bearing fault.pdf

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Bearing fault prognosis based on health state probability estimation Hack-Eun Kim a,, Andy C.C. Tan a , Joseph Mathew a , Byeong-Keun Choi b a CRC for Integrated Engineering Asset Management, School of Engineering Systems, Queensland University of Technology, G.P.O. Box 2434, Brisbane, QLD 4001, Australia b Department of Energy and Mechanical Engineering, Institute of Marine Industry, Gyeongsang National University, 445 Inpyeong-dong, Tongyoung City, Gyeongnam-do 650-160, South Korea article info Keywords: Prognosis Degradation stage Support Vector Machine (SVM) Remaining useful life (RUL) High pressure LNG pump abstract In condition-based maintenance (CBM), effective diagnostic and prognostic tools are essential for main- tenance engineers to identify imminent fault and predict the remaining useful life before the components finally fail. This enables remedial actions to be taken in advance and reschedule of production if neces- sary. All machine components are subjected to degradation processes in real environments and they have certain failure characteristics which can be related to the operating conditions. This paper describes a technique for accurate assessment of the remnant life of bearings based on health state probability esti- mation and historical knowledge embedded in the closed loop diagnostics and prognostics system. The technique uses the Support Vector Machine (SVM) classifier as a tool for estimating health state proba- bility of machine degradation process to provide long term prediction. To validate the feasibility of the proposed model, real life fault historical data from bearings of High Pressure-Liquefied Natural Gas (HP-LNG) pumps were analysed and used to obtain the optimal prediction of remaining useful life (RUL). The results obtained were very encouraging and showed that the proposed prognosis system based on health state probability estimation has the potential to be used as an estimation tool for remnant life prediction in industrial machinery. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction An important objective of condition-based maintenance (CBM) is to determine the optimal time for replacement or overhaul of a machine. The ability to accurately predict the remaining useful life of a machine system is crucial for its operation and can also be used to improve productivity, prolong machine usage and enhance sys- tem safety. In CBM, maintenance is usually performed based on an assessment or prediction of the machine health instead of its ser- vice time, which leads to extended usage of the machine, reduced down time and enhanced operation safety. An effective prognostics programe will provide ample lead time for maintenance engineers to schedule a repair and to acquire replacement components before catastrophic failures occur. Recent advances in computing and information technology have accelerated the production capability of modern machines and reasonable progress has been achieved in machine fault diagnostics, but not in prognostics. Although today’s expert diagnostic engineers have significant information and experience about machine failure and degradation health states by continuously monitoring and analysing the machine condition in industry; unfortunately, well understood systematic methodologies and supporting systems on how to predict machine remnant life are still not available. The prognostic task still relies on human expert knowledge and experience. There- fore, there is an urgent need to continuously develop and improve prognostic models which can be implemented in intelligent main- tenance systems with minimum human involvement. Numerous prognostic models have been proposed and reported in technical literature, however most prognostic methodologies are still faced with the problem and ability to provide accurate long- term prediction for industrial application. Arguably, prognosis is considerably more difficult to formulate than diagnosis since its accuracy is subjected to stochastic processes that failure events are yet to occur. Current prognostic methods can be classified as being associated with one or more of the following two ap- proaches: data-driven and model-based. The data-driven approaches are derived directly from routinely monitored system operating data (such as calibration data, calori- metric data, spectrometric data, power, vibration and acoustic sig- nal, temperature, pressure, oil debris, currents and voltages). In many applications, measured input/output data is the major source of knowledge to understand the system degradation behav- iour. The data-driven approaches rely on the assumption that the statistical characteristics of data are relatively consistent unless a malfunctioning event occurs in the system (Vachtsevanos, Lewis, Roemer, Hess, & Wu, 2006). They are built based on past historical records and produce prediction outputs based on condition moni- toring (CM) data. These approaches are also based on statistical 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.11.019 Corresponding author. E-mail address: [email protected] (H.-E. Kim). Expert Systems with Applications 39 (2012) 5200–5213 Contents lists available at SciVerse ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

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Page 1: bearing fault.pdf

Expert Systems with Applications 39 (2012) 5200–5213

Contents lists available at SciVerse ScienceDirect

Expert Systems with Applications

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

Bearing fault prognosis based on health state probability estimation

Hack-Eun Kim a,⇑, Andy C.C. Tan a, Joseph Mathew a, Byeong-Keun Choi b

a CRC for Integrated Engineering Asset Management, School of Engineering Systems, Queensland University of Technology, G.P.O. Box 2434, Brisbane, QLD 4001, Australiab Department of Energy and Mechanical Engineering, Institute of Marine Industry, Gyeongsang National University, 445 Inpyeong-dong, Tongyoung City,Gyeongnam-do 650-160, South Korea

a r t i c l e i n f o

Keywords:PrognosisDegradation stageSupport Vector Machine (SVM)Remaining useful life (RUL)High pressure LNG pump

0957-4174/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.eswa.2011.11.019

⇑ Corresponding author.E-mail address: [email protected] (H.-E. Kim

a b s t r a c t

In condition-based maintenance (CBM), effective diagnostic and prognostic tools are essential for main-tenance engineers to identify imminent fault and predict the remaining useful life before the componentsfinally fail. This enables remedial actions to be taken in advance and reschedule of production if neces-sary. All machine components are subjected to degradation processes in real environments and they havecertain failure characteristics which can be related to the operating conditions. This paper describes atechnique for accurate assessment of the remnant life of bearings based on health state probability esti-mation and historical knowledge embedded in the closed loop diagnostics and prognostics system. Thetechnique uses the Support Vector Machine (SVM) classifier as a tool for estimating health state proba-bility of machine degradation process to provide long term prediction. To validate the feasibility of theproposed model, real life fault historical data from bearings of High Pressure-Liquefied Natural Gas(HP-LNG) pumps were analysed and used to obtain the optimal prediction of remaining useful life(RUL). The results obtained were very encouraging and showed that the proposed prognosis system basedon health state probability estimation has the potential to be used as an estimation tool for remnant lifeprediction in industrial machinery.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

An important objective of condition-based maintenance (CBM)is to determine the optimal time for replacement or overhaul of amachine. The ability to accurately predict the remaining useful lifeof a machine system is crucial for its operation and can also be usedto improve productivity, prolong machine usage and enhance sys-tem safety. In CBM, maintenance is usually performed based onan assessment or prediction of the machine health instead of its ser-vice time, which leads to extended usage of the machine, reduceddown time and enhanced operation safety. An effective prognosticsprograme will provide ample lead time for maintenance engineersto schedule a repair and to acquire replacement components beforecatastrophic failures occur. Recent advances in computing andinformation technology have accelerated the production capabilityof modern machines and reasonable progress has been achieved inmachine fault diagnostics, but not in prognostics.

