increase chancesof false alarm. Suppose the bearing vibration data is acquired after every 10 min, so one point on the trended condition monitoringparameter plot corresponds to 10 min. Therefore the assumption of considering initiation of degradation in bearing when 5consecutive points (50 min) cross the threshold gives a detection accuracy band (resolution) of 50 min, which for a bearing life spanof even several thousand hours, is justified. The selection of ‘P’ value will be influenced by factors like tolerance for false alarm,frequency of data acquisition intervals and sensitivity of the measurement system.

After application of Z-statistics the JRD plot is used for degradation monitoring. Although the value of condition monitoringparameter aids in quantifying degradation, the vibration signatures of same bearing type and size can exhibit variation while

Fig. 6. (a) Flowchart explaining the proposed bearing health monitoring methodology along with fault detection methodology. (b) Flowchart explaining the proposedfault classification methodology.

Table 1Different stages of bearing health.

Stage Type CV standard

Stage I Healthy 0.8 < CV < 1Stage II Slight Degradation 0.5 < CV < 0.8Stage III Medium degradation 0.3 < CV < 0.5Stage IV Severe degradation 0 < CV < 0.3

degrading even under same operating conditions. Therefore a parameter value of a condition monitoring parameter in one bearingmay correspond to a different health state for another bearing. Hence a standardized index to quantify degradation value of differentbearings on a common platform is needed. To monitor the level of health degradation, a confidence value (CV), which ranges fromzero and unity, is proposed here, with CV=1 indicating a perfect health condition and CV=0 indicating failure. The idea behindevaluating a CV is to standardize the quantification of bearing degradation assessment.

As the basic requirement from CV is to be close to 0 for fully deteriorated bearing and should be 1 for healthy states, JRD valueobtained after Z-statistics methodology needs to be normalized. Traditional approach is to use the Min-Max normalizationtechnique, but evaluation of CV by this technique is not possible as the maximum value of the JRD (at failure) may not be availablebeforehand. It is well established that the degradation signal behavior of rolling element bearings can be approximated by anexponential functional [7,52,53]. The degradation behavior of rolling element bearings mimics an exponential decay. Therefore thefollowing normalization function based on Sigmoid function is proposed:

= 2 − 21 + a JRD− ( ) (16)

where ‘a’ is a scaling parameter which will help in making the CV of a failed bearing close to 0. This scaling parameter will beevaluated from the JRD values of the healthy state of the bearing using:

a CV CVMean Healthy

= − ln( /2 − )( JRD values)

initial initial

where CVinitial for the healthy state can be assumed to be 0.95–0.99. The CV at any newly acquired data can be calculated from thefollowing steps:

Fig. 7. The load distribution of a bearing (b) Effect of unbalance for an outer race defect (c) Effect of unbalance for an inner race defect.

1. Evaluate the outlier free trend of the JRD.2. Find the cumulative of the above JRD values.3. Evaluate the scaling parameter for the particular bearing using the mean value of the divergence for the healthy state.4. The cumulative JRD value can be converted into CV using Eq. (16).

Bearing health status can be categorised under four different stages given in Table 1.In Stage I, the bearing operates in healthy state and therefore the CV starts at a high value (0.95–0.99). Under normal working

conditions the bearing operates in this stage, during most of its life. In Stage II, slight degradation occurs due to wear and tear andthe rate of decrease of the CV value is swift in comparison to Stage I but still no damage initiation takes place. Once the CV value goesbelow 0.5 the rate of decrease of the CV increases, and the bearing enters Stage III. In this stage the defect type is prominent and canbe identified. The maintenance personnel may need to plan for replacement of the bearing. Finally as the CV value goes beyond 0.3the bearing is under severe degradation and is close to the end of its life. To avoid secondary damage to the machine, the bearingneeds to be replaced.

4. Fault diagnosis based on simulated signal

The proposed approach is tested on simulated vibration signal using a mathematical model. In this section, vibration signal of abearing under healthy state, bearing with outer race defect and bearing with inner race defect are simulated. The modelling includesmost of the practical issues encountered in the measured data such as rotor unbalance, radial load variation, speed variation andsignal noise. The simulations aim to test the following-:

a) The robustness of the proposed EEMD energy distribution based JRD measure under the effects of variable operating conditions.The simulation study will ensure that the JRD parameter works for all conditions (unbalance, load variations and speedfluctuations) and for any defect type.

b) The fault classification capability of the proposed EEMD based envelope spectrum will be examined under the effect of variableoperating conditions along with high level of noise.

Simulations will test the broad applicability of proposed method and ensure that it is independent of the effects of operatingconditions.

For baseline data, vibration signals generated by healthy bearings, predominantly contain shaft rotational frequency and itsharmonics contaminated with white Gaussian noise, and can be expressed as:

∑x t A πmf t n t( ) = cos(2 ) + ( )Hm

m s=1 (18)

where m is the number of shaft rotation harmonics, Am is the amplitude of the mth harmonic, fs is the shaft rotation frequency andn(t) is random noise.

4.1. Modelling of a single point defect [54]

Modelling of generation of vibration signal from a bearing with localized defect is discussed in the past [54] and is briefly outlinedhere for the sake of completeness. The purpose is to highlight how practical signal are simulated so that the bearing degradationassessment can be tested on such simulated signal before verifying it on experimental data.

For a constant shaft speed, impulses generated through the interaction of rolling elements on the race with localized point defectby a single point defect may be expressed as [54]:

∑d t d δ t kT( ) = ( − )ok

where d(t) is the impulse function, δ(t) is the Dirac delta function, do is the magnitude of the impulse, Tdo is the reciprocal ofcorresponding defect frequency and k represents a positive integer. In order to account for the variation in the speed of rotation, Tdois modified as [54]:

T kT R r kd t d δ t kT R r k

= ± ( , )( ) = ∑ ( − ∓ ( , ))

o k d=0∞

R r k r T( , ) = * d (21)

represents time deviation from the expected period of repetition of kth impulse due to the possible variation in the shaft speed orslippage of rolling elements. For this study the random variation of speed is assumed to be within 10% of Td (r=0.1).

For a bearing, the load distribution on various rolling elements as a function of time is modelled using the Stribeck equation [44]as follows-:

q t q t θ for θ θ( ) = ( )[1 − ( )(1 − cos )] <0 elsewhere

o ε12

32 max

⎪⎪

⎧⎨⎩

⎫⎬⎭ (22)

where qo(t) is the applied radial load on the shaft; ε represents the load distribution factor, and θmax is the angle limiting the loadzone. The load distribution of a rolling element bearing under radial load is shown in Fig. 7(a). In practice, due to a variety of reasonsthe radial load qo(t) may vary with time and the variation may be periodic or random. In order to introduce the effects of shaft loadvariation the applied load is defined as following:

q t q q t( ) = + ( )o mean v (23)

where qv is the random variation of the load within 10% of the mean radial load qmean.In general, there is always some inherent unbalance in the rotor bearing system. For the case of an outer race defect, the applied

radial load acting on the defect remains fixed whereas the unbalance load will keep on changing with rotation (Fig. 7(b)). Thereforefor an outer race defect, the load Eq. (23) is modified as follows-:

q t q t q π f t ϕ( ) = ( ) + cos (2 + )outer o unbalance shaft outer (24)

For an inner race defect the phase of unbalance will remain constant relative to the defect location (Fig. 7(c)). Therefore theunbalance will contribute as a constant additional increase in the load. The load Eq. (23) for an inner race defect is modified asfollows [54]-:

q t q t θ q ϕ for θ θq ϕ elsewhere

( ) = ( )[1 − ( )(1 − cos )] + cos <cos

innero ε unbalance inner

unbalance inner

32 max

⎧⎨⎪⎩⎪

⎫⎬⎪⎭⎪ (25)

Based on ISO 1940-1 (Mechanical vibration Balance quality requirements for rotors in a constant (rigid) state Part 1:Specification and verification of balance tolerances) for general class balance grade G6.3 and shaft speed of 1400 RPM, thepermissible unbalance force (qunbalance) is close to 10% of the mean radial load qmean and the same is considered in thesimulations.

