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2009 15: 1079 originally published online 20 March 2009Journal of Vibration and ControlFagang Zhao, Jin Chen, Lei Guo and Xinglin Li

Neuro-fuzzy Based Condition Prediction of Bearing Health  

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Neuro-fuzzy Based Condition Prediction of BearingHealth

FAGANG ZHAOJIN CHENLEI GUOState Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University,Shanghai 200240, China (email: fagang@sjtu.edu.cn)

XINGLIN LIState Test Laboratory of Hangzhou, Bearing Testing & Research Center, Hangzhou, 310088,China

(Received 13 June 2008� accepted 6 November 2008)

Abstract: A reliable prognostic model is very useful for industries to forecast equipment behaviors. Theaim of this research is to verify the effectiveness of the neuro-fuzzy model in predicting the health conditionof bearings. Simulation and an experiment have been carried out to verify the model, with results showingthat the neuro-fuzzy model is a reliable and robust forecasting tool, and more accurate than a radial basisfunction network. In the experiment, vibration data collected from the equipment is used to predict the futurecondition.

Keywords: Prediction, neuro-fuzzy, bearing vibration, RBF network.

1. INTRODUCTION

The manufacturing and industrial sectors are increasingly required to produce more andhigher quality products but avoid accidents as far as possible. As manufacture equipmentbecomes more complex and sophisticated, machine breakdowns are common. In order toprevent unexpected failures from shutdown, and reduce economic losses, a reliable prognos-tic system is very useful to provide an alarm before a fault reaches critical levels accordingto the prediction of the fault propagation, so that maintenance personnel can schedule themaintenance for the faulty equipment.

Prognosis technologies have developed rapidly all over the world. The methods can bedivided into the following three main categories: reliability-based prognostic approaches�physics-based prognostic approaches� and data-driven prognostic models.

Reliability-based prognostic approaches are based on the distribution of event recordsof a population of identical units. Numerous models, such as exponential, Weibull, and log-

Journal of Vibration and Control, 15(7): 1079–1091, 2009 DOI: 10.1177/1077546309102665

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1080 F. ZHAO ET AL.

normal distributions, have been used to model machine reliability. Reliability analyses havebeen extensively studied and developed in recent decades (Crowder et al., 1994� Elsayed,1996� Lawless, 2002). However, these methods only provide general overall estimates forthe entire population of identical units, which are of little value to a specified componentcurrently running in the machine.

Physics-based prognostic models typically require the construction of technically com-prehensive mathematical models to describe the physics of the system and failure modes,such as crack propagation and spall growth. Li (1999) and Lindsay (2005) related rollingelement bearing defect growth rate with the instantaneous defect area size and material con-stants based on Paris’ law. Li and Lee (2005) also employed Paris’ law to model spur gearcrack growth. Orsagh et al. (2003) used a stochastic version of the Kotzalas–Harris pro-gression model to estimate the time to failure. Although it has been verified numericallyand experimentally, the model mainly depends on the solution of two differential equationsand requires some initial condition, such as defect size threshold, which restricts its use ingeneral applications. Furthermore, the instantaneous defect area size is usually unavailablewithout interrupting the machine operation.

Data-driven approaches attempt to derive models directly from routinely collected on-line data instead of constructing models based on comprehensive system physics and humanexpertise. They are constructed based on historical records and produce prediction outputsdirectly in terms of online data. The conventional data-driven methods include simple projec-tion models, such as exponential smoothing (Batko, 1984) and autoregressive models. Thesetechniques are simple to calculate. However, most of these methods assume that the systemsmonitored are stationary. Artificial intelligence (AI) methods are currently the most com-monly used in the prognostic literature. Numerous studies across various disciplines havedemonstrated the merits of AI. Shao and Nezu (2000) predicted bearing running states vianeural networks and logic rules. Wang and Vachtsevanos (2001) applied dynamic waveletneural networks to predict the fault propagation process and estimate the remaining usefullife before a fault reaches a given value. Gebraeel et al. (2004) developed models based onneural networks to predict bearing life, and then compared these with actual lives of the vali-dation bearings. Yam et al. (2001) applied a recurrent neural network to predict the machinecondition trend. Wang et al. (2002) proposed a wavelet neural network prediction algorithmfor performance evaluation, and evaluated and predicted the wearing condition of machinespindle and cutting tools. Besides AI methods, the hidden Markov model is also a powerfultool for predicting remaining useful life (Kwan et al., 2003). Orchard (2006) has employedparticle filtering to provide non-linear projection in forecasting the growth of a crack in aturbine engine blade.