Although today’s expert diagnostic engineers have significantinformation and experience about machine failure and degradationhealth states by continuously monitoring and analysing themachine condition in industry; unfortunately, well understoodsystematic methodologies and supporting systems on how to

ll rights reserved.

).

predict machine remnant life are still not available. The prognostictask still relies on human expert knowledge and experience. There-fore, there is an urgent need to continuously develop and improveprognostic models which can be implemented in intelligent main-tenance systems with minimum human involvement.

Numerous prognostic models have been proposed and reportedin technical literature, however most prognostic methodologies arestill faced with the problem and ability to provide accurate long-term prediction for industrial application. Arguably, prognosis isconsiderably more difficult to formulate than diagnosis since itsaccuracy is subjected to stochastic processes that failure eventsare yet to occur. Current prognostic methods can be classified asbeing associated with one or more of the following two ap-proaches: data-driven and model-based.

The data-driven approaches are derived directly from routinelymonitored system operating data (such as calibration data, calori-metric data, spectrometric data, power, vibration and acoustic sig-nal, temperature, pressure, oil debris, currents and voltages). Inmany applications, measured input/output data is the majorsource of knowledge to understand the system degradation behav-iour. The data-driven approaches rely on the assumption that thestatistical characteristics of data are relatively consistent unless amalfunctioning event occurs in the system (Vachtsevanos, Lewis,Roemer, Hess, & Wu, 2006). They are built based on past historicalrecords and produce prediction outputs based on condition moni-toring (CM) data. These approaches are also based on statistical

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Fig. 1. Two health states in similarity-based diagnostics and prognostics models.

H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213 5201

and learning techniques, as well as approaches including the the-ory of pattern recognition (Jianhui, Pattipati, & Kawamoto, 2003).Several signal based techniques used in conjunction with data-driven have been reported in the literature (Garga, Meclintic,Campbell, Yang, & Lebold, 2000; Swanson, 2001; Wang &Vachtsevanos, 1999; Wang & Wong, 2002; Yang, 2001; Zhang,Basseville, & Benveniste, 1994). These techniques mainly focuson monitoring of signals related to the system health by estimatingcertain parameters from the condition signals.

The most promising data-driven approach is based on artificialintelligent approaches. These approaches utilise statistical andlearning techniques, including the theory of pattern recognition,such as hybrid SVM-Bayesian Network (BN) model (Ramesh,Mannan, Poo, & Keerthi, 2003), Neuro-fuzzy model (Wang,Golnaraghi, & Ismail, 2004), Neural Networks (Gebraeel, Lawley,Liu, & Parmeshwaran, 2004; Shao & Nezu, 2002), Back PropagationNeural Network (BPNN) (Dong, Yu-Jiong, & Yang, 2004; Huanget al., 2007), Dynamic Wavelet Neural Network (DWNN) (Wang &Vachtsevanos, 2001), and Recurrent Neural Networks (RNNs) (Tse& Atherton, 1999; Yam, Tse, Li, & Tu, 2001). The advantage of data-driven techniques is their ability to transform high-dimensionalnoisy data into lower dimensional information for diagnostic/prog-nostic decisions. The main drawback of data-driven approaches isthat their efficacy is highly dependent on the quantity and qualityof system operational data.

Model-based approaches however, require an accurate mathe-matical model to be developed and use residuals as features, whereresiduals are the outcomes of consistency checks between thesensed measurements of a real system and the outputs of a math-ematical model (Vachtsevanos et al., 2006). Statistical techniquesare normally used to define thresholds to detect the presence offaults. Several statistical models have been reported recently, suchas Recursive Least Square (RLS) (Li et al., 1999), Proportional Inten-sity Model (PIM) (Vlok, Wnek, & Zygmunt, 2004), ProportionalHazards Models (PHMs) (Banjevic & Jardine, 2006; Gasmi, Love,& Kahle, 2003), and Hidden Markov Model (HMM) (Chinnam &Baruah, 2003). Model-based approaches are applicable in situa-tions where accurate mathematical models can be constructedfrom first principles. However, model-based approaches may notbe the most practical approach since the fault type in question isoften unique, varies from component to component, and is hardto be identified without interrupting the operation.

In general, the prognosis of machine failures entails large-grainof uncertainty because machine degradation is dynamic andundergoes a stochastic process usually consisting of a series of deg-radation states. The traditional condition-based diagnostics andprognostics are based on recognising indications of fault in thebehaviour of the machine failure. If signatures describing systembehaviour in the presence of a given fault are available from thehistorical condition data, it is possible to evaluate current machinecondition by quantitative assessment between the newly arrivedsignatures and historical failure behaviours.

Fig. 1 illustrates the conventional similarity-based technique forfault diagnostics and prognostics. The figure shows two healthstates in machine degradation. The most recent behaviour coversthe transients of normal and faulty conditions. This methodologycan provide the level of degradation and forecast a specific faultybehaviour for machine diagnostics and prognostics. Liu, Djurdja-novic, Ni, Casoetto, and Lee (2007) suggested the similarity basedmethod for manufacturing process diagnosis and performance fail-ure prediction. In their paper, similarities with historical data wereused to predict the probabilities of failure over time by evaluatingthe overlaps between predicted feature distributions and featuredistributions related to unacceptable equipment behaviour forlong-term prediction of process performance. However, this meth-od only considers two health states, namely Normal and Faulty

conditions. In real-life situations, machine faults normally gothrough various health degradation states until final failure. Accu-rate and precise prognosis of the time to failure of a failing compo-nent or subsystem need to consider the critical-state variablesassociated with the change of physical conditions.

In this paper, for accurate prediction of the remnant life of ma-chine, the authors propose a machine prognostics model based onhealth state probability estimation. The proposed prognostic mod-el considers the discrete health state probability in the machinedegradation process, which can effectively represent the dynamicand stochastic degradation of machine failure.

An effective prognosis requires performance assessment, devel-opment of degradation models, failure analysis, health manage-ment and prediction, feature extraction and historical knowledgeof faults (Lee, Ni, Djurdjanovic, Qiu, & Liao, 2006). In general, eachmachine system has its inherent characteristics that could be usedto identify the source of failure. Therefore, prior analysis of ma-chine characteristics and knowledge of failure pattern are essentialfor accurate prediction of remnant life.

