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BEARING PERFORMANCE DEGRADATION ASSESSMENT BY ORTHOGONAL LOCALPRESERVING PROJECTION AND CONTINUOUS HIDDEN MARKOV MODEL

Tao Liu, Xing Wu, Yu Guo and Chang LiuFaculty of Mechanical & Electrical Engineering, Kunming University of Science & Technology,

Chenggong University Town, Kunming, P.R. ChinaE-mail: [email protected]; [email protected]; [email protected]; [email protected]

IMETI 2015, SM5003_SCINo. 16-CSME-67, E.I.C. Accession 3953

ABSTRACTBearing is the key component in rotating machine. It is important to assess the performance degradationdegree of bearings for making proactive maintenance and realizing near-zero downtime. A methodologybased on orthogonal local preserving projection (OLPP) and continuous hidden Markov model (CHMM)is introduced in bearing performance degradation assessment. Firstly, the time domain, frequency domainand time-frequency domain features are extracted from the vibration signals. Then, the multi-dimensionalfeatures are reduced by OLPP. And the selection of the adjacent paragraph parameters in OLPP is optimizedadaptively by minimizing the ratio of between-class distance to within-class distance. A CHMM is trainedby using the reduced feature in normal condition. At last, the test bearing data are input into the pre-trainedCHMM to calculate the log-likelihood of the test data, which can assess the performance degradation ofbearings quantitatively. A bearing accelerated life experiment is performed to validate the feasibility andvalidity of the proposed method.

Keywords: orthogonal local preserving projection; Distance judgment, Continuous hidden Markov model;Condition monitoring; Rolling element bearing; Performance degradation assessment.

ÉVALUATION CONTINUE DE LA DÉGRADATION DE LA PERFORMANCED’UNROULEMENT PAR LA PROJECTION ORTHOGONALE MARKOV CACHÉE

RÉSUMÉLe roulement est l’élément clé dans une machine rotative. Il est important d’évaluer le degré de dégradationde la performance pour une maintenance proactive réalisée quasi sans temps d’interruption. Une méthodolo-gie de préservation basée sur la projection orthogonale locale sur le modèle markovien caché est introduitepour l’évaluation de la dégradation de performance. En premier lieu, le domaine temporel, le domaine desfréquences et le temps-fréquence sont extraits des signaux de vibration. Ensuite, les caractéristiques multi-dimensionnelles sont réduites selon le modèle markovien, et la sélection adaptive des paramètres adjacentsest optimisée par la diminution du ratio de la “distance entre catégories” et la “distance à l’intérieur des caté-gories”. Le modèle markovien caché est formé en utilisant les fonctionnalités dans des conditions normales.Enfin, les données des tests des roulements sont introduites dans la version préformée pour calculer la valeurdu log-vraisemblance des données du test, lesquelles pourront évaluer la dégradation de la performance desroulements quantitativement. Une expérience en accélérée de la durée de vie d’un roulement est exécutéepour valider la faisabilité et la validité de la méthode proposée.

Mots-clés : projection orthogonale locale ; jugement de la distance ; modèle Markov caché ; surveillance.

Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5, 2016 1019

1. INTRODUCTION

Equipment maintenance is usually carried out when failures are serious or even have been occurred inrotating machine, which causes high maintenance expenses. Condition based monitoring (CBM) of rotatingmachines health that can detect, classify and assess the machine faults is vital for decreasing the cost ofoperation and maintenance. Sometimes, the rotating machines health can prevent the serious accidents[1].Rolling element bearing is one of most important component in rotating machine, and its performanceinfluences the whole machine. The methods of CBM in bearing performance degradation assessment havereceived considerable attentions. The difficulty in performance assessment is that it is hard to convert themonitoring data into the performance index to guide the maintenance [2]. Therefore, feature extraction(FE) of original monitoring data and model of bearing performance degradation is valuable in equipmentmaintenance.