Data-driven prognostics models are often more available in many practical cases, as it iseasier to gather data than to build accurate system physics models. Usually, these methodsare easy to implement but difficult when it comes to forecasting the behavior of complex dy-namic systems. For example, bearings signals are non-linear, non-Gaussian, non-stationary,and difficult to model using conventional mathematical methods. In this paper, an auto-matic and real-time prognostic model for bearing health condition prediction is developed.A neuro-fuzzy scheme is put forward with extracted features to achieve a more reliable pre-diction. The reason for employing the neuro-fuzzy scheme is that the prognostic knowledgefrom the expertise and online/offline learning can be incorporated into the fuzzy system,

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NEURO-FUZZY BASED CONDITION PREDICTION OF BEARING HEALTH 1081

whereas the fuzzy membership functions can be optimized by using neural networks (Janget al., 1997� Abe, 2001). Good prognosis needs reliable predictors, which are quite usefulfor industries to forecast states of equipment. Generally, the predictor is extracted frominformation carriers such as operating temperature, debris properties of the lubrication oil,acoustic signals, and vibration. Presently, vibration-based approaches are the most popular(Luo et al., 2003� Amarnath et al., 2004� Estocq et al., 2006� Roemer and Byington, 2007�Sassi et al., 2007� Yang et al., 2007) due to their convenience in measurement and analysis.Thus vibration signals are also used in this paper.

2. NEURO-FUZZY MODEL

Fuzzy systems and neural networks are naturally complementary tools in constructing intel-ligent systems, and they have been researched in many fields. Neural networks are low-levelcomputational structures that perform well when dealing with raw data, while fuzzy logicdeals with higher-level reasoning. However, fuzzy systems lack the ability to learn or ad-just themselves. Takagi and Sugeno (1985) proposed a non-linear model which can producefuzzy rules from given input–output data. So a system integrated with neural network anda fuzzy system provides a promising approach for constructing bearing condition predictionmodels.

2.1. Time series

The neuro-fuzzy model is a fuzzy system based on neural networks. The prediction reason-ing is conducted by fuzzy logic. The fuzzy inference structure is determined by expertise�whereas its membership functions are trained by means of neural networks. As will beproved in the following, the membership function sequences to be predicted are character-ized by a chaotic behavior. In this case, a generic chaotic sequence X �n� can be consideredas the output of a chaotic system that is observable only through X �n�. Consequently, thesequence X �n� should be embedded in order to reconstruct the state-space evolution of thissystem (Kantz and Schreiber 2003). The standard embedding technique, which is useful forchaotic sequences, is based on the determination of both the embedding dimension M of thereconstructed state-space attractor and the time lag T between the embedded past samples ofX �n�:

X �n� � [x �n� � x�n � T �� ���� x�n � 2T �� x�n � �M � 1�T �]

In applications the key for the state-space reconstruction is determining its optimal parame-ters. When the embedding dimension is larger than the minimum embedding dimension, thetrajectory of reconstructed vectors can reflect the true state-space evolution of chaotic sys-tems. From a mathematical point of view the time delay is arbitrary, since the data items areassumed to have infinite precision. In applications the time delay should not be taken to beso small that there is little difference between the different elements of the delay vectors, norso large that the different coordinates may be almost uncorrelated.

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1082 F. ZHAO ET AL.

Figure 1. Structure of the neuro-fuzzy model. Layer 1 represents inputs, layer 2 input membershipfunction, layer 3 rules, layer 4 output membership function, layer 5 weighted sum output, and layer 6output.