In the proposed model, prior historical failure knowledge isembedded in the integrated diagnostics and prognostics system.The historical failure knowledge includes prior knowledge of faults,failure patterns and machine degradation process. Li et al. (1999)suggested that a reliable diagnostic model is essential for the over-all performance of a prognostics system. The outcome of diagnosismodule provides reliable information for the estimation of ma-chine health state and system redesign by employing the precisefailure pattern of the impending fault. Therefore, by using an inte-grated system of diagnosis and prognosis, pre-determined domi-nant fault obtained in the diagnostic process with prior historicalfailure knowledge can be used to improve the accuracy of progno-sis in estimating the remnant life.

The health state probability estimation is carried out throughexploring a full failure degradation process of the machine by opti-mal selection of the optimum number health degradation statesover time from new to final failure stages. The cases of using toomany health states in the degradation process can lead to theover-fitting problem of classification performance. On the otherhand, insufficient number of health states may results in under-fit-ting. Therefore, both cases can significantly affect the performanceof the classifier and will affect the remnant life prediction accuracy.In this work, the optimum number of health states is selectedthrough the investigation of classification results with severalhealth state cases.

With the historical knowledge, historical failure data and eventswill be applied to determine the number of discrete failure degrada-tion stages. This approach produces an effective feature extractionfor diverse faults and the construction of discrete degradationstages for the impending faults. With this new approach, theauthors aim to develop a practical prognostics tool which couldbe used in on-line condition monitoring to predict the remaininguseful life (RUL) of a failing component.

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In the proposed model, intelligent fault diagnosis and healthstates estimation of discrete failure degradation is performed usinga range of classification algorithms, such as Artificial Neural Net-works (ANNs), Support Vector Machines (SVMs), Classificationand Regression Trees (CART) and Random Forests, Linear Regres-sion and others. Among the available classifiers, SVMs shows out-standing performance in the classification process compared withthe other classifiers (Niu, Han, Yang, & Tan, 2007a; Niu et al.,2007b; Pal & Mather, 2004; Yan & Xue, 2008). In this work, thehealth state probability estimations were conducted using the clas-sification ability of SVM and with subsequent machine prognosticsbeing conducted based on the probability distributions of eachhealth states. To validate the feasibility of the proposed model,bearing fault cases of High Pressure-Liquefied Natural Gas (HP-LNG) pumps were analysed to obtain the failure degradation pro-cess. To select effective features for the classification of healthstates, the distance evaluation technique was employed. Severalhealth states were investigated to determine the optimal numberof health states (degradation stages) for accurate estimation of ma-chine remnant life. The results show that the proposed prognosismodel with five degradation stages has the potential to be usedas an estimation tool for machine remnant life prediction in reallife industrial applications.

The remaining part of the paper is organised as follows. Section2 presents the proposed prognosis model based on health stateprobability estimation with embedded historical knowledge. InSection 3, the case study using bearing failure cases of HP-LNGpumps is presented. We conclude the paper in Section 4 with asummary for future research work.

2. Prognostics model based on health state probabilityestimation

In this research, an innovative prognostics model based onhealth state probability estimation with embedded historicalknowledge is proposed.

Fig. 2 illustrates the conceptual integration of diagnostics andprognostics with embedded historical knowledge. For accurateassessment of machine health, a significant amount of past knowl-edge of the assessed machine is required because the correspond-ing failure modes must be known in advance and well-described inorder to assess the current machine state (Jardine, Lin, & Banjevic,2006). In this model, through prior analysis of the historical dataand events, major failure patterns that affect the entire life of themachine are identified for diagnostics and prognostics. The histor-ical knowledge to be used in diagnostics and prognostics will pro-vide key information on the organisation of this system. Forexample, it could be used to determine appropriate techniquesfor signal processing and feature extraction.

Fig. 3 presents the flowchart of the integration of historicalknowledge, diagnostics and prognostics systems for remnant lifeprediction. The proposed system consists of three sub-systems,

Fig. 2. Closed loop prognostic system.

namely, historical knowledge, diagnostics and prognostics. The en-tire sequence includes condition monitoring, classification ofimpending fault, health state estimation and prognostics, and isperformed by linking them to case based historical knowledge.Through prior analysis of historical data, the historical knowledgeprovides useful information for the selection of suitable conditionmonitoring techniques, such as sensor (data) type and signal pro-cessing techniques which are dependent on machine fault type.In the proposed model, feature extraction and selection techniquesin the diagnostics module are linked with historical knowledge.The pre-determined discrete failure degradation of the machinewhich is located in the historical knowledge module can be usedto estimate the health state of the machine which is located inthe prognostics module. The final output of the prognostics moduleof certain impending faults can also be accumulated to update thehistorical knowledge. This accumulated historical knowledge canthen be used to update the system and improve the prognosticmodel by providing reliable posterior degradation features for di-verse failure modes and fault types.

The detail of these three modules, historical knowledge, diag-nostics and prognostics in this integrated system are described inthe following sections.

2.1. Historical knowledge

In this model, historical knowledge is closely related to machinefault diagnostics and prognostics as depicted in Fig. 3. More specif-ically, prior analysis of historical data and failure pattern in termsof historical knowledge provides key references for fault isolationof a particular fault and health/degradation state estimation. Thehistorical knowledge provides useful information for effectiveimpending fault detection and isolation. For example, past faulthistorical data can be used for intelligent fault classification perfor-mance by providing the training set of historical faults in machine.This module provides the following three types of diagnostic/prog-nostic information as shown by the three branches in Fig. 3.

(1) Analysis of historical data and event: provides past failure pat-tern information for the selection of appropriate signal pro-cessing and feature extraction techniques depending onfault types and degradations.

(2) Main faults: given a typical main fault data of the machine, itis possible to determine the impending fault type that hasoccurred by providing the training set for intelligent faultclassification (i.e., fault detection and isolation).

(3) Degradation stages of each failure pattern: analysis of pastcondition monitoring data provides qualitative understand-ing about the sequence of discrete failure degradation stagesof each failure pattern for the estimation of the currenthealth state of the machine.