The aim of FE is to obtain the information relevant to system health for better understanding and inter-pretation of bearing condition. Many correlative noteworthy techniques have been carried in this field, andthey have furthered the development of bearing fault diagnosis. These technics mainly include statisticalbased time domain [3, 4], frequency domain [5] and time-frequency domain, for instance, empirical modedecomposition (EMD) [6], ensemble empirical mode decomposition (EEMD) [7] and wavelet transform [8],etc. However, it should notice that, there is not a feature can detect all bearings’ faults in various workingconditions. And it is hard to find a sensitive feature to detect the variety of bearing performance in wholelife time. In order to evaluate the bearing performance, the features extracted from various methods shouldbe as sufficient as possible. However, the information from different features may be redundant and it willcause the increase of computing time. Furthermore, the contradictory of features may result in the errorof assessment. In order to improve the assessment accuracy and enhance the efficiency, some methods areadopted, and one of those methods is feature selection. The feature selection method can be utilized toselect the features which are most suitable to evaluate the bearing performance . The preferable featurescan be used to assess the bearing performance with fewer features. Similarly, these selected features cannotassess the bearing performance at all conditions. Although the adaptive method can be utilized to selectthe proper features automatically, it will increase the computing time. Another way is feature reduction.The method can reduce the feature dimension and preserve the main information which is extracted fromvibration signals of bearing. The traditional feature reduction methods such as principal component analysis(PCA), linear discriminate analysis (LDA), etc., have been used in feature reduction , but the PCA and LDAare linear feature reduction methods. The bearings vibration signals are often nonlinear so the linear featurereduction methods are poor to express the nonlinear structure of signals. Therefore, the kernel-based featurereduction method is introduced in bearing fault diagnosis [9]. Although the kernel function improves thecomputing efficiency of kernel method, the kernel method is based on samples. With the increase of sam-ples, the computing speed of kernel-based feature reduction method will slow down. Manifold learning is anew feature reduction [10], the method such as local linear embedding (LLE) [11], curvilinear componentanalysis (CCA) [12], isometric feature mapping (ISOMAP) [13] and locality preserving projections (LPP)[14], etc., have been introduced in bearing fault diagnosis. In these methods, the OLPP is one of the mostfacilitate feature reduction algorithm. Essentially, the OLPP is a linear projective algorithm which can mapthe nonlinear data from high dimension into low dimension space. Because the method retains the neigh-borhood relationship of data, it can reduce the nonlinear data quickly. Compare to the LPP, OLPP methodproduces orthogonal basis functions and can have more locality preserving power than LPP [15]. The abil-ity and suitability for LDA about extracting useful features as inputs of the bearing performance assessmentmodels will be investigated in this paper.

After the features are obtained, how to effectively evaluate the performance degradation based on theextracted features is still a challenge. Many machine learning methods such as artificial neural networks

1020 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 5, 2016

(ANN) and support vector machine (SVM) have been utilized in bearing performance degradation assess-ment [16, 17]. The ANN is difficult to explain the reasoning and the inference basis of model, and theselection of ANN structure is lack of guide. SVM is proper in small samples, but for the other samples,the structure of model needs to be improved. Continuous hidden Markov model (CHMM) is a powerfulprobabilistic framework for modeling a nonstationary process which has become popular in various areasin recent years. Generally speaking, CHMM is a time series statistical models with a doubly embeddedstochastic process in which an underlying stochastic process is not observable but can be observed throughanother set of stochastic processes that produce the sequence of observations [18].

The dual random and mathematical reasoning ability promote the CHMM widely used in speech, se-mantic recognition and fault diagnosis [19–21]. In this paper, CHMM is introduced to assess the bearingperformance degradation in whole life time.

This paper is organized as follows. In Section 2, the proposed method is presented after introducing theOLPP and CHMM. In Section 3, a method based on CHMM to assess the bearing performance degradationis revealed. Then, an experiment is proposed to validate the feasibility and the effectiveness of this method.Our conclusion is shown in Section 4.