The bearing and support structure responds to the impulse generated from the interaction of rolling elements with the defect onthe races/balls. If the response to unit impulse is given by h t τ( − ), then the impulse represented by d(t) with applied radial load onthe bearing given by q(t), yields the response of the bearing as sensed by a sensor as:

∫x t d τ q τ h t τ dτ n t( ) = { ( ) ( )} ( − ) + ( ) (26)

where Noise(t) is the white Gaussian noise added to the simulated signal. The assumed parameters for the simulated accelerationsignal are listed in Table 2.

4.2. Application of the method for outer race defect

Initially time domain vibration signal is obtained from Eq. (26) considering no speed variation, no load variation, no noise, andwithout any unbalance. Fig. 8(a) and (b) shows the time and frequency domain representation respectively, the latter highlights theouter race defect frequency (fouter) and its higher harmonics.

Fig. 8(c-d) show the results for simulations considering unbalance and variation in shaft load. In Fig. 8(c) both variation in shaftload and unbalance affect the amplitude of the impulse and not the time of impact. The amplitude modulation of the peaks of theimpulses can be observed in Fig. 8(c). The corresponding FFT of the time domain signal is depicted in Fig. 8(d). Harmonics of outerrace defect frequency (fouter) can again be seen in the spectrum along with very weak sidebands of fshaft.

Fig. 8(e-f) show a simulated vibration signal for an outer race defect considering variation in shaft speed and presence of rotorunbalance. The time gap between consecutive impulses varies (Fig. 8(e)) due to the variation in the rotor speed. The amplitude of theimpulses are modulated due to the rotating unbalance force. The frequency spectrum of the signal is shown in Fig. 8(f). Due tovariation in shaft speed there is smearing of energy with increasing noise floor and the low frequency region (Fig. 8(f)) shows onlythe first two harmonics of the outer race defect frequency with decreasing amplitude.

Next, the simulated signal is mixed with white Gaussian noise so that the signal represents field vibration data. Fig. 8(g-h) show

Table 2Parameters of the simulation study.

Shaft frequency fshaft 23 HzOuter race defect frequency fouter 149 HzInner race defect frequency finner 201 HzResonance frequency of bearing/supporting structure 3.5 kHzSampling rate 10 kHzAngle limiting the load zone θmax 60° (overall load zone 120°)SNR (dB) 7.5 dBqunbalance 10% of the mean radial load qmean

Fig. 8. Simulated vibration data for an outer race defect (a-b) Ideal case (c-d) Unbalance with load variation (e-f) Unbalance with speed variation (g-h) Unbalancewith load variation, speed variation and noise (SNR, 7.5 dB).

simulated vibration signal for an outer race defect considering for the combined effect of the unbalance, radial load variation,variation in the shaft speed and added noise (SNR=7.5 dB). Due to the combination of load/speed fluctuations and noise, thefrequency spectrum is difficult to interpret (Fig. 8(h)) and the outer race defect frequency and its harmonics are not fully noticeable.This signal will be used to investigate the robustness of the proposed JRD measure to the temporal variability in load and speedincluding noise and unbalance effect for an outer race defect.

Table 3 lists down the break-up of the overall vibration signal (65 s data) considered for the simulation study. A total of 13 stateseach of 5 s duration form one case. The simulated 5 s vibration signal (from every state) are split into 1 s long non-overlappingsegments. The parameter do (see Eq. (19)) represents the amplitude level of defect in each state and hence represents defect severity.The parameter ‘V’ represents the variation in load or speed and is considered to vary between 0–10%. In this study for each level ofdefect (do =0.5, 0.6,..etc.), two cases are considered: (a) load variation of 10% (V=10%) with constant speed and (b) speed variationof 10% (V=10%) with constant load. Thus, for load variation case of V=10%, qv(t) in Eq. (23) varies within 10% and for speedvariation case, V=10% represents assigning an appropriate value to r in Eq. (21) so that the value Tdo reflects the 10% speedvariation effect. The two cases of load variation and speed variation are individually tested for both outer and inner race defects.Table 3 thus represents first block of 5 s data representing healthy state of bearing without any defect. The second block of data from6 s to 10 s represents state 2 with defect amplitude of do=0.5 and V=0 (indicating that there is no load variation). Similarly, State 3dataset for 11–15 s represents signal for outer race defect with severity of do=0.5 and load variation of 10%, and so on. Datasetsindicated by states 4 and 5 in table (for duration 16–20 s and 21–25 s respectively) represent similar data as in 2 and 3, except withhigher defect severity (do=0.6 instead of do=0.5). Similar datasets are arranged with increasing defect severity (up to do=1.0), eachwith and without load variation. The foregoing dataset of 0–65 s (referred as Case I) represents a signal for outer race defect withincreasing defect severity and load variation (keeping the speed constant). Similar dataset of 65 s duration is compiled with speedvariation (V=10% representing 10% variation in mean speed), wherein load is maintained constant. This dataset forms the Case II.

Considering an outer race defect signal with load variation (Case I), the individual 1 s signal segments (Table 3) are decomposedusing EEMD analysis to generate the IMFs. For the signal under consideration, with the variation of load the sensitivity indices βmfor defective states do not change significantly. The load variation mainly influences the part of the signal that is decomposed in thelower IMFs, leaving the top IMFs relatively unchanged. Since the lower order IMFs have a lower correlation with the original signal,they continue to lie in the insensitive cluster and does not influence the subsequent signal analysis for defect characterization. Withincreasing level of defect amplitude (from do=0.5 to do=1) the value of the sensitivity indices βm does change marginally, but thisonly alters the sequence of IMFs when sorted in descending order. However the appropriate sensitive IMFs remain the samethroughout the defective signal (from 6 to 65 s data) for the load variation case and no shift of any IMF from sensitive to insensitivecluster is observed. Similarly, for the case of an outer race defect with speed variation (Case II), the sensitive IMFs do not change forthe range of defect amplitudes (do=0.5–1.0) and speed variation (V=0–10%). However, if the defect size is increased substantially, itmay alter the frequency distribution of the signal and the same may influence the choice of sensitive IMFs. However, for earlydetection capability, the present approach offers more robust methodology.

As discussed above, for both load and speed variation cases, the sensitivity indices βm for a simulated outer race defect do notchange significantly to alter the set of sensitive and not-so-sensitive IMF clusters with changes in load/speed. The representativevalues of βm for the case of do=1 and V=10% are reported in Table 4. It may be mentioned that the relative change of normalizedPearson's correlation coefficient values become significantly large from 8th IMF onwards. These corresponding IMFs giving a largerelative change do not form a part of the sensitive IMFs. Based on this relative change, it was found that the set of relevant IMFs

Table 3Structure of the vibration signal for simulation study.