2.2. Diagnostics

The diagnostics sub-system follows the typical procedure ofintelligent fault diagnostics including condition monitoring, signalprocessing, feature extraction and fault classification in this inte-grated system. In general, raw data acquired from sensors requiresignal processing to obtain appropriate features. A range of fea-tures is calculated to cover the preliminary impending faults ofthe machine. Effective selection of features is necessary to avoidthe problem of dimensionality and high training error value whichmay cause a significant amount of computer burden and over-fit ofdata training, known as the Feature Selection Problem (Weston,Chapelle, Poggio, 2000).

The goal of dimensionality reduction is to reduce high-dimen-sional data samples into a low-dimensional space while preserving

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Fig. 3. Flowchart of the integration of historical knowledge, diagnostic system and prognostics system based on health state probability estimation.

H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213 5203

most of the intrinsic information contained in the data set. Oncedimensionality reduction is carried out appropriately, compactrepresentation of the data for various succeeding tasks such asvisualisation and classification can be utilised. An effective featureselection can lead to better performance of the predictor, cost-effective and better understanding of the underlying process thatgenerated the data (Guyon & Elisseeff, 2003). Several feature selec-tion algorithms have been proposed in recent literatures as re-viewed in references (Guyon & Elisseeff, 2003; Weston et al., 2000).

In this paper, for the outstanding performance of fault classifi-cation and the reduction of computational effort, effective featureswere selected using the distance evaluation technique of featureeffectiveness introduced by Knerr et al. (Hwang & Yang, 2004;Knerr, Personnaz, & Dreyfus, 1990). After feature extraction (fea-ture selection), predetermined major fault data were trained usingclassification algorithms. Through this training of major faults ofmachine system, current impending faults can be isolated andidentified in the diagnostics module.

The diagnostic procedure of this paper follows the typical intel-ligent fault classification steps, but the output of diagnostics doesnot provide any information on the severity of faults. Instead, amore precise failure pattern from a number of historical degrada-tion data in historical knowledge module can be employed in theprognostic module through this verification (isolation) of impend-ing fault in the diagnostic module.

Fig. 4. Illustration of discrete health

2.3. Health state probability estimation and RUL prediction

After identifying the impending fault in the diagnostic module,the discrete failure degradation stages determined in historicalknowledge module are employed in the health state estimationmodule as depicted in Fig. 3. The proposed prognostic model in thispaper assumed that machine degradation consists of a series of de-graded states (health states) which is essential as machine failureis nonlinear or in the presence of dynamic and stochastic process.Fig. 4 illustrates the discrete health states of machine degradation.The discrete health states can effectively represent the dynamic ofthe failure process according to the changes of physical conditionin machine degradation.

The historical failure patterns also can be used to determine theoptimum number of health stages for estimation of the machineremnant life. In the estimation of health state, predetermined dis-crete degradation stages were trained before being used to test thecurrent health state. Through prior training of each failure degra-dation stage, current health condition is obtained in terms of prob-abilities of each health state of the machine using the capability ofclassification algorithms. At the end of each prognostic process, theoutput information will also be used to update the historicalknowledge. In this paper, the capability of SVM classifier is em-ployed for the health state estimation to be used in predicting rem-nant life of machine. The following subsections provide a brief

states in machine degradation.

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5204 H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213

summary of the proposed health state estimation methodologyand URL prediction using the SVM classifier.

2.3.1. Application of SVM for health state probability estimationSVM is based on the statistical learning theory introduced by

Vapnik and his co-workers (Vapnik, 1995, 1999). SVM is alsoknown as maximum margin classifier with the abilities of simulta-neously minimising the empirical classification error and maximis-ing the geometric margin. Due to its excellent generalisationability, a number of applications have been addressed with the ma-chine learning method in the past few years (Niu et al., 2007a,2007b; Pal & Mather, 2004; Yan & Xue, 2008). The theory, method-ology and software of SVM are readily available in references (Cris-tianini & Shawe-Taylor, 2000; Hsu & Lin, 2002; Vapnik, 1995,1999). Although SVMs were originally designed for binary classifi-cation, multi-classification can be obtained by the combination ofseveral binary classifications. Several methods have been pro-posed, such as ‘‘one-against-one’’, ‘‘one-against-all’’, and directedacyclic graph SVMs (DAGSVM). Hsu and Lin (2002) presented acomparison of these methods and pointed out that the ‘‘one-against-one’’ method is suitable for practical use than the othermethods. Consequently, in this study, the authors employed the‘‘one-against-one’’ method to perform the classification of discretefailure degradation stages.

For given observations~xt ¼ ðxt1; xt2; . . . ; xtmÞ, m is the number ofobservations and t is the time index. Let yt be the health state(class) at time (t) and yt = 1,2, . . .,n, where n is the number of healthstates. For multi-classification of n-health state (class) event, the‘‘one-against-one’’ method has n(n � 1)/2 classifiers, where eachclassifier is trained on data from two classes. For training data fromthe ith and the jth classes, SVM solves the following classificationproblem:

minimise :12kwijk2 þ C

Xtnij

t ðwijÞT ð1Þ

subject to : ðwijÞT/ð~xtÞ þ bij P 1� nijt ; if yt ¼ i;

ðwijÞT/ð~xtÞ þ bij6 �1þ nij

t ; if yt ¼ j;

nijt P 0; j ¼ 1; 2; . . . ; l

where the training data~xt is mapped to a higher dimensional spaceby function /; /ð~xtÞ is the kernel function, (xt,yt) is the ith or jthtraining sample, w 2 Rn is the coefficient vector, b 2 R is the biasof the hyper-plane, nij

t is the slack variable and C is the penaltyparameter. For detailed explanations on the weighting factors, slackvariable and penalty parameter the reader is referred to Vapnik(1995).

There are different methods which can be used in future testingafter all the n(n � 1)/2 classifiers are constructed. After a series oftests, the decision is made using the following strategy: if signðwijÞT/ð~xtÞ þ bij says ~x is in the ith class, then the vote for the ith

Fig. 5. Illustration of health state probability distrib

class is added by one. Otherwise, the jth value is increased byone. Then the jth class is predicted using the largest vote. The vot-ing approach described above is also called as Max Win strategy(He, Kong, & Shen, 2005). From the above SVM multi-classificationresult (yt), we obtain the probabilities of each health states (Si)using the smooth window and indicator function (Ii) as following:

ProbðSt ¼ ij~xt ; . . . ; ~xtþu�1Þ ¼Xtþu�1

j¼t

IiðyjÞ=u ð2Þ

IiðyÞ ¼0 y – i

1 y ¼ i

where St is the smoothed health state and u is the width of thesmooth window.