2. TECHNICAL BACKGROUND

2.1. OLPPThe OLPP is developed from Laplacian eigenmaps (LE), and it builds a graph incorporating neighborhoodinformation of original data set. The transformation matrix can be obtained by Laplacian operator, and thenthe data set can be mapped into low dimensional space. The orthogonal basis function in the OLPP makesit have more discriminating power than LPP. The algorithm maintains the local structure of original data setafter mapping [22]. The algorithm of OLPP can be stated as follows [15]:

(1) PCA projection. In order to remove the zero eigenvalue, the PCA is utilized to project the originaldata set at first. The transformation matrix can be denoted as WPCA.

(2) Constructing the adjacency graph. Let X be the training data set and G denote a graph with nodes. Ifdata points xi and x j are “adjacent”, then the nodes i and j are connected. There are two variations:

• ε-neighborhoods (parameter ε ∈ R). Nodes i and j are connected by an edge if ‖xi− x j‖2 < ε .

• k-neighborhoods (parameter k ∈ N). Nodes i and j are connected by an edge if i is among k nearestneighbors of j or j is among k nearest neighbors of i.

(3) Choosing the weights. If nodes i and j are jointed, the connected edge can be weighted. The simpleminded weight can be 1 if two nodes are jointed, and 0 if there is no such edge. The weight can be definedas S.

(4) Computing the orthogonal basis functions. Let D be a diagonal matrix whose entries are column (orrow) sums of S, Dii = ∑ j S ji. Similarly, the matrix L can be defined as L = D−S. Let {a1,a2, . . . ,ad} be theorthogonal basis vectors, and define A(k−1) = [a1,a2, . . . ,ak−1], B(k−1) = [A(k−1)]T (XDXT )−1A(k−1). Thenthe orthogonal basis vectors can be computed as follows:

• a1 equal to the eigenvector corresponded to the smallest eigenvalue of M(k);

• ak equal to the eigenvector associated to the smallest eigenvector of M(k), and

M(k) = {I− (XDXT )−1A(k−1)[B(k−1)]−1[A(k−1)]T}(XDXT )−1XLXT


(5) Eigenmaps calculation. Let WOLPP = [a1,a2, . . . ,ai], l � d; here, the eigenvectors corresponding tothe first lth eigenvalue (l� n) are selected, and the low l-dimensional data set can be computed by

yi =W T x1, W T = [w1,w2, . . . ,wl] (1)

where x is the original data set, y is the low-dimensional data set, W is the transformation matrix and

W =WPCAWOLPP (2)

2.2. Continuous Hidden Markov ModelCHMM is a powerful probabilistic framework for modeling non-stationary process which becomes popularin various areas in last decades. It consists of two doubly embedded stochastic processes: the underly-ing state process and the observable observation process. After training and estimating, the performanceof bearing can be evaluated. The first order left-to-right Markov chain is used in practice. The hiddenstochastic state sequence S = {S1,S2, . . . ,SN} in CHMM can be estimated by an observation sequenceO = {o1,o2, . . . ,oN}. Their joint probability can be evaluated by

P(Q,O | λ ) = ∏t

P(qt | qt−1)P(ot | qt) (3)

where λ expresses the model, qt is the state in time t. P(qt | qt−1) is the state transition probability andP(ot | qt) is the observation probability. Formally, the components of a CHMM can be described as follows[18]:

λ = (π,A,B) (4)

Let N be the number of states in the model and M be the number of distinct observation symbols per state.In Eq. (4), the state transition probability matrix can be defined as A = {ai j} , where

ai j = P(qt+1 = S j | qt = Si), 1≤ i, j ≤ N (5)

The observation probability matrix can be defined as B = {b j(k)}, where

b j(k) = P(Ot = vk | qt = S j), 1≤ j ≤ N,1≤ k ≤M (6)

The initial state distribution π = {πi}, which can be defined as

πi = P(q1 = S1), 1≤ i≤ N (7)