Break-up of the 65 s vibration data

State 1 State 2 State 3 State 4 State 5 State 6 State 7(0–5 s) (6–10 s) (11–15 s) (16–20 s) (21–25 s) (26–30 s) (31–35 s)Healthy do=0.5 do=0.5 do=0.6 do=0.6 do=0.7 do=0.7

V=0% V=10% V=0% V=10% V=0% V=10%

State 8 State 9 State 10 State 11 State 12 State 13(36–40 s) (41–45 s) (46–50 s) (51–55 s) (56–60 s) (61–65 s)do=0.8 do=0.8 do=0.9 do=0.9 do =1 do=1V=0% V=10% V=0% V=10% V=0% V=10%

Table 4Sensitivity index βm of IMFs of simulated outer race defect.

IMF No.

Case 1 2 3 4 5 6 7 8 9 10

CASE I: Load variation 1 0.903 0.769 0.478 0.283 0.188 0.124 0.077 0.028 0CASE II: Speed Variation 1 0.894 0.845 0.444 0.259 0.196 0.134 0.063 0.028 0

corresponds to sensitivity index βm > 0.1. Thus, in the present work the IMFs having sensitivity index more than 0.1 are treated assensitive IMFs. For load variation case the first seven IMFs (βm > 0.1) are sensitive IMFs and for speed variation case also the firstseven IMFs form the sensitive IMFs. It is thus clear that with nominal variations in the load and speed, the sensitive IMFs do notchange. The cluster of selected sensitive IMFs are then used to form the probability distribution. JRD is calculated using the fault-free case as the reference distribution.

In order to demonstrate that the proposed EEMD based JRD parameter is sufficiently robust to variations in operatingconditions, it is compared with energy entropy parameter [22]. The EEMD energy entropy is used for comparison with the JRDvalue. The entropy at healthy bearing condition is more and decreases with defect progression, whereas JRD is approximately zerofor healthy condition and increases as the bearing begins to deteriorate. Hence for comparison purposes the mirror image of theentropy trend about the mean entropy of the healthy condition is used in the study. To highlight the importance of the sensitive IMFselection methodology, JRD is evaluated and compared for three different situations: using only sensitive IMFs as identified by theproposed methodology, fewer number of IMFs (say first 5) and almost all the IMFs.

Fig. 9 shows the comparison between the JRD and energy entropy for Case I for the selected appropriate number of IMFs.Fig. 9(a) depicts the JRD plot and Fig. 9(b) depicts the energy entropy plot. Each data point corresponds to one second segment dataand the first 5 s of data corresponds to healthy bearing. It is found that there is substantial change in the value of both theparameters for all cases after the 5th data point which is indicative of the shift from healthy (State 1) to defective state (State 2). Itmay be noticed in Fig. 9(a) that the amplitude level of defect is same for data between 6 and 15 s. However load variation of 10% isintroduced between 11 and 15 s. JRD shows an increase in value only when there is a change in the defect amplitude (at 16th, 26th,36th, 46th, 56th data points) and is otherwise constant even when 10% change in load is induced. In comparison to the JRD, energyentropy fluctuates substantially for a constant defect amplitude, as shown in Fig. 9(b). In order to gauge the variability in the trend ofboth the parameters in Fig. 9(a,b), standard deviation is used as a measure in this study. For example standard deviation betweendata points 16–25 and 26–35 for JRD is 6.53e-5 and 4.67e-5, whereas the same for energy entropy it is quite high at 4.6e-3 and5.2e-3 respectively. Energy entropy also fails to show an increase in value with change in defect size (from do =0.5 to do =0.6 at 16thdata point and do=0.9 to do=1 at 56th data point) and at many locations low defect amplitude signals have a higher energy entropyvalue in comparison to high defect amplitude signals. For example energy entropy at data point 9 is more than that at data point 16,although defect size at data point 9 is lower. Thus energy entropy as a parameter is not able to generate enough and consistent shiftin its value as defect level changes. In contrast, as revealed in Fig. 9(a) the JRD parameter has exhibited a consistent and appreciableshift in its value with change in defect size while maintaining this difference even in presence of reasonable variations in load. Thisindicates the robustness of JRD parameter to temporal variations of load for the case of an outer race defect.

The effect of selecting a lower number than the appropriate number of IMFs for an outer race defect is demonstrated inFig. 10(a). Variation in JRD (Fig. 10(a)) between data points 6–15, 16–25, 26–35, 36–45, 46–55 and 56–65 has increased when

Fig. 9. (a) JRD and (b) EEMD energy entropy for a simulated outer race defect with load variation (CASE I) for appropriate number of sensitive IMFs.

Fig. 10. JRD plots for a simulated outer race defect with load variation (CASE I) (a) fewer number of IMFs (first 5) and (b) almost all the IMFs.

compared to Fig. 9(a). For example for this case standard deviation between data points 16–25 and 26–35 increases to 1.097e-4 and1.008e-4 respectively, in comparison to their value in Fig. 9(a). JRD also fails to show an increase with change in defect size fromdo=0.5 to do=0.6 at 16th data point. This is so because JRD was unable to reflect the valuable energy contribution that belongs to themissing IMFs.

The effect of selecting a larger number than the appropriate number of IMFs is demonstrated in Fig. 10(b). The last few IMFsobtained through the decomposition of the simulated defective signal consist of bearing fault characteristic frequency mixed withshaft rotational frequency, unbalance, load variation and their harmonics. The energy of these IMFs decreases gradually and hencethe energy probability distribution forms the case with larger randomness (as discussed in Section 2.1.3). For a simulated healthysignal, the lower IMFs consist of only shaft rotational frequency and its harmonics with a very low amplitude. Hence the healthysignal forms a case of lower level of randomness (as discussed in Section 2.1.3).

Therefore selecting a larger number than the appropriate IMFs may give a higher Rényi entropy for a defective signal and a lowerRényi entropy for healthy signal. However, as JRD evaluates the deviation between two distributions, it correctly shows a value closeto zero for healthy signals and a higher value for defective signals (Fig. 10(b)). But due to the false representation of the randomness(small and large) of energy distributions of the signals it shows a constant value.

The foregoing discussions highlighted two aspects: superior performance of JRD than energy entropy and secondly the upsettingeffect of selecting different number of IMFs than the sensitive IMFs with load variation. Similar discussion on these two aspects isshown in Fig. 11 for Case II to highlight the influence of speed variation in case of outer race defect. It may be noticed that theobservations and conclusions drawn in Fig. 9 and Fig. 10 broadly apply for the case in Fig. 11 and Fig. 12 respectively. Hence, it canbe concluded that load and speed variations within the specified limits do not influence the JRD parameter and that selection andconsideration of appropriate IMFs is very important for bearing degradation monitoring based on JRD parameter.

In order to further demonstrate the effectiveness of EEMD based evaluation of JRD, a comparison with the wavelet packetdecomposition based evaluation of JRD is carried out in Fig. 13. The cases of load and speed variation are analysed using db10mother wavelet. The signals are decomposed using four level WPD-tree, which produced 16 terminal nodes. WPD is unable toproperly decompose the low SNR signals and only provides a quantitative estimation of difference between healthy and defectivesignals. It fails in quantitative indication reflecting on the various step changes in defect amplitude after every 10 data points.

