04798444

2008 IEEE Region 10 Colloquium and the Third ICIIS, Kharagpur, INDIA December 8-10. PAPER IDENTIFICATION NUMBER: 409

978-1-4244-2806-9/08/$25.00 2008 IEEE

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Fault diagnosis of rolling element bearing using time-domain features and neural networks

B. Sreejith, A.K. Verma and A. Srividya Interdisciplinary Programme in Reliability Engineering, Indian Institute of Technology Bombay, Mumbai - 400 076, India,

Email:[email protected], [email protected], [email protected],

Abstract Rolling element bearings are critical mechanical components in rotating machinery. Fault detection and diagnosis in the early stages of damage is necessary to prevent their malfunctioning and failure during operation. Vibration monitoring is the most widely used and cost-effective monitoring technique to detect, locate and distinguish faults in rolling element bearings. This paper presents an algorithm using feed forward neural network for automated diagnosis of localized faults in rolling element bearings. Normal negative log-likelihood value and kurtosis value extracted from time-domain vibration signals are used as input features for the neural network. Trained neural networks are able to classify different states of the bearing with 100% accuracy. The proposed procedure requires only a few input features, resulting in simple preprocessing and faster training. Effectiveness of the proposed method is illustrated using the bearing vibration data obtained experimentally.

Keywords-bearing vibration; time domain feature; log-likelihood value; automated diagnosis

I. INTRODUCTION Rolling element bearings are responsible for most of the

failures in rotating machinery. Vibration analysis has been used extensively for condition monitoring of bearings. The vibration signal contains huge information, which can be applied for condition monitoring without interfering with machinery operation. When a localized fault in a bearing surface strikes another surface, impact vibrations are generated. Condition monitoring is performed by analyzing the changes in the vibration signature due to the presence of these impulses. Fault diagnosis helps to identify the location of the fault so that corrective action can be taken and maintenance can be planned accordingly.

Analysis techniques applied for processing the raw measured vibration signals for condition monitoring of rolling element bearings can be classified as: time-domain, frequency domain and time-frequency or time-scale analysis methods. The most popular method is the frequency domain analysis which needs the assistance of an expert to interpret the results. Techniques such as averaging [1], adaptive noise cancellation [2], bispectrum analysis [3] and high frequency resonance technique (HFRT) [4] have been used to improve the signal to noise ratio to make the spectrum analysis more effective. Frequency domain analysis methods tend to average transient

vibrations and hence, become more sensitive to background noise. Reliability of condition monitoring can be increased by automating the process, which also provides savings in time and cost. Moreover, automatic fault diagnosis does not depend on subjective human judgment [5]. The application of ANNs has been gaining importance in the area of automated fault detection and diagnosis of rotating machinery [6], [7], [8]. The neural networks have the advantages of adaptive learning, nonlinear generalization, fault tolerance, resistance to noisy data, and parallel computation abilities. Techniques based on time domain analysis [9], [10], frequency domain analysis [11], [12] and time-frequency/scale analysis [12], [13] have been used to extract input features for rolling element bearing fault diagnosis using neural networks. A method for automatic fault diagnosis of rolling element bearings is presented in this paper.

In the proposed method, time domain features are extracted from the vibration signal and pattern recognition using ANN is used for bearing fault diagnosis. Normal negative log-likelihood value and kurtosis value of the time-domain signals are used as input features. Vibration signals measured from a single location are used in the proposed method. Some of the previous works dealt with signals from multiple locations for fault detection [10], [14]. The number of input parameters used in the proposed algorithm is less compared to that of previous works [6], [7], [8], [9], [10], [11], [12], [13] and hence, training speed is high. Moreover, additional signal processing required for frequency domain analysis and time-frequency/scale analysis is not required for the proposed algorithm. The performance of the negative log-likelihood values are compared with other time-domain features and it has been observed that they perform better when used as input features of ANN for the fault diagnosis of bearings. Different algorithms used for the training of ANN are compared and it is observed that Levenberg-Marquardt (LM) algorithm converges faster than other algorithms in this context.

II. FEATURE EXTRAVTION Feature selection has a significant impact on the success of

pattern recognition. Following time domain statistical parameters are usually used to detect incipient bearing damage:

Peak value, Pv =(1/2)[max(xi) - min(xi)] (1)

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978-1-4244-2806-9/08/$25.00 2008 IEEE

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where xi, (i = 1, ...,N) is the amplitude at sampling point i and N is the number of sampling points.

RMS value, RMS = N

2i

i=1

1 (x )N (2)

Standard deviation, SD =N

2i

i=1

1 (x - x)N (3)

Kurtosis value, Kv = ( )

( )

4N

ii=1

4

1 x - xNRMS value

(4)

Crest factor, Crf = Peak value / RMS value (5)

Clearance factor, Clf = 2Ni

i=1

peak value1 xN

(6)

Impulse factor, Imf = Ni

i=1

Peak value1 xN

(7)

Shape factor, Shf = Ni

i=1

RMS value1 xN

(8)

Weibull negative log-likelihood value was used recently for feature extraction from vibration signals [14]. The Weibull negative log-likelihood value (Wnl) and the normal negative log-likelihood value (Nnl) of the time domain vibration signals are used as input features along with the other features defined above in this study. The negative log-likelihood function is defined as

( )N i 1 2i=1

- = - log f