Because the vibration signals in practice are continuous, a GMM is used to model the observation proba-bility

b j(ot) =M j

∑m=1

c jmN(ot ,µ j,U jm), 1≤ j ≤ N (8)

where ot is the observation at time t, M j is the number of Gaussian mixtures in state S j, c jm is the mixtureweight of the mth Gaussian mixture in state S j. N(·) is a Gaussian density with mean vector µ jm andcovariance matrix U jm for the mth Gaussian mixture component in state S j. In the paper, the number ofGaussian mixture component is 3. Generally, a CHMM can be defined as

λ = (A,C,µ,U,π) (9)

where C = {c jm}, µ = {µ jm}, U = {U jm}.


Fig. 1. The scheme of bearing performance degradation assessment based on OLPP and the CHMM.

When we reestimate the parameters in CHMM, the mixture density of coefficients can be expressed as

c′jm =∑

Tt=1 γt( j,m)

∑Tt=1 ∑

M jm=1 γt( j,m)

(10)

µ′jm =

∑Tt=1 γt( j,m)ot

∑Tt=1 γt( j,m)

(11)

Cov′jm =∑

Tt=1 γt( j,m)− (ot −µ jm)(ot −µ jm)

T

∑Tt=1 γt( j,m)

(12)

where γt( j,m) is probability of the mth component at time t and state is Si.

γt( j,m) = P(qt = S j,z jt = Z jm | O,λ )

=αt( j)βt( j)

∑Nj=1 αt( j)βt( j)

c jmN(ot ,µ jm,Cov jm)

∑M jm=1 c jmN(ot ,µ jm,Cov jm)

(13)

Here, z jt is the Gauss component which state is S j at time t, Z jm is the mth Gauss component at state Si.

2.3. Bearing Performance Degradation Based on OLPP and CHMMOLPP is effective and facilitate in feature reduction, and the CHMM is convenient for building the recogni-tion model. In this paper, OLPP and CHMM are utilized in bearing performance degradation model. Firstly,the features extracted from vibration signals consist of the feature set. Then, the OLPP is utilized to reducethe dimension of feature set. At last, the CHMM is used to train the model. The output of testing samplesin CHMM is used to assess the bearing performance. The discussed process is shown in Fig. 1. The mainsteps of the method are as follows:

(1) Feature extraction. The traditional time-domain and frequency-domain methods such as RMS, peakto peak, skewness factor, kurtosis factor, peak factor, clearance factor, pulse factor, shape factor, spectral


overall vale and amplitude spectral entropy are used to extract the features of bearing. Furthermore, waveletpacket transform (WPT) is introduced in FE. It decomposes the details of wavelet packet (WT) coefficientsinto finer frequency bands, which can hereby provide better resolution in the details compared with WT[23]. In this paper, the db8 wavelet is used for wavelet packet analysis, and the normalized WT coefficientsat level 3 are extracted as features. Therefore, a feature set which consists of 18 features is extracted.

(2) Feature reduction. The feature set of the bearing in whole life time is reduced by the OLPP. Here,we select three new features to replace the original feature set. We should notice that the adjacency graphstructure in OLPP greatly influence the final analysis; therefore, we need to consider the initial value ofparameter ε or k. In this paper, we introduce a distance judgment method based on Fisher discriminantanalysis [24] to optimize the selection of adjacency parameter. The separable index can be defined as

J = argmaxj

|SW +SB||SW |

(14)

where SW is within class scatter and SB is between class scatter.

SW =c

∑j=1

N j

∑t=1

(x ji −µ j)(x

ji −µ j)

T (15)

SB =c

∑j=1

N j(µ j−µ)(µ j−µ)T (16)

Here, c is the number of samples categories, x ji is the sample belonging to class j in class c, N j is the

number of samples in class j. µ j is the mean of samples belonging to class j (1 ≤ j ≤ c), µ is the meanvalue of all samples. The index J minimizes the scatter within the class and maximizes the scatter betweenclasses in data set, which reflect the difference of data under different status. Moreover, the J will obtain themaximum by the most optimal adjacency parameter.