When compared to the FFT in Fig. 8(h), it is noted that the conventional FFT spectral information is not able to identify the outerrace defect frequency due to a very weak SNR. In order to demonstrate the fault identification capability of the proposed EEMDbased envelope spectrum methodology, kurtosis is evaluated for all the sensitive IMFs obtained from the time domain data inFig. 8(g). IMF 3 is found to have the maximum kurtosis value. Envelope spectrum of the first three IMFs are plotted in Fig. 14.

It may be noted that IMF 1 and IMF 2 which are proposed by earlier researchers to contain the maximum fault information showno distinct peak corresponding to the outer race defect frequency. On the contrary, IMF 3 yields not only a strong outer race defectfrequency component but its harmonic as well. This emphasizes that it is necessary to identify an appropriate IMF from among the

Fig. 11. (a) JRD and (b) EEMD energy entropy for a simulated outer race defect with speed variation (CASE II) for appropriate number of sensitive IMFs.

Fig. 12. JRD plots for a simulated outer race defect with speed variation (CASE II) (a) fewer number of IMFs (first 5) and (b) almost all the IMFs.

top few, rather than simply presuming that the first one or two IMF bear all the information on bearing state particularly for a signalwith weak SNR. The proposed approach is thus generic for all types of field data and is more robust in the diagnosis.

4.3. Application of the method for inner race defect

The vibration signal using Eq. (26) with Tdo corresponding to inner race defect is obtained and shown in Fig. 15(a-b) (i.e. withoutnoise, unbalance, load variation and speed fluctuations effects).

The effect of transfer path in case of inner race defects is clearly visible in the time domain data (Fig. 15(a)) as the impulsesdisappear as the defect moves away from the load zone. Fig. 15(b) shows the FFT spectrum where shaft rotation frequency (fs) andits multiples, inner race defect frequency (fi) and its multiples along with sidebands (due to fs and its harmonics) are clearlynoticeable.

Fig. 15(c-d) show the simulated time and frequency domain vibration signal for inner race defect with unbalance and loadvariation, while the corresponding data for the case of shaft speed variation and unbalance is shown in Fig. 15(e-f). Due to thevariable time gap between impulses, which is evident from the time domain signal in Fig. 15(e), leakage of energy is apparent in theFFT spectrum in Fig. 15(f). Fig. 15(g-h) depicts the simulations for an inner race defect having the combined effect of unbalance,load variation, speed variation including the influence of noise (SNR ratio=7.5 dB) as per Eq. (26). The vibration signal for this caseis again used to demonstrate the robustness of the proposed EEMD energy probability distribution based JRD measure.

An inner race defect signal, with load variation (parameter V denotes the variation of load here) is considered as per the plan

Fig. 13. WPD based JRD plots for a simulated outer race defect (a) load variation (CASE I) (b) speed variation (CASE II).

Fig. 14. Envelope spectrum of the IMFs for a simulated vibration signal of an outer race defect including unbalance, speed variation, load variation and noise(SNR=7.5 dB) (a) IMF 1 (b) IMF 2 (c) IMF 3.

given in Table 3. Sensitivity indices βm for a simulated inner race defect with load variation for one particular state, do=1 andV=10% are reported in Table 5. The first six IMFs are sensitive IMFs (with βm > 0.1).

Fig. 16(a-b) depict the JRD and energy entropy plots for different combinations of variation of load as discussed in Table 3. Itmay be noticed that the observations and conclusions drawn in Fig. 9 for Case I of an outer race defect broadly apply for the inner

Fig. 15. Simulated vibration data for an inner race defect (a-b) Ideal case (c-d) Unbalance with load variation (e-f) Unbalance with speed variation (g-h) Unbalancewith load variation, speed variation and noise (SNR, 7.5 dB).

race defect case as well (Fig. 16). Results similar to the ones shown in Figs. 10–13 (shown for the case of outer race defect) are alsoobserved for the case of inner race defect and are not repeated here. The results, however, validate that the practical load and speedvariations do not influence the JRD parameter even for the inner race defect and the results and conclusions drawn for the outer racedefect apply for the inner race defect.

Fig. 15(h) shows that the conventional FFT spectrum does not distinctly show the inner race defect frequency in presence ofnoise. The level of noise floor is quite high due to a very weak SNR ratio. Applying the proposed EEMD based envelope spectrummethodology on the time domain data in Fig. 15(g), IMF 3 is found to have the maximum kurtosis value. Envelope spectrum of thefirst three IMFs are plotted in Fig. 17. Similarly to the outer race defect case, it is found that in case of weak SNR ratio signals it is notnecessary that the first two IMFs will contain the fault information. In fact IMF1 and IMF2 show no distinct peak corresponding tothe inner race defect, whereas IMF 3 contains sharp peaks at shaft frequency and its harmonics, inner race defect frequency, itsharmonics, and sidebands around the defect frequency spaced at shaft rotation frequency and harmonics.

5. Fault diagnosis method on experimental data

The previous section explored application and effectiveness of the proposed JRD measure on simulated vibration signal for bothinner and outer race defects. In order to check its performance on actual test data, two experimental case studies are undertaken.

a) In the first study, the proposed JRD measure is tested on experimental bearing vibration signals with artificially seeded damage.The aim is to validate its effectiveness in correlating to the severity of the fault (outer race and inner race). This study will explorethe capability of JRD measure to detect change of health state as the severity of the fault changes on the measured data. It willalso explore the potential of ‘α value’ and PFI's in fault classification (as per Eqs. (13) and (15), Section 2.2.2).

b) In the second case study, the performance of the methodology proposed in Section 3 is tested on two accelerated life test data inassessing the degradation of bearing under naturally induced and naturally progressed faults. Chebyshev's inequality is appliedon JRD for online monitoring and detection of change in damage state. Fault type identification using PFI at the points of healthstate change can identify the defect initiation point. Finally, the evaluated JRD parameter is converted into a generalizedconfidence value in assessing remaining life.

5.1. Bearings with artificially induced damage

Fig. 18(a) shows experimental setup for testing bearings with measured seeded defect. The vibration signals have been acquiredon this rig in the past [33] on Double Row Angular Contact bearings (DRAC, NBC make AU1103M) using accelerometers. Thismeasured vibration time domain data is used for the application of the proposed methodology. The rotating spindle is supported by apair of DRAC bearings, one each on either end. To simulate damage, the bearings were seeded in the form of a fine slit of varyingwidths and constant depth. Three different widths of 500 µm, 1000 µm and 1500 µm with a constant depth of 200 µm were seededon outer race and inner race respectively (Fig. 18(b) and (c)), by electrode discharge machining.

During the experiment, the shaft speed was kept constant at 1400 rpm, the applied radial load was 25% of the dynamic loadcapacity of the bearing and thrust load was 15% of the applied radial load. Vibration data was acquired using a B &K make 4508-001accelerometer, which has a sensitivity of 10 mV/g. The accelerometer signals were collected at a sampling frequency of 51.2 kHz

Table 5Sensitivity index of IMFs of simulated inner race defect arranged in descending order.

IMF No.

Case 1 2 3 4 5 6 7 8 9 10

CASE I: Load variation 1 0.635 0.576 0.363 0.231 0.141 0.080 0.024 0.011 0

Fig. 16. (a) JRD and (b) EEMD energy entropy for a simulated inner race defect with load variation (CASE I) for appropriate number of sensitive IMFs.

using a LMS data acquisition system under one healthy state and six damage states (three severity levels for outer race defect andthree severity levels for inner race defect). The data acquisition was initiated after an initial running in period of 30 min and thevibration data was acquired from both the healthy and defective bearings for a period of 10 s after every 10 min.