2.2. Neuro-fuzzy architecture

Neuro-fuzzy modeling refers to the method of applying various learning techniques devel-oped in the neural network literature to fuzzy modeling or a fuzzy inference system (Brownand Harris, 1994]. A neuro-fuzzy system combines neural networks and fuzzy logic. It hasattracted a lot of interest in research and applications. It utilizes the benefits of fuzzy andneural network technologies as it facilitates an accurate initialization of the network in termsof the parameters of the fuzzy reasoning system.

The Neuro-fuzzy architecture of the first-order Takagi–Sugeno inference system is shownin Figure 1. The entire system consists of six layers, and the relationship between the inputand output of each layer is summarized as follows. Layer 1 is the input layer. The nodes inlayer 1 transmit the indexes to the next layer directly. Once the input and output variables areidentified, the neuro-fuzzy system is realized by means of a neural network. The relationshipamong the inputs, outputs and node functions of each layer will be explained below.

Layer 2 is the fuzzification layer. It describes the membership function of each inputfuzzy set. Each node in this layer acts as a membership function, which is either a singlenode that performs a simple activation function or multilayer nodes that perform a complexfunction:

�Ai � exp

���

1��

x � ci

ai

�2bi��

(1)

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where x is the input data and �ai � bi � ci� is the premise parameter set.Layer 3 is the inference layer. Each node in this layer is a fixed node and represents

the IF part of a fuzzy rule. This layer aggregates the membership grades using any fuzzyintersection operator, such as “and” and “or”. Here it performs and operation (Klir andYuan, 1995). The output is the product of all input signals, and represents the activation levelof a rule with the expression

� i � �A1 �x1�� �A2 �x2�� �A3 �x3�� �A4 �x4� � (2)

Layer 4 is the normalization layer. It computes the ratio of the rule’s activation level tothe total of all activation levels. The output of this layer is denominate as normalized firingstrength:

�� i � � i

�1 � �2 � ���� �M(3)

where i � 1� 2� � � � �M and M is total number of rules.Layer 5 is the output layer. Each node in this layer is an adaptive node, whose output is

simply the product of the normalized firing strength. Thus, the output of this layer is givenby

Oi � �� i fi (4)

where �� i is from layer 4 and fi is a linear function of input variables.Layer 6 is the defuzzification layer. It computes the weighted average of output signals

of the output layer as

O ��

i

Oi ��

i

�� i fi ��

i � i fi�i � i

� (5)

In order to evaluate model accuracy, we choose the various standard statistical perfor-mance evaluation criteria to decide whether the prediction result is good or not. The perfor-mance of the model developed in this tudy was evaluated by these criteria. The statisticalmeasures considered are absolute value error (AVE), root mean square error (RMSE) andmean absolute percentage error (MAPE):

AV E �N�

i�1

y�i�� y�i� (6)

RM SE ���� 1

N

N�i�1

y�i�� y�i��2

(7)

M AP E � 1

N

N�i�1

y�i�� y�i�y�i�

� 100 (8)

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Table 1. The prediction performance for MG series.

AVE RMSE MAPERBF 1.0269 0.0053 0.4750Neuro-fuzzy 0.5700 0.0033 0.3610

where N denotes the number of prediction data� y �i� is the predicted value� and y �i� isthe true value. The total number of iterations is N . Equations 6–8 give measures of theprediction accuracy of the model. The RMSE on the training set indicates the success oftraining, that is, the ability of the experimental structure and parameter estimation method tocode the training data patterns into its structure.