(3) Building of the CHMM model. The data in the normal condition is utilized to train the parametersof CHMM, and the object of modeling is used to adjust the parameters λ = (π,A,B) to maximize theprobabilities of the observations sequence O. That is, the object is to find λ ∗, where

λ∗ = argmax

λ

P(O | λ ) (17)

(4) Bearing performance assessment. The testing samples are computed in training CHMM. Therefore,we would get the probabilities of the testing samples. Furthermore, the bearing performance degradation canbe presented by the probability. In order to weaken the influences about feature sequence and the numberof the channels, we will process the log-likelihood of the CHMM. Thus, the new equipment performanceindex is given by

PI =logP(O | λ )

T(18)

where T is the length of the feature sequence.One application of PI is to guide the setting of alarm threshold. In fact, the degradation of bearing is the

outlying samples deviated from the normal samples. Therefore, the method such as Grubbs criterion can beutilized to evaluate the alarm threshold. The Grubbs criterion can be expressed as [25]

gi =|xi−µ|

σ> c (19)

where µ is the mean, σ is the standard deviation and c is the coefficient. In this study, we use the strin-gent level, c = 3.381. If the gt of sample xi satisfy gt > 3.381, then xt is on the outside of the range


Fig. 2. The bearing test rig and schematic diagram.

[µ−3.381σ ,µ +3.381σ ]. The probability of the result is only 0.5%, so we can watch xt deviate the previ-ous status, and the threshold can be set as [µ−3.381σ ,µ +3.381σ ]. In order to avoid the false alarm, thenew alarm threshold will be updated when outlying samples appear 10 times continuously.

3. EXPERIMENTAL VALIDATION

The effectiveness and facility of the method will be demonstrated by a full life time bearing degradationexperiment. The test data is from University of Cincinnati [26].

3.1. Experimental DescriptionThe test rig and sensors installations can be seen in Fig. 2. Four Rexnord ZA-2115 double row bearingswere installed on one shaft. All bearings were forced to be lubricated. On each bearing, two PCB 353B33High Sensitivity Quartz ICP accelerometers were installed on vertical Y and Horizontal X. There were 8accelerometers in the test. The rotation speed kept constantly at 2000 RPM, and 6000lb radial load wasplaced onto the shaft. A National Instruments DAQCard-6062E data acquisition card was utilized to acquirethe vibration data every 20 minutes. There are 2156 group of data which were collected. The data samplingrate is 20 kHz.

The test was carried out for 35 days until a significant amount of metal debris was found on the magneticplug of the test bearing. Bearing faults can be observed after the bearings were dissembled.

3.2. Results and AnalysisSince these bearings are working independently, the experimental data from different bearings can be ana-lyzed respectively. Figure 3 shows the RMS value of four bearings is extracted from the vibration data offour vertical Y accelerometers. It can be seen from the figure that there is only small variety in RMS valuefor bearing 1 and bearing 2. Moreover, the faults of these two bearings are not obvious after dissemblingbearing 1 and bearing 2. Although the faults can be found in both bearing 3 and bearing 4, the RMS valueof bearing 3 would change dramatically. Therefore, the bearing 3 is selected to assess the performancedegradation in this paper.

The increase of RMS in bearing 3 reflects the severity of bearing’s vibration. Generally, the bearingalways runs from normal to degradation to final failure. Figure 4 shows time waveform of bearing 3 at the360th group data, the 2120th group data and the 2155th group data. In Fig. 4(a), it is clear that the amplitudeof vibration signal fluctuates slightly, and there is not significant impulse component. However, in Fig. 4(b)the appearance of the impulse component can be found. The faults may have emerged in the bearing. In


Fig. 3. The RMS of four bearings in whole life time: (a) the RMS and (b) local enlargement of (a).