In the given smooth window subset, the sum of each healthstate probabilities is shown in Eq. (3)

Xm

i¼1

PrðSt ¼ ij~xt ; . . . ; ~xtþu�1Þ ¼ 1 ð3Þ

From the result of each health probabilities, the probability distri-bution of each health state subject to time (t) can be obtained asillustrated in Fig. 5.

Fig. 5 shows an example of health state probability distributionwhich has a simple linear degradation process consisting of n num-ber of discrete health states. As the probability of one state de-creases, the probability of the next state increases. At the pointof intersection there is a region of over-lap between the two healthstates, which is a natural phenomenon in linear degradation pro-cess. However, the probability distribution of failure process iscomplex due to the dynamic and stochastic degradation processin a real environment.

2.3.2. Prediction of RULAfter the estimation of current health state in term of probabil-

ity distribution of each health state, the RUL prediction is per-formed. For the prediction of machine remnant life, twoparameters are used in the proposed model, such as each healthstate probabilities at a certain time t and historical remaining lifeat each trained health state. The probabilities of each health stateat certain time t provide a real time failure index in the machinefailure process for RUL prediction. The RUL prediction of machinecan be expressed as Eq. (4) accordingly,

RULðTtÞ ¼Xm

i¼1

PrðSt ¼ i~xt; . . . ; ~xtþu�1Þj � si ð4Þ

where St is current probabilities of each health state at time t, si ishistorical remaining life at each trained health state i and m is num-ber of health state.

utions of a simple linear degradation process.

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H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213 5205

At the end of each prognostics process, the output informationis used to update the historical knowledge for further improve-ment of failure analysis by providing reliable posterior degradationcharacteristics for diverse failure modes and fault types.

3. Case study using bearing failure data of HP-LNG pumps

In this industrial case study, RUL prediction tests were con-ducted using bearing failure data of HP-LNG pumps to validatethe feasibility of integrating health state probability estimationwith historical knowledge for accurate long term failure prediction.

3.1. High pressure LNG pump

Liquefied natural gas (LNG) takes up six hundreds of the volumeof natural gas at or below the boiling temperature (�162 �C),which can be used for storage and easy transportation. In an LNGreceiving terminal, HP-LNG pumps are used to boost the LNG pres-sure to 80 bar for evaporation of LNG into highly compressed nat-ural gas in order to be delivered via a pipeline network across largedistances.

The numbers of HP-LNG pumps determine the amount of LNGto be delivered at the receiving terminal. It is critical equipmentin the LNG production process and need be maintained to keep

Fig. 6. Pump schematic and vi

the operation at optimal conditions. As a result, vibration and noiseof HP-LNG pumps are regularly monitored and managed based onpredictive maintenance techniques. Fig. 6 shows the HP-LNG pumpschematic and vibration measuring points.

As shown in Fig. 6, HP-LNG pumps are enclosed within a suctionvessel and mounted with a vessel top plate. Three ball bearings areinstalled to support the entire dynamic load of the integrated shaftof pump and motor. The submerged motor and bearings are cooledand lubricated by a predetermined portion of the LNG beingpumped. For condition monitoring of the pump, two accelerome-ters are installed on the housing near the bottom bearing assemblyand in two radial directions. These high-pressure LNG pumps aresubmerged and operate at super cooled temperatures. They areself-lubricated at both ends of the rotor shaft and tail bearingsusing LNG. Due to the low viscous value (about 0.16cP) of LNG,the three bearings of the pump are poorly lubricated and thesebearings must be specially designed. Table 1 shows the pumpspecifications.

It is very difficult to detect the symptom of pump failure at anincipient stage because certain bearing components can result in ra-pid bearing failure due to poor lubricating conditions and high oper-ating speed (3600 rpm). Hence, in the case of an abnormal problemoccurring, one would not have sufficient time to analyse the possi-ble root cause of pump failure. Furthermore, due to material prop-erty variations of cryogenic pumps at super low temperatures and

bration measuring points.

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Table 1Pump specifications.

Capacity Pressure Impeller stage Speed Voltage Rating

241.8 m3/h 88.7 kg/cm2 g 9 3585 rpm 6600 V 746 kW

Upper bearing No. Bottom bearing No. Tail bearing No. Rotor bar quantity Diffuser vane No. Current

6314 6317 6311 41 EA 8 EA 84.5 A

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difficulties in measuring the vibration signals on the submergedpump housing, there are some restrictions for diagnosis of pumphealth and the study of vibration behaviour. Hence, there is a needto use the historical failure knowledge of failure patterns for accu-rate estimation of remnant life. Accurate long term prediction offailures is essential for safe operation and prolonging utilisation ofthe pump’s production capability.

3.2. Vibration data acquisition of bearing failure

For machinery fault diagnostics and prognostics, signals such asvibration, temperature and pressure are commonly used. In this re-search, the authors used vibration data because it was readilyavailable and the trend of vibration features closely related tothe bearing failure process. Fig. 7 shows the frequency spectrumplots of P301D pump. The bearing resonance component increasedover the period of the operation hours. The first symptom of apump failure was detected as early as 14 months before the bear-ing final failure. Other bearing fault components appeared progres-sively until the bearing failed completely.

Vibration data were collected through two accelerometers in-stalled on the pump housing as shown in Fig. 6. The vibration datafrom two HP-LNG pumps of identical specification were used forprediction of the remaining useful life. Due to the random opera-tion of the pumps in order to meet the total production target,there were some restrictions to collect complete data over the en-tire life of the pump. The acquired vibration data are summarisedin Table 2. As shown in Table 2, a total 136 vibration samples forP301 C and 120 vibration samples for P301 D were collected duringthe full range of operation over the life of the pump, for trainingand testing of the proposed prognostic model, respectively.

Fig. 8 shows the damage of (a) the outer raceway spalling ofP301 C and (b) inner raceway flaking of P301 D, respectively.Although these two bearing faults had different fault severitieson the inner race and the outer race, these faults occurred on bear-ings located at the same location of the pump.

3.3. Features calculation and selection

In this paper, the authors calculated 10 statistical parametersusing the time domain data. These feature parameters were mean,rms, shape factor, skewness, kurtosis, crest factor, entropy estima-tion, entropy estimation error, histogram lower and upper. In addi-tion to these parameters, four parameters (rms frequency,frequency centre, root variance frequency and peak) in the fre-quency domain were also calculated. A total of 28 features (14parameters, 2 positions) were calculated as shown in Table 3.