3. SIMULATION

We consider the time series generated by the Mackey–Glass (MG) equation (Mackey andGlass, 1977) given by

dy �t�

dt� 0�2y �t � ��

1� y10 �t � �� � 0�1y �t� � (9)

where � � 17. This is a time-delay ordinary differential equation displaying well-knownchaotic behaviors, widely used for testing the performance of models� its chaotic naturemakes it a universally acceptable representation of many nonlinear processes. The timedelay � is a source of complications in the nature of the time series. Data sets generatedby equation 9 have chaotic, non-linear, and non-convergent properties, which make themsuitable to train forecasting schemes for general application purposes. The objective of theneuro-fuzzy model is to predict the value of the time series based on previous values. Inthis case, four values were chosen, y �t�, y �t � 6�, y �t � 12� and y �t � 18�, which are usedto predict y �t � 6�. The training is carried out on 250 samples and the model is tested onthe remaining time series. The comparison of the prediction of prediction accuracy usingthe neuro-fuzzy model and RBF network model is summarized in Table 1, which shows 1that the neuro-fuzzy model preformed better during MG series prediction. The neuro-fuzzymodel improved the RBF network prediction of 44.5%, 37.7% and 24% reduction in AVE,RMSE and MAPE, respectively. It is clear that the neuro-fuzzy predictor provides a muchbetter forecasting performance.

For the MG time series, it demonstrates that the neuro-fuzzy model provides lower errorcompared to the RBF network. Therefore it can be concluded that a trained neuro-fuzzysystem will be more accurate in predicting time series. Although neuro-fuzzy systems haveshown great potential in non-linear and stochastic time-series predictions, there has not beenany application to bearing health condition prognosis. So we will introduce the neuro-fuzzymodel into bearing health condition prognosis in this paper.

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Figure 2. Sketch of data acquisition system.

4. NEURO-FUZZY-BASED BEARING CONDITION PREDICTION

4.1. Experiment setup

Bearings are widely used in modern machinery, typically in automobiles, power turbines,and steel mills, for example. A bearing experiment is used to verify the neuro-fuzzy modelfor prediction, and an RBF network will be used for comparison purposes. Vibration-basedbearing condition prognosis uses the available vibration symptoms to predict future states bymonitoring one or more parameters, which are extracted using signal processing techniques,such as peak-peak (P-P), root mean squares (RMS), crest factor, skew, kurtosis, waveletindex and energy factor. In order to acquire data on the entire process of bearing vibrationfrom normal to final failure, a bearing life acceleration test was carried out on an acceleratedbearing life tester (ABLT-1A) which was provided by the Hangzhou Bearing Test & ResearchCenter (HBRC), China, and can host four tested bearings on one shaft driven by an AC motorand coupled by rub belts. In the monitoring system, four thermocouples are used to recordtemperatures of the outer race of bearings and three acceleration sensors used to collectvibration signals. Figure 2 is a sketch of the data acquisition system, which includes sensorsand signal conditioner, regulated power supply, and data acquisition computer. Then afterthe signal has been conditioned and anti-aliasing filtered, the information is collected bycomputer on an NI-6023E data acquisition card. Data acquisition software is programmedwith National Instruments LabView. The data sampling rate is 25.6 kHz and data length is20 480 points� one group of data was collected per minute. The experimental equipment isshown in Figure 3.

There are many steps in the prediction of bearing life. The first step is to condition thevibration signals specific to the bearing of interest. The signals are amplified and isolatedin order to improve their properties and reliability. Then the anti-aliasing filter is used to

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Figure 3. Equipment used in experiment.

filter the interference signal in an 8-channel dynamic signal acquisition device, the PXI-4472 (National Instruments, http://sine.ni.com/nips/cds/view/p/lang/en/nid/5031). The fea-tures or parameters of the time domain, frequency domain and wavelet domain (Altmann andMathew, 2001) are extracted by employing the corresponding signal processing techniquesand filtering processes. After the features are extracted, they are compared to establish whichis best for prediction. The bearing health condition is conducted by employing a properlytrained neuro-fuzzy scheme. After a fault occurs, when the vibration level reaches the alarmlevel, the remaining useful life can be estimated according to the indices. According tothe condition prediction result, the maintenance department can make the maintenance de-cision (condition-based maintenance). All the employed signal processing techniques, thedecision-making scheme, and training algorithms are coded in MATLAB (see Figure 4).