Fig. 4. The time domain wave changes of bearing 3 in performance degradation: (a) the 360th group data, (b) the2120th group data and (c) the 2155th group data.

Fig. 4(c), a lot of impulse can be observed, and the vibration amplitude is higher than before. To referencethe rapid increase of RMS, the bearing performance shall be considered about running to degradation and itmay fail in the near future.

In order to evaluate the variety of bearing performance, more features and assessment model need to beintroduced. The fault diagnosis mainly focused on detecting and identifying various faults, however, the per-formance degradation assessment has some differences which need to estimate the equipment performancedegradation degree. In this study, the OLPP and CHMM are applied in bearing fault diagnosis.

Similarly, the features are necessary in bearing performance degradation, so 18 features presented inSection 2.3 are extracted, and all features form an original feature set. In order to improve the computingefficiency and accuracy, the OLPP is used to reduce the features’ dimension. Firstly, the features in fulllife time are selected to estimate the OLPP eigenmaps. Here, the normal samples (201 to 250 group),degradation samples (1851 to 1900 group) and failure samples (2120 to 2151 group) are utilized to calculatethe projection vectors. These 150 samples are denoted as Tmap. The adjacency graph is constructed with k-neighborhoods and the simple minded weight is used. The parameter k is selected adaptively by the distancejudgment method which is mentioned in Section 2.1. In order to demonstrate the affectivity of the method,Fmap with three status are used to calculate the parameter k. Twenty samples of three every status which areselected as train sample to build the eigenmaps. The rest (90 samples) are used as test samples. The resultcan be seen in Fig. 5. It is obvious that the new OLPP features have better classification ability. Figures 5(a)and 5(b) reveal that the samples from normal, degradation and failure status can be separable. Furthermore,


Fig. 5. The feature reduction results of test bearing data based on OLPP: (a) the distribution of the first two OLPPfeatures, and (b) the distribution of OLPP1 and OLPP3.

Table 1. The diagnosis results of PCA, OLPP, BPNN, k-Means and CHMM.Classifier Average accuracy of testing samples (%) Average testing

NC IRF ORF RBF accuracy (%)PCA + CHMM 80 99.2 95.6 83.3 89.5OLPP + BPNN 89.7 79.7 99.7 82.5 87.9OLPP + k-Means 67.5 88.3 94.4 75.3 81.4OLPP + CHMM 91.4 95.8 99.2 95.3 95.4

the contribution rate of the first three OLPPs is 97.1%. Therefore, these three OLPP features are convenientin bearing performance assessment.

In order to validate the effectiveness of OLPP and CHMM, some methods such as PCA, LDA and Back-propagation neural network (BPNN) are utilized to classify the bearing faults. The data were from CaseWestern University website [27]. The bearing type is 6205-2RS JEM SKF in drive-end. The faults wereprocessed by electric discharge machining in inner race, outer race and rolling body of bearing. The faultsizes were 0.007, 0.014, 0.021 and 0.028 inch. The experiment rig includes a Reliance Electric 2H IQPreAl-ert. The loads of bearings were from 0 to 3 horsepower, and the rotor speed was 1972, 1772, 1750 and 1730rpm respectively. The samples of bearing consist of normal condition (NC), inner race fault (IRF), outerrace fault (ORF) and rolling body fault (RBF). Data were collected with 12 kHz. There are 20 samples foreach state. In each state, 40% of the samples are selected as training data, and the remaining samples areused as testing samples. As comparison, a BPNN includes one input layer, one hidden layer and one outputlayer is selected. The architecture of BPNN can be learned from [28]. The number of input nodes is equalto number of features, the nodes of hidden layer is 21. The number of output nodes is 4 which equal to thestates of bearing. All results are calculated by 10-fold cross-validation. The result is shown in Table 1. Itis obvious that the CHMM is more accurate than k-Means and BPNN. And diagnose accuracy of OLPP ishigher than PCA. Therefore, the OLPP and CHMM are more effective in classifying the bearing’s condition.