Although bearing faults are primary causes of machine break-down, a number of other component faults can also be embeddedin the bearing fault signals which make it problematic in bearingdiagnosis/prognosis. Currently, a number of physical model-basedprognosis have been reported which focused on identifying appro-priate features of damages or faults. However, current researchesof prognostics only concentrate on specific component degrada-tions and do not include other types of fault. In this paper, theauthors aim to address a generic and scalable prognosis modelwhich is applicable for different faults in identical machines. The

conventional statistical parameters from vibration signals are usedto establish the generic and scalable prognosis model.

In order to select optimal parameters that can fully represent afailure degradation process, effective features were selected usingthe distance evaluation technique introduced by Knerr et al.(1990), Hwang and Yang (2004) as depicted below. The reductionof feature dimension also leads to better performance of SVMand reduction in computational effort.

The average distance (di,j) of all the features in state i can be de-fined as follows:

di;j ¼1

N � ðN � 1ÞXN

m;n¼1jPi;jðmÞ � Pi;jðnÞj ð5Þ

The average distance ðd0i;jÞ of all the features in different states is

d0i;j ¼1

M � ðM � 1ÞXM

m;n¼1jPai;m � Pai;nj ð6Þ

where, m, n = 1,2, . . .N, m – n, Pi,j: eigen value, i: data index, j: classindex, a: average, N: number of feature and M: number of class.

When the average distance (di,j) inside a certain state is smalland the average distance ðd0i;jÞ between different states is big, theseaverages represent that the features are well separated among theclasses. Therefore, the distance evaluation criteria (ai) is defined as

ai ¼ d0ai=dai ð7Þ

The optimal features can be selected from the original featuresets according to the large distance evaluation criteria (ai). In thiswork, a total 14 of features were used to extract effective featuresfrom each signal sample measured at identical accelerometer posi-tion. The distance evaluation criteria (ai) of 14 features in this workare shown in Fig. 9, with almost zero value for histogram upper(No. 9). In order to select the effective degradation features, theauthors defined a value greater than 1.3 of normalised distanceevaluation criteria, ai/aN P 1.3, where ai is distance evaluation cri-teria and aN is mean value of ai. The ratio of 1.3 is selected based onpast historical records for this particular bearing/pump. From theresults, the authors selected three features, Kurtosis {5}, Entropyestimation value {7} and Entropy estimation error value {8} forhealth state estimation. They meet the large distance evaluationcriteria (ai) as compared with other features. These features couldminimise the classification training and test errors of each healthstate.

Fig. 10 shows the feature trends of kurtosis, entropy estimationand entropy estimation error value, respectively. All the three fea-tures show increasing trends which indicate the failure degrada-tion process of the machine over time.

3.4. Selection of number of health states for training and classification

To select the optimal number of health states to represent thebearing degradation process, several number of health stages wereinvestigated using the data sets of P301 D for training and predic-tion tests. As the basic kernel function of SVM, a polynomialfunction was used in this paper. Multi-class classification using‘‘one-against-one’’ was applied to perform the classification ofbearing degradation as described in Section 2. Sequential minimal

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Fig. 7. Spectrum plots of P301D pump from 14 months to 1 week before final bearing failure.

H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213 5207

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Table 2Acquired vibration data of the LNG pump.

Machine No. Total operation hours Reason of remove and root cause No of sample data Sampling frequency (Hz)

P301 C 4698 High vibration and outer raceway sampling 136 12,800P301 D 3511 High vibration and Inner raceway flaking 120 12,800

Fig. 8. Outer and inner race bearing failures.

Table 3Statistical feature parameters and attributed label.

Position Time domain parameters Frequency domain parameters

Acc. (A) Mean {1}, RMS {2}, Shape factor {3}, Skewness {4}, Kurtosis {5}, Crest factor {6} RMS frequency value {11}, Frequency centre value{12}

Acc. (B) Entropy estimation value {7}, Entropy estimation error {8}, Histogram upper {9} and Histogram lower{10}

Root variance frequency {13} and Peak value {14}

Note: {} represents the feature number.

Fig. 9. Distance evaluation criteria of features.

5208 H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213

optimisation (SMO) proposed by Platt (1999) was used to solve theSVM classification problem. For the selection of optimal kernelparameters, the authors used the cross-validation technique to ob-tain effective classification performance suggested by Hsu, Chang,Lin (2005). This was done to avoid over-fitting or under-fitting.The training and prediction errors against the number health states

are plotted in Fig. 11. The average prediction error value was calcu-lated using the following equation.

Average prediction errorð%Þ ¼PN

i¼1jl0i � lijN

!� 100 ð8Þ

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Fig. 10. Feature trends of selected features.

H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213 5209

where N is number of data, l0 is actual RUL (%) and li is estimatedRUL (%).

A total of nine different states were investigated, ranging fromtwo to ten states. As shown in Fig. 11, although low number of healthstates had low classification training error values, they showed highprediction error values compared with other higher number ofhealth states. On the contrary, high number of health states alsohad high training error values but relatively low prediction error val-ues. From this result, the authors selected five health states as theoptimal number of health states. Beyond five health states the train-ing error values increased rapidly and without significant decreasein the prediction error values. The training error and prediction errorvalues of using five states were 10% and 5.6%, respectively.

Table 4 shows the training data sets of the five selected degra-dation states used in this work and with eight sets of samples in

each state using three selected features. Initially (Stage 1) the per-centage of RUL is almost 100% (99.89%) and progressively reducedto 3.02% in stage 5.

3.5. RUL prediction

In the prediction of bearing remaining useful life, closed andopen tests were conducted. The closed test was involved usingidentical data sets for model training and prediction. On the otherhand, different test data sets were applied in the open test. Identi-cal training data sets were used in both tests.

In the closed test, the five states were trained using the listedtraining data sets shown in Table 4, and full data sets from P301D (136 data sets) were tested to obtain the probabilities of the five

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Fig. 11. Result of investigation to determine optimal number of health states.

Table 4Classification training data sets for the five degradation states using the three selectedfeatures [P301D].