All the bearings were again disassembled at the end of the test run and it was found that there was no defect propagation in all

Fig. 17. Envelope spectrum of the IMFs for a simulated vibration signal of an inner race defect including unbalance, speed variation, load variation and noise(SNR=7.5 dB) (a) IMF 1 (b) IMF 2 (c) IMF 3.

Fig. 18. Experimental set up (a) Test rig (courtesy: N.E.I., Jaipur) (b) Test bearings with defect size of 500 µm on the outer race (c) Test bearings with defect size of500 µm on the inner race.

the cases considered. The characteristic defect frequencies for the given bearings are 149 Hz and 201 Hz for outer race defect andinner race defect respectively. In the study, four stages (consisting of healthy bearing, 500 μm fault bearing, 1000 μm fault bearingand 1500 μm fault bearing respectively) are considered for outer race defect and four stages (consisting of healthy bearing, 500 μmfault bearing, 1000 μm fault bearing and 1500 μm fault bearing respectively) are considered for inner race defect. A total of fivesignals from every bearing are considered (5 each for healthy, 500 μm, 1000 μm and 1500 μm defect sizes) with each signal of 10 sand is broken down further into 10 parts i.e each part is of 1 s. Signal data set for each stage consists of 50 sets of 1 s data signals.The aim of this study is to verify the performance of JRD measure in distinctly identifying defect stages and show significant changesin the JRD values as the stage changes after every 50 data points. The fault identification capability of the proposed EEMD basedenvelope spectrum using ‘α value’ and PFI indices is also tested on the seeded defect data.

Fig. 19. Time domain plot, FFT spectrum and FFT spectrum for low frequency region for, (a-c) Healthy data; (d-f) 500 µm defect; (g-i) 1000 µm defect; (j-l) 1500 µmdefect for an outer race defect.

Table 6Sensitivity index of IMFs of seeded outer race defect.

500 µm IMF 5 IMF 4 IMF 3 IMF 1 IMF 2 IMF 6 IMF 7 IMF 10 IMF 9 IMF 81 0.987 0.887 0.785 0.727 0.333 0.0709 0.0363 0.005 0

5.1.1. Outer race defectFig. 19 depicts the raw time domain signal, complete frequency spectrum and low frequency region view of the frequency

spectrum for signals of the four cases: one case of healthy and three cases of outer race defect of increasing severity levels (500 µmdefect, 1000 µm defect and 1500 µm defect respectively.

It can be clearly seen that there is a definite change in the peak to peak amplitude of the raw time domain vibration data as thedefect size changes (Fig. 19(a,d,g,j)). The outer race defect frequency is barely noticed in the spectrum for 500 µm and 1000 µmdefect. Since the impulses generated due to the impact of the rolling elements on the defect become strong, distinct and lessdominated by noise for 1500 µm defect, the defect frequency is clearly seen for this case. The increase in defect size increases theenergy level in the high frequency regions (10–25 kHz).

EEMD technique is used next to decompose the time domain signals to obtain IMFs and the sensitivity indices of the IMFs areevaluated (Table 6). The first six IMFs are considered as the sensitive IMFs. The correlation values give a broad idea about the energycontent of the signal as well. For 500 µm defect most of the signal energy is distributed in first six IMFs whereas for 1500 µm defectall the energy is concentrated in the first two IMFs. The JRD exploits change in the probability distribution of the IMFs. It may beobserved that for 500 µm defect, IMF 3 shows a maximum correlation with original signal highlighting that IMF 1 and IMF 2 are notalways the ones having the highest fault information, although for a severe defect (1500 µm) IMF 1 is the most important IMF.

The vibration data from healthy bearing and bearings with various severity levels (500–1500 µm), are stacked one after the other(50 data points corresponds to each level of damage) to simulate a test data with increasing severity of fault. Fig. 20 shows the trendof the JRD with respect to the data points for the case of outer race defect. It can be observed that as the damage stage changes, anoticeable shift in the value of the JRD is observed. Fig. 20 clearly shows the increasing value of the JRD with increase in the defectsize after every 50 data points.

As the JRD value monitors the condition and severity level of the defect, the defect classification is attempted by evaluating the ‘αvalue’ and the PFI based on Eqs. (13) and (15). The values of ‘α’ for outer race, inner race and ball defect is evaluated for all the 50datasets and is shown in Fig. 21. As expected, the value of ‘α’ & PFIi (i=ORDF/IRDF/BDF) are well within threshold value of 2.5 and2 respectively for healthy data at all 50 data points as noticed in Fig. 21(a,b). An average value of α=8 and PFI=12 corresponding toouter race defect is noted for data of 500 µm outer race defect in Fig. 21(c,d). ‘α value’ and the PFI for inner race and ball defect arefound to be within threshold limits indicating that defect is correctly classified as outer race defect. Similar result is noticed for thecase of 1000 µm and 1500 µm defect size (Fig. 21(e,f)).

The importance of using the combination of ‘α value’ and PFI's can be realized from 1500 µm defect case. The mean value ofPFIinner and PFIball for 1500 µm defect is approximately around 5 in Fig. 21(h), and if we use PFI's (absolute amplitude ratio of thedefect frequencies) as a sole criteria for fault identification, then these two cases may false identify a severe outer race defect alongwith weak inner and ball defects thus decreasing the fault classification accuracy. But the ‘α value’ corresponding to ball and innerrace defect for 1500 µm defect size always lies below the set threshold of 2.5, indicating the absence of a sharp peak at theselocations. The false identification of inner race/ball defect based on PFI value could be due to a general rise in noise floor due to asevere defect of other type. The combined use of ‘α value’ and PFI increases the robustness of the diagnosis.

5.1.2. Inner race defectFig. 22 depicts the raw time domain signal, complete frequency spectrum and low frequency region of the frequency spectrum for

four cases one case of healthy and three cases of inner race defect of increasing severity levels; 500 µm defect, 1000 µm defect and1500 µm defect.

Relative to the healthy time domain vibration data, a considerable change in the peak to peak amplitude for the increasing defectsize can be observed in Fig. 22(a,d,g,j). The inner race defect frequency value is quite suppressed for the 500 µm defect and is hardlyvisible.

The increase in its amplitude for the 1000 µm and 1500 µm is marginal, although the amplitude of the second harmonic of innerrace defect frequency increases significantly.

The sensitivity indices of the decomposed IMFs are given in Table 7. The first seven IMFs are considered to form the sensitiveIMFs. Fig. 23 shows the trend of the JRD for the case of inner race defect. It can be observed that as the damage stage changes, there

Fig. 20. (a) JRD divergence plot for the simulation study from the seeded outer race defect data, 0–50→healthy data, 51–100→500 µm defect, 101–150→1000 µmdefect and 151–200→1500 µm defect.

is a considerable change in the JRD value after every 50 data points.Inner race defect data is also used to verify the proposed fault identification methodology based on EEMD envelope spectrum.

Similar to the previous case ‘α value’ and PFI's are evaluated for the three cases of inner race defect and are shown in Fig. 24. It isfound that although all the PFI's PFIouter, PFIinner and PFIball are higher than the set threshold for all the defect sizes, only ‘αinner’ liesconsistently above its threshold for the three cases, which confirms an inner race defect.

Fig. 21. (a, c,e, g) ‘α value’ and (b, d, f, h) PFI's for healthy bearing, 500 µm fault bearing, 1000 µm fault bearing and 1500 µm fault bearing respectively.