Figure 6(a) reveals the relationship between parameter k and separable index J. The optimal value k = 8is calculated automatically. And the reduction results of the first three OLPP features in whole lifetimeare shown in Fig. 6(b). Compared with RMS, the reduced OLPP features are more sensitive and benefit ininteroperating the variety of bearing conditions.

After the OLPP features are obtained, the normal samples CHMM will be trained. Furthermore, thetesting samples are input into CHMM to estimate the bearing performance in full life time, in which thelog likelihood in Eq. (14) will be used to present the degradation states. And the alarm threshold will becalculated adaptively by Eq. (15). In this study, a CHMM with three states (N = 3) and M = 3 mixtures is


Fig. 6. Result of OLPP in the bearing’s whole lifetime: (a) relation curve of parameter k and class separable acuity Jin OLPP, N = 150 and (b) the first three OLPP features in the whole lifetime.

Fig. 7. The bearing performance degradation assessment results by CHMM.

selected. The number of observation is equal to the dimension of OLPP. Furthermore, the length of obser-vation is 2155, which ensure the convergence of the result. The initial value of state transition probabilitiesobeys standard stochastic constraints. The normal data (1 to 300 group) are adopted to calculate the CHMMparameters in Eq. (13). Then, the full life time testing data are input into CHMM. The performance indicatorand alarm threshold curves are shown in Fig. 7. It is obvious that the bearing condition in CHMM can beclassified more distinctly. Before the 1895 group, the bearing is in normal condition. Then, the bearingperformance is deteriorating between the 1895 to 2001 group, whereas after the 2119 group, the bearingfalls into failure rapidly.

Figure 8 shows an enlargement of Fig. 7. The PI index decreases from 0.1275 (838 group) to –0.2062(921 group), which means that the bearing performance starts to worsen. The early fault occurred on thebearing. The alarm threshold is updated at the 839 group. Then in Fig. 8(b), the PI index decreases from–0.3684 (1555 group) to –3.15 (1895 group), which means that the bearing performance degraded further.We should pay attention to the bearing working condition. In Fig. 8(c), the bearing performance decreasesfrom –3.439 (1999 group) to –6.637 (2119 group), and then drops rapidly. This means that the bearing fallsinto failure rapidly. The alarm threshold is updated at 2122 group.

It is clear that the PI is more sensitive in estimating the bearing performance than the RMS value. Forinstance, the PI value decreases 0.3337 in the early fault of bearing, whereas the RMS value almost does notchange. Similarly, the RMS increased at 2120 group which means the bearing began to failure. However, thePI value has decreased from 1999 group, which is earlier than RMS. Therefore, whatever in early warningand fault alarm, the PI provides a more effective index in bearing performance assessment, which is helpfulin guiding the equipment maintenance.


Fig. 8. Enlargement of Fig. 7: (a) 600 to 1200 group, (b) 1500 to 1950 group and (c) 1951 to 2156 group.

4. CONCLUSION

In this paper, CHMM is applied to bearing performance degradation assessment. In this new scheme, OLPPis used to reduce the dimensions of features. In order to obtain the adjacency parameter, a distance judgmentmethod is introduced to evaluate the parameter adaptively. Then, the normal samples of new OLPP featuresare utilized to estimate the parameters of CHMM. Finally, the full life time data is tested in the CHMM,and the performance degradation indicator validates the reasonable and reliable of the method. The declinecurve of the performance index is consistent to the trend of bearing damage. The setting of adaptive alarmthreshold is helpful to guide the maintenance. Therefore, the method is intuitive and effective in bearingperformance degradation assessment, and feasible in guiding the CBM of rotating equipment.

ACKNOWLEDGEMENTS

This work is supported by the Yunnan Province Personal Training Project (Grant Nos. KKSY201401096)and the National Natural Science Foundations of China (Grant Nos. 51405211).We appreciate the supportof bearing data set by the IMS, University of Cincinnati.

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