Stage no. No. of samples (u) Average operation hours (si) RUL (%)

1 1–8 4 99.89%2 25–32 503 85.67%3 41–48 843 75.99%4 81–88 2501 28.77%5 121–128 3405 3.02%

5210 H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213

degradation states. Fig. 12 shows the probability distribution of thefive health states of P301 D. The first state probability starts at100% and decreases as long as the next state probability increases.For example, the first state (solid lines) shows the probabilitiesdropping and increasing again until about 90% and eventuallydropping to zero (at sample 30). Simultaneously the second state(dotted lines) reached 100%. Some overlaps between the statesand non uniformity of the distribution can be explained due to dy-namic and stochastic degradation processes. The uncertainty ofmachine health condition or inappropriate data acquisition in areal environment could also be factors. The entire probabilities ofeach state follow a non-linear degradation process and are dis-tinctly separated.

In the open test, similar bearing fault data (P301 C), which con-sisted of 120 sample sets, was tested to obtain the probability dis-tribution of each health state using identical training data sets

Fig. 12. Probability distribution of each

shown in Table 4. Fig. 13 shows the probability distributions ofthe five health states of P301 C. Similar non-linear probabilitiesdistribution and overlaps between states are also observed dueto reasons explained above.

The machine remnant life of bearing failure was estimatedusing historical operation hours (si) of each training data sets de-scribed in Table 4 and their probabilities evaluated using Eq. (4).Fig. 14 shows the results of closed tests in estimating the bearingremnant life and its comparison with the actual RUL. As shownin Fig. 14, although there are some discrepancies, the overall trendof the estimated RUL follows the gradient of the actual remaininguseful life of the machine. The average prediction accuracy was94.4% using Eq. (9) over the entire range of the data set. The esti-mated RUL at the final state matched closely to the actual RUL.

Average prediction accuracyð%Þ

¼ 1�PN

i¼1jl0i � lijN

!� 100 ð9Þ

where N is number of sample, l0 is actual RUL(%), and li is esti-mated RUL(%).

Fig. 15 shows the results of open test in estimating the bearingremnant life and its comparison with the actual RUL. There is alarge difference in remnant life prediction at the initial degradationstates as shown in Fig. 15. In the open tests, the estimated RUL timewas obtained based on the training data sets (P301 D) which had3511 h in total operation while the actual operating time of P301C is 4698 h. This causes the discrepancy between the actual RUL

health state [Closed Test, P301 D].

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Fig. 13. Probability distribution of each health state [Open Test, P301 C].

Fig. 14. Comparison of actual RUL and estimated RUL [Closed Test, P301 D].

H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213 5211

and the estimated RUL at the beginning of the test. However, as itapproaches the final bearing failure, the estimated RUL matchedvery closely to the actual remaining useful life than those in theinitial and middle states.

In this case study, several tests using different health stateswere conducted to verify the optimum number of health states,ranging from two states to ten states using the same test data(P301 C). Fig. 16 shows the test result of training and prediction er-rors of these health states. Health state numbers from two to five

Fig. 15. Comparison of actual RUL and e

show high prediction errors and settled down at about 7.45% errorat state No. 5, while the training error increases as the number ofstates increases and stabilised between states Nos. 4 and 5. How-ever, beyond five states, the training error values increased rapidlyin the classification while the average prediction errors remain rel-atively constant. Therefore, the selected five health states wereverified as the optimal number of health states for the estimationof bearing health probability. It has to be noted that differenthealth stages need to be evaluated for different case studies.

stimated RUL [Open Test, P301 C].

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Fig. 16. Training and prediction values of several health states [P301 C].

5212 H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213

4. Conclusion

This paper has proposed an innovative bearing fault prognosisbased on health state probability estimation. Through prior analy-sis of historical failure data, discrete failure degradation stageswere employed to estimate the health state probability for accu-rate long term machine prognosis. This implementation providesthe severities of impending faults and estimates the probabilityof current machine health state for RUL prediction. By employingexisting classification algorithms, a number of damage sensitivefeatures can be used to estimate current machine health state inthe feature space. To verify the proposed model, bearing failuredata from HP-LNG pumps were used to extract prominent featuresand to determine the probabilities of degradation states. The selec-tion of number of optimal health states of bearing failure is vital toavoid high training error with no improvement in the predictionaccuracy. To select the optimal number of health states of bearingfailure, several health states were investigated. The health stateprobability estimation was carried out using a full failure degrada-tion process by optimally selecting the number of health state fromnew to final failure stages. The result from an industrial case studyindicates that the proposed method can provide accurate estima-tion of bearing health condition and assist in the long-term predic-tion of bearing remnant life. The proposed model also effectivelyrepresents the dynamic and stochastic degradation process ofbearing failure. The knowledge of failure patterns and physicaldegradation from different historical data of machine faults stillneeds further investigation.

Acknowledgements

This research was conducted with financial support from QUT-International Postgraduate Award and the CRC for Integrated Engi-neering Asset Management, established and supported under theAustralian Government’s Cooperative Research CentresProgramme.

References

Banjevic, D., & Jardine, A. K. S. (2006). Calculation of reliability function andremaining useful life for a Markov failure time process. IMA Journal ofManagement Mathematics, 17, 115–130.

Chinnam, R. B., & Baruah, P. (2003). Autonomous diagnostics and prognosticsthrough competitive learning driven HMM-based clustering. In Proceedings ofthe international joint conference on neural networks (pp. 2466–2471).

Cristianini, N., & Shawe-Taylor, N. J. (2000). An Introduction to Support VectorMachines. Cambridge: Cambridge University Press.

Dong, Y.-L., Yu-Jiong, G., & Yang, K. (2004). Research on the Condition BasedMaintenance Decision of Equipment in Power Plant. in Machine Learning andCybernetics.

Garga, A. K., Meclintic, K. T., Campbell, R. L., Yang, C. C., & Lebold, M. S. (2000).Hybrid reasoning for prognostic leaning in CBM systems. IEEE, 2957–2969.

Gasmi, S., Love, C. E., & Kahle, W. (2003). A general repair, proportional-hazards,framework to model complex repairable systems. IEEE Transactions onReliability, 52, 26–32.

Gebraeel, N., Lawley, M., Liu, R., & Parmeshwaran, V. (2004). Residual lifepredictions from vibration-based degradation signals: A neural networkapproach. IEEE Transactions on Industrial Electronics, 51, 694–700.

Guyon, I., & Elisseeff, A. (2003). An introduction to variable and feature selection.Journal of Machine Learning Research, 3, 1157–1182.

He, L. M., Kong, F. S., Shen, Z. Q., (2005). Multiclass SVM based on land coverclassification with multisource data. In Proceedings of the fourth internationalconference on machine learning and cybernetics (pp. 3541–3545).