4.2. Bearing life prognosis

In condition monitoring, the monitoring indices should be sensitive to pattern modulationdue to machinery faults but insensitive to noise. Many signal processing techniques havebeen proposed in the literature for bearing health prognostics, each with its merits and lim-itations. Following investigations by Williams et al. (2001) and Huang and Xi (2007) andafter comparison of features in this experiment (shown in Figure 5), we chose RMS as theprediction index for the monitoring and prognosis.

The bearing data were divided into two sets,the training and validation test data. Inthe training phase, the first part of the data was used to train the model and the remainingdata were used in the validation phase. In order to show the potential of the neuro-fuzzymodel, the prediction results using the RBF network model are also presented. The RBF net-

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Figure 4. Feature extraction and prognostics scheme.

Table 2. The prediction performance for bearing series.

ES RMSE MAPERBF 0.5227 0.0031 7.1159Neuro-fuzzy 0.3334 0.0017 5.0451

work model was trained and tested with the same data sets used for the neuro-fuzzy model.Figure 6 shows the forecasting results of the normalized RMS values for bearings with theneuro-fuzzy model and RBF network, respectively. It can be seen that both models performreasonably well from 2111 minutes to about 2300 minutes. After the bearing defect is intro-duced (at about 2300 minutes) and becomes more serious, the neuro-fuzzy model (Figure 6b)responds more quickly than the RBF network (Figure 6a) to recapture the bearing system’snew dynamic characteristics.

The comparison of prediction accuracy using the neuro-fuzzy model and RBF networkmodel is also summarized in Table 2. It can be seen that the neuro-fuzzy model preformedbetter during the prediction phase. The neuro-fuzzy improved on the RBF network predictionof 36.2%, 45.2% and 29.1% reduction in AVE, RMSE and MAPE respectively. The mainadvantage of the neuro-fuzzy model is its superior ability to capture the major and minortrends effectively in the bearing condition series. So the comparison shows that the neuro-fuzzy model is able to predict the series. These are very valuable indications for bearingsystem condition monitoring.

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Figure 5. Features of the vibration data: (a) RMS value� (b) peak-peak value� (c) peak value� (d)impulsion value� (e) tolerance value� (f) kurtosis.

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Figure 6. Predicted series based on (a) RBF network and (b) neuro-fuzzy model.

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5. CONCLUSIONS AND FUTURE WORK

Because of the non-linear nature of the vibration of bearings, the neuro-fuzzy model is in-troduced into times series prediction of vibration in this paper. Firstly, we determine theembedding dimension D of the reconstructed state-space and the time lag T , and then applythe neuro-fuzzy model to predict bearing condition.

To provide a more reliable and real-time prognostic tool for the bearing condition, wedeveloped a neuro-fuzzy prediction method to predict the behavior of dynamic systems inthis paper. For comparison purposes, a RBF network was also used to examine the advan-tages of the neuro-fuzzy model. According to the example given above, it can be concludedthat it is useful when implemented for bearing residual life prediction. The test results of thisstudy showed that the neuro-fuzzy model is a more reliable forecasting tool. It can capturethe system’s dynamic behavior quickly and track the system’s features accurately. It is alsoa robust forecasting tool by virtue of its ability to adapt to different system operation condi-tions and variations of a system’s dynamic characteristics. The training technique is efficientin improving the forecasting performance by modifying the properties of the decision spaceboundaries and by preventing possible trapping due to local minima. The forecasting accu-racy of the proposed predictor is higher than that of the RBF network-based predictor, whichis superior to those based on the feed-forward networks (Tse, 1999).

Further research could usefully be done in two areas: one is to implement a better methodfor equipment residual life prediction and develop new strategies for predictions, for exampleby combining several models� the other is to find out if there is a better way to reduce noiseand find the rules to support the prediction of residual life.

Acknowledgements. The research was supported by the National Natural Science Foundation of China (ApprovedGrant: 50675140) and the National High Technology Research and Development Program of China (863 Program,NO. 2006AA04Z175).

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