5.2. Run-to-failure test case

5.2.1. Bearing experimental settingsExperimental data sets of bearing run-to-failure tests under constant load conditions on a specially designed test rig has been

measured and reported in [55]. The bearing test rig hosts four test Rexnord ZA-2115 double row bearings on one shaft. The rotationspeed was kept constant at 2000 rpm. A radial load of 6000 lbs was added to the shaft and bearing by a spring mechanism. A PCB353B33 High-Sensitivity Quartz ICP Accelerometer was installed on each bearing housing. The data sampling rate was 20 kHz andthe data length was 20480 points.

Though all the 12 bearings used in the study [55] have been subjected to the same load and speed conditions, all bearings

Fig. 22. Time domain plot, FFT spectrum and FFT spectrum for low frequency region for, (a-c) Healthy data; (d-f) 500 µm defect; (g-i) 1000 µm defect; (j-l) 1500 µmdefect respectively for an inner race defect.

Table 7Sensitivity index of IMFs of seeded inner race defect.

Fig. 23. JRD plot for the simulation study from the seeded inner race defect, 0–50→healthy data, 51–100→500 µm defect, 101–150→1000 µm defect and 151–200→1500 µm defect.

Fig. 24. (a, c, e) ‘α value’ and (b, d, f) PFI's for 500 µm fault bearing, 1000 µm fault bearing and 1500 µm fault bearing, respectively for an inner race defect.

degrade at different rates and only few achieved complete failure with distinct failure modes and different failure times. In thepresent work, measured data of Bearing 1 of Test 2 and Bearing 4 of Test 1 is used to test the proposed methodology and arehenceforth referred as Test Case 1 and Test Case 2 respectively.

Based on the geometry of the bearing, the three defect frequencies are found to be ORDF=236 Hz, IRDF=297 Hz andBDF=279 Hz while the shaft rotational frequency is 33.33 Hz.

Fig. 25(a) depicts the raw time domain vibration data of Test case 1. JRD measure for the test is shown in Fig. 25(b). As per theproposed methodology Chebyshev's inequality was used to remove outliers and identify change in health stage. The JRD after theapplication of the Z-statistics is shown in Fig. 25(c). It was found that after all the outlier are filtered, only the genuine changes ofstate get highlighted. The data set for which a change of state is detected is further examined to identify the fault type. If no fault typeis identified then the next change of state data point is examined for the same until a probable fault is detected. For example in thiscase the data points 343 and 533 were identified by Z-statistics as probable datasets where the initial defect occurred.

Evaluating the ‘α value’ and PFI's in the vicinity of these two data points, an outer race defect is identified at point 533. Fig. 26depicts the ‘α value’ and PFI's for datasets near the point 533. Both αouter and PFIouter surpass their respective thresholds at 533 andshow an increasing trend for more than 5 data points. Hence the defect initiation alarm is raised at point 533. The entire process ofapplication of the proposed methodology has successfully detected presence of the outer race defect, which is the actual recordeddefect in the bearing. The outlier free trend of Fig. 25(c) is finally converted into a CV plot as shown in Fig. 25(d). The purpose of thisCV value is to follow the degradation pattern (using Eq. (16)) based on the JRD value. Further in general it will provide an idea aboutthe health state of a rolling element bearing and more importantly indicate current health vis-à-vis complete failure. Since CV of 0 isindicative of failure, the value of CV at any point in time during the life of bearing can give a measure of its current health. As shown

Fig. 25. Application of the proposed methodology on life tests data for Test Case1: (a) Acceleration of bearing 1 of testing 2 ending with outer race failure (b) JRDplot (c) JRD plot after application of Z-statistics (d) Confidence value plot.

Fig. 26. (a) ‘α value’ and (b) PFI's close to the vicinity of 533 data point of Test Case 1.

in the Fig. 25(d), the condition is broadly categorized in defect stages (Stage I-Stage IV). The classification of the current stage ofbearing health can be useful in devising appropriate condition monitoring interval or maintenance/replacement schedule.

In order to highlight the superiority of the EEMD based envelope spectrum in identifying the fault type for naturally occurringdefects, a comparison with the conventional FFT technique is shown in Fig. 27. The spectra are plotted for three zones (1) healthystate (Fig. 27(a-b)) corresponding to data point 3, (2) defect initiation state (Fig. 27(c-d)) corresponding to data point 533 and (3)failure state (Fig. 27(e-f)) corresponding to data point 982. The FFT spectra are depicted in Fig. 27(a,c,e) and the envelope spectraare plotted in Fig. 27(b,d,f). It may be noticed that though the FFT spectrum indicates distinct presence of defect frequency withreasonable amplitude at data point 533 (Fig. 27(c)), it does not give a clear indication at the highest level of degradation (near thedata point 982) due to the absence of first two harmonics of ORDF (Fig. 27(e)). On the contrary, the EEMD spectra (Fig. 27(d) and(f)) show very dominant presence of all the harmonics of the ORDF with almost twice the amplitude compared to that observed inFFT spectra.

To check the consistency of the methodology for a different dataset, Test Case 2 is also examined. The raw time domain vibrationdata and JRD values for the test is shown in Fig. 28(a) and (b) respectively. The JRD after the application of the Z-statistics is shownin Fig. 28(c). The health state change locations are identified at data points 157, 905, 1854, and 2060. While examining the ‘α value’and PFI's in the vicinity of these points an inner race defect is identified at point 2060. The ‘α value’ and PFI's in the vicinity of point2060 are shown in Fig. 29. It is found that αinner has larger value compared to αouter/αball. However the value of αinner does notincrease consistently and keeps on fluctuating above the threshold, while the αouter and αball values are always found under thethreshold limit. The examination of the PFI's shows steady PFIinner above the threshold, confirming an inner race defect. It isinteresting to note that the overall vibration amplitude does not show significant rise towards the end of the bearing life (time unit2000–2156 in Fig. 28(a)). However the JRD shows significant rise in its measure (Fig. 28(b)). The confidence value plot also

Fig. 27. (a, c, e) FFT spectrum and (b, d, f) Envelope spectrum for three zones healthy (data point 3), defect initiation (data point 533) and failure (data point 982)for Test Case 1.

classifies the damage stages appropriately giving possibility of identifying how far is the current health from final failure point(CV=0) as discussed earlier.

Fig. 30 shows a comparison of the conventional FFT technique with the proposed EEMD envelope spectrum for Test case 2.Spectra are plotted for three zones (1) healthy state (Fig. 30(a-b)) corresponding to data point 3, (2) defect initiation state (Fig. 30(c-d)) corresponding data point 2060 and (3) failure state (Fig. 30(e-f)) corresponding to data point 2150.

The FFT spectrums are depicted in Fig. 30(a,c,e) and the envelope spectrums are plotted in Fig. 30(b,d,f). For the healthy case theFFT spectrum Fig. 30(a) and the envelope spectrum Fig. 30(b) show a suppressed peak at shaft rotation frequency. For the defectinitiation data point the FFT spectrum again shows a peak at the outer race defect frequency (ORDF=236 Hz) in Fig. 30(c). Howeverthe envelope spectrum indicates an inner race defect with strong frequency component at 297 Hz, its second harmonic at 594 Hz andthird harmonic at 904 Hz along with sidebands of the shaft frequency and harmonics around each of them in Fig. 30(d). Based onthe FFT spectrum near failure (Fig. 30(e)) it is noticed that few sidebands around 3nd harmonic of IRDF and 2nd harmonic of IRDFis noticed in the FFT spectrum in Fig. 30(e), although IRDF is not present. On the contrary, the envelope spectra distinctly andconsistently exhibits presence of IRDF, its 2nd harmonics and their sidebands (Fig. 30(f)). It may be emphasized that with anincrease in defect size sidebands become more prominent. In fact the very strong presence of a large number of sidebands of highamplitudes is a distinctive difference between the spectra of the outer and inner race defects.

6. Conclusions

In this work, it is demonstrated that EEMD based Jensen Rényi divergence (JRD) as a degradation parameter has the potential to

Fig. 28. (a) Acceleration of bearing 3 of testing 1 ending with inner race failure (b) JRD plot (c) JRD plot after application of Z-statistics (d) Confidence value plot ofTest Case 2.

Fig. 29. (a) ‘α value’ and (b) PFI's close to the vicinity of 2060 data point for Test Case 2.

accurately monitor the bearing health. The JRD measures the change in the energy probability distribution of IMF's through Rényientropy. Only a selected few IMFs are expected to contain the bearing fault related information, hence a new IMF selection approachproposed in this work clusters IMFs in two groups of sensitive and not so sensitive IMFs. Evaluating JRD by selecting sensitive IMFs,improves its sensitivity as a diagnosis parameter, eliminates interference of other components unrelated to the fault and makes itlargely unaffected by change/fluctuations in operating conditions. In addition, the JRD is a non-parametric measure that evaluatesdistance between the energy probability distributions as the bearing degrades, without making any assumptions about theunderlying distribution and bearing physical characteristics.

Fault identification uses a systematic approach based on Z-statistics to identify the status of bearing health using an algorithmbased on Chebyshev's inequality. The algorithm identifies the exact points of the change in bearing health and also ensures that theoutliers are not identified as change points. The identified change points are investigated for fault classification as possible locationswhere defect initiation could have taken place. Two parameters ‘α value’ and Probable Fault Index (PFI) are proposed and evaluatedfrom the time domain data of the change points using EEMD envelope spectrum of an appropriately selected IMF. The ‘α value’identifies the existence of specific characteristic defect frequency, whereas the PFI confirms the presence of the defect and accountsfor the noise floor in the spectrum. The IMF containing the maximum fault related information is selected using a systematicapproach from the group of sensitive IMFs. It is further established (both with simulations and experimental data) that unlikementioned in the literature, IMF 1 and IMF 2 do not always contain the maximum fault information and hence underscores thesignificance of the IMF selection process. The selection process is independent of the operating conditions, level of noise and doesnot require any prior knowledge for training purposes.

The value of the diagnosis parameter (JRD) for one bearing may correspond to a different health state for a similar bearing evenfor same operating conditions. Hence, a standardized index to quantify the degradation level, a Confidence value parameter isproposed. It quantifies the degradation level in a range of zero (complete failure) and unity (healthy), giving a qualitative indication

Fig. 30. (a, c, e) FFT spectrum and (b, d, f) Envelope spectrum for three zones healthy (data point 3), defect initiation (data point 2060) and failure (data point 2150)for Test Case 2.

of the current bearing health status. Based on the current estimated CV of the bearing, its current health state vis-à-vis final failurecan be ascertained so that the maintenance/replacement be scheduled or inspection intervals can be adjusted.

The effectiveness of the proposed methodology is demonstrated using a simulation study, seeded defect data and two acceleratedbearing life tests. One of the main advantage of the proposed approach is that it does not require data from individual degradationmodes for training at any point unlike other machine learning methods proposed in the past. Additionally, it does not require largeamounts of data for training, and uses only the current data of the bearing under consideration. Although some user input isrequired for setting the threshold PFI value, which is currently set equal to 2 on the conservative side, the combined use of ‘α value’and PFI gives reasonably accurate fault classification. The proposed method also accurately assess the bearing degradation statusand can provide information in advance regarding the bearing health status. This can help to avoid unexpected failures and reducethe loss in production time and increase efficiency. The proposed method represents a more robust and practical tool for bearingperformance assessment in condition based maintenance.

References

[1] R.B. Randall, J. Antoni, Rolling element bearing diagnostics—a tutorial, Mech. Syst. Signal Process. 25 (2011) 485–520.[2] Y.N. Pan, J. Chen, X.L. Li, Bearing performance degradation assessment based on lifting wavelet packet decomposition and fuzzy c-means, Mech. Syst. Signal

Process. 24 (2010) 559–566.[3] R.B.W. Heng, M.J.M. Nor, Statistical analysis of sound and vibration signals for monitoring rolling element bearing condition, Appl. Acoust. 53 (1998)

211–226.[4] Y. Shao, K. Nezu, Prognosis of remaining bearing life using neural networks, Proc. Inst. Mech. Eng. I: J. Syst. Control Eng. 214 (3) (2000) 217.[5] H. Qiu, J. Lee, J. Lin, G. Yu, Robust performance degradation assessment methods for enhanced rolling element bearing prognostics, Adv. Eng. Inform. 17

(2003) 127–140.[6] P.W. Tse, Y.H. Peng, R. Yam, Wavelet analysis and envelope detection for rolling bearing fault diagnosis—their effectiveness and flexibilities, J. Vib. Acoust. 123

(2001) 303–310.[7] N. Gebraeel, M. Lawley, R. Liu, V. Parmeshwaran, Residual life predictions from vibration-based degradation signals: a neural network approach, IEEE Trans.

Ind. Electron. 51 (2004) 694–700.[8] G.F. Bin, J.J. Gao, X.J. Li, et al., Early fault diagnosis of rotating machinery based on wavelet packets—empirical mode decomposition feature extraction and

neural network, Mech. Syst. Signal Process. 27 (2012) 696–711.[9] R. Huang, L. Xi, X. Li, C. Richard Liu, H. Qiu, J. Lee, Residual life predictions for ball bearings based on self-organizing map and back propagation neural

network methods, Mech. Syst. Signal Process. 21 (2007) 193–207.[10] Y.N. Pan, J. Chen, L. Guo, Robust bearing performance degradation assessment method based on improved wavelet packet-support vector data description,

Mech. Syst. Signal Process. 23 (2009) 669–681.[11] Y.N. Pan, J. Chen, X.L. Li, Spectral entropy: a complementary index for rolling element bearing performance degradation assessment, Proc. Inst. Mech. Eng. C:

J. Mech. Eng. Sci. 223 (2009) 1223–1231.[12] J. Yu, Bearing performance degradation assessment using locality preserving projections, Expert Syst. Appl. 38 (2011) 7440–7450.[13] J. Yu, Bearing performance degradation assessment using locality preserving projections and Gaussian mixture models, Mech. Syst. Signal Process. 25 (2011)

2573–2588.[14] J. Yu, A hybrid feature selection scheme and self-organizing map model for machine health assessment, Appl. Soft Comput. 11 (5) (2011) 4041–4054.[15] L. Mi, W. Tan, R. Chen, Multi-steps degradation process prediction for bearing based on improved back propagation neural network, Proc. Inst. Mech. Eng. C.-

J. Mech. Eng. Sci. 227 (2012) 1544–1553.[16] Z. Wang, C. Lu, Z. Wang, H. Liu, H. Fan, Fault diagnosis and health assessment for bearings using the Mahalanobis-Taguchi system based on EMD-SVD, Trans.

Inst. Meas. Control 35 (2013) 798–807.[17] R. Li, P. Sopon, D. He, Fault features extraction for bearing prognostics, J. Intell. Manuf. 23 (2012) 313–321 (ISSN 0956-5515).[18] S. Hong, Z. Zhou, E. Zio, K. Hong, Condition assessment for the performance degradation of bearing based on a combinatorial feature extraction method, Digit.

Signal Process. 27 (2014) 159–166.[19] P. Shakya, M.S. Kulkarni, A.K. Darpe, A novel methodology for online detection of bearing health status for naturally progressing defect, J. Sound Vib. 333

(2014) 5614–5629.[20] J. Ben Ali, N. Fnaiech, L. Saidi, B. Chebel-Morello, F. Fnaiech, Application of empirical mode decomposition and artificial neural network for automatic bearing

fault diagnosis based on vibration signals, Appl. Acoust. 89 (2015) 16–27.[21] J. Hu, L. Zhang, W. Liang, Dynamic degradation observer for bearing fault by MTS-SOM system, Mech. Syst. Signal Process. 36 (2) (2013) 385–400.[22] Y. Yang, D.J. Yu, J.S. Cheng, A roller bearing fault diagnosis method based on EMD energy entropy and ANN, J. Sound Vib. 294 (2006) 269–277.[23] L. Jiang, J. Xuan, T. Shi, Feature extraction based on semi-supervised kernel Marginal Fisher analysis and its application in bearing fault diagnosis, Mech. Syst.

Signal Process. 41 (2013) 113–126.[24] Y.G. Lei, Z.J. He, Y.Y. Zi, A new approach to intelligent fault diagnosis of rotating machinery, Expert Syst. Appl. 35 (2008) 1593 (160).[25] P. Boškoski, Đ. Juričić, Fault detection of mechanical drives under variable operating conditions based on wavelet packet Rényi entropy signatures, Mech. Syst.

Signal Process 31 (2012) 369–381.[26] P. Boškoski, M. Gašperin, D. Petelin, Đ. Juričić, Bearing fault prognostics using Rényi entropy based features and Gaussian process models, Mech. Syst. Signal

Process 52–53 (2015) 327–337.[27] J. Lee, H. Qiu, G. Yu, J. Lin, RT Services Bearing data set, in: U.O. Cincinnati (Ed.)NASA Ames Prognostics Data Repository, IMS, University of Cincinnati,

2007.[28] N.E. Huang, Z. Shen, S.R. Long, et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc.

R. Soc. Lond. A 454 (1998) 903–995.[29] Z.H. Wu, N.E. Huang, Ensemble empirical mode decomposition: a noise-assisted data analysis method, Adv. Adapt. Data Anal. 1 (2009) 1–41.[30] Y.G. Lei, M.J. Zuo, Fault diagnosis of rotating machinery using an improved HHT based on EEMD and sensitive IMFs, Meas. Sci. Technol. 20 (2009)

2280–2294.[31] Z.H. Wu, N.E. Huang, A study of the characteristics of white noise using the empirical mode decomposition method, Proc. R. Soc. Lond. 460 A (2004)

1597–1611.[32] V. Rai, A. Mohanty, Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert–Huang transform, Mech. Syst. Signal Process. 21 (2007)

2607–2615.[33] P. Shakya, A.K. Darpe, M.S. Kulkarni, Vibration-based fault diagnosis in rolling element bearings: ranking of various time, frequency and time-frequency

domain data-based damage identification parameters, Int. J. Cond. Monit. 3 (2013) 53–62.[34] R. Baraniuk, P. Flandrin, A. Janssen, O. Michel, Measuring time-frequency information content using the Renyi entropies, IEEE Trans. Inform. Theory 47

(2001) 1391–1409.[35] B. Tao, L. Zhu, H. Ding, Y. Xiong, An alternative time-domain index for condition monitoring of rolling element bearings—A comparison study, Reliab. Eng.

Syst. Saf. 92 (2007) 660–670.

[36] J. Neyman, Fourth Berkeley Symposium on Mathematical Statistics and Probability Announced, Science 131 (1960) 1595–1596.[37] A.O. Hero, B. Ma, O. Michel, J. Gorman, Alpha-Divergence for Classification, Indexing and Retrieval (Technical Report CSPL-328), Communications and Signal

Processing Laboratory, The University of Michigan, 2002.[38] D. Markel, H. Zaidi, I. El Naqa, Novel multimodality segmentation using level sets and Jensen-Renyi divergence, Med. Phys. 40 (2013) 121908.[39] A. Ben-Hamza, H. Krim, Jensen–Rényi divergence measure: theoretical and computational perspectives, in: Proceedings of the IEEE International Symp. on

Inform. Theory., 2003, 257.[40] J. Príncipe, Information Theoretic Learning, Springer, New York, 2010.[41] Y. He, A.B. Hamza, H. Krim, A generalized divergence measure for robust image registration, IEEE Trans. Signal Process. 51 (2003) 1211–1220.[42] B. Dolenc, P. Boškoski, Đ. Juričić, Robust information indices for diagnosing mechanical drives under non-stationary operating conditions, In: Proceedings of

CMMNO, 2014, pp. 139–149[43] A. Hayter, Probability and Statistics for Engineers and Scientists, PWS Publishing Co., Boston, MA, 1996.[44] P.D. McFadden, J.D. Smith, Vibration monitoring of rolling element bearings by the high-frequency resonance technique—a review, Tribol. Int. 17 (1) (1984)

3–10.[45] R. Rubini, U. Meneghetti, Application of the envelope and wavelet transform analyses for the diagnosis of incipient faults in ball bearings, Mech. Syst. Signal

Process. 15 (2001) 287–302.[46] Y. Yang, D. Yu, J. Cheng, A fault diagnosis approach for roller bearing based on IMF envelope spectrum and SVM, Measurement 40 (2007) 943–950.[47] Y. Zhang, S. Ai, EMD based envelope analysis for bearing faults detection (in:)Intell. Control Autom. (2008) 4257–4260.[48] Q.H. Du, S.N. Yang, Application of the EMD method in the vibration analysis of ball bearings, Mech. Syst. Signal Process. 21 (2007) 2634–2644.[49] W.C. Tsao, Y.F. Li, D.L, An insight concept to select appropriate IMFs for envelope analysis of bearing fault diagnosis, Measurement 45 (2012) 1489–1498.[50] M.C. Pan, W.C. Tsao, Using appropriate IMFs for envelope analysis in multiple fault diagnosis of ball bearings, Int. J. Mech. Sci. 69 (2013) 114–124.[51] F.F. Diego, M.R. David, F.R. Oscar, et al., Automatic bearing fault diagnosis based on one-class ν-SVM, Comput. Ind. Eng. 64 (2013) 357–365.[52] K.B. Goode, J. Moore, B.J. Roylance, Plant machinery working life prediction method utilizing reliability and condition-monitoring data, Proc. Inst. Mech. Eng.

E: J. Process Mech. Eng. 214 (2000) 109–122.[53] N. Gebraeel, M. Lawley, R. Li, J. Ryan, Residual-life distributions from component degradation signals: a Bayesian approach, IIE Trans. 37 (2005) 543–557.[54] P. Shakya, A.K. Darpe, M.S. Kulkarni, Bearing damage classification using instantaneous energy density, J. Vib. Control. (2015).[55] H. Qiu, J. Lee, J. Lin, G. Yu, Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics, J. Sound. Vib. 289

(4–5) (2006) 1066–1090.

bearing damage assessment using jensen-rényi divergence...

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