Hsu, C. W., Chang, C. C., & Lin, C. J. (2005). A practical guide to support vectorclassification, in Technical Report, Department of Computer Science andInformation Engineering, National Taiwan University. Available at: <http://www.csie.ntu.edu.tw/’cjlin/papers/guide/guide.pdf>.

Hsu, C. W., & Lin, C. J. (2002). A comparison of methods for multiclass support vectormachines. IEEE Transaction on Neural Network, 13, 415–425.

Huang, R., Xi, L., Li, X., Richard Liu, C., Qiu, H., & Lee, J. (2007). Residual lifepredictions for ball bearings based on self-organizing map and backpropagation neural network methods. Mechanical Systems and SignalProcessing, 21, 193–207.

Hwang, W. W., & Yang, B. S. (2004). Fault diagnosis of rotating machinery usingmulti-class support vector machines. in Korea Society for Noise and VibrationEngineering, 14, 1233–1240.

Jardine, A. K. S., Lin, D., & Banjevic, D. (2006). A review on machinery diagnostics andprognostics implementing condition-based maintenance. Mechanical Systemand Signal Processing, 20, 1483–1510.

Jianhui, L., Namburu, M., Pattipati, K. Liu, Q., Kawamoto, M., & Chigusa, S. (2003).Model-based prognostic techniques. In Proceedings of the AUTOTESTCON 2003.IEEE systems readiness technology conference (pp. 330–340).

Knerr, S., Personnaz, L., & Dreyfus, G. (1990). Single-layer learning revisited: Astepwise procedure for building and training a neural network. In J. Fogelman(Ed.), Neuro-computing: Algorithms. Architectures and Applications. New York:Springer-Verlag.

Lee, J., Ni, J., Djurdjanovic, D., Qiu, H., & Liao, H. (2006). Intelligent prognostics toolsand e-maintenance. Computers in Industry, 57, 476–489.

Li, Y., Billington, S., Zhang, C., Kurfess, T., Danyluk, S., & Liang, S. (1999). AdaptivePrognostics for Rolling Element Bearing Condition. Mechanical Systems andSignal Processing, 13, 103–113.

Liu, J., Djurdjanovic, D., Ni, J., Casoetto, N., & Lee, J. (2007). Similarity based methodfor manufacturing process performance prediction and diagnosis. Computers inIndustry, 58, 558–566.

Niu, G., Han, T., Yang, B. S., & Tan, A. C. C. (2007a). Multi-agent decision fusion formotor fault diagnosis. Mechanical Systems and Signal Processing, 21,1285–1299.

Niu, G., Son, J. D., Widodo, A., Yang, B. S., Hwang, D. H., & Kang, D. S. (2007b). Acomparison of classifier performance for fault diagnosis of induction motorusing multi-type signals. SAGE Publications.

Pal, M., & Mather, P. M. (2004). Assessment of the effectiveness of support vectormachines for hyperspectral data. Future Generation Computer Systems, 20,1215–1225.

Platt, J. (1999). Fast training of support vector machines using sequential minimaloptimization. In B. Scholkopf et al. (Eds.), Advances in Kernel Methods-SupportVector Learning. Cambridge: MIT Press.

Ramesh, R., Mannan, M. A., Poo, A. N., & Keerthi, S. S. (2003). Thermal errormeasurement and modelling in machine tools, Part II. Hybrid Bayesiannetwork-support vector machine model. International Journal of Machine Tools& Manufacture, 43, 405–419.

Shao, Y., & Nezu, K. (2002). Prognosis of remaining bearing life using neuralnetworks. Proceedings of the Institution of Mechanical Engineers. Part I: Journalof Systems and Control Engineering, 217–230.

Swanson, D. (2001). A general prognostic tracking algorithm for predictivemaintenance. In Proceedings of the IEEE international conference on aerospace(Vol. 6, pp. 2971–2969).

Page 14: bearing fault.pdf

H.-E. Kim et al. / Expert Systems with Applications 39 (2012) 5200–5213 5213

Tse, P., & Atherton, D. (1999). Prediction of machine deterioration using vibrationbased fault trends and recurrent neural networks. Transactions of the ASME:Journal of Vibration and Acoustics, 121, 355–362.

Vachtsevanos, G., Lewis, Frank., Roemer, M., Hess, A., & Wu, B. (2006). Intelligentfault diagnosis and prognosis for engineering systems. New Jersy: John Wiley &Sons, Inc.

Vapnik, V. N. (1995). The nature of statistical learning theory. New York: Springer-Verlag.

Vapnik, V. N. (1999). An overview of statistical learning theory. IEEE Transactions onNeural Networks, 10(5), 988–999.

Vlok, P.-J., Wnek, M., & Zygmunt, M. (2004). Utilising statistical residual lifeestimates of bearings to quantify the influence of preventive maintenanceactions. Mechanical Systems and Signal Processing, 18, 833–847.

Wang, P., & Vachtsevanos, G. (1999). Fault prognosis using dymamic wavelet neuralnetworks. In Proceedings of the maintenance and reliability conference, MARCON.

Wang, W. Q., Golnaraghi, M. F., & Ismail, F. (2004). Prognosis of machine healthcondition using neuro-fuzzy systems. Mechanical Systems and Signal Processing,18, 813–831.

Wang, P., & Vachtsevanos, G. (2001). Fault prognostics using dynamic waveletneural networks. AI EDAM, 15, 349–365.

Wang, W., & Wong, A. (2002). Autoregressive model based gear fault diagnosis.Journal of Vibration and Acoustics, 124, 172–179.

Weston, J., Mukherjee, S., Chapelle, O., Pontil, M., Poggio, T., & Vapnik, V. (2000).Feature selection for SVMs. Proceedings of the advances in neural informationprocessing systems (vol. 12, pp. 526–532). MIT Press.

Yam, R. C. M., Tse, P. W., Li, L., & Tu, P. (2001). Intelligent Predictive Decision SupportSystem for CBM. The International Journal of Advanced Manufacturing Technology,17, 383–391.

Yan, W., & Xue, F. (2008). Jet engine gas path fault diagnosis using dynamic fusion ofmultiple classifiers. In Proceedings of the international joint conference on neuralnetworks (pp. 1585–1591).

Yang, W. (2001).Toward dynamic model-based prognostics for transmission gears.In Proceedings of the SPIE Conference (Vol. 4733, pp. 157–167).

Zhang, Q., Basseville, M., & Benveniste, A. (1994). Early warning of slight changes insystems. Automatica, 30, 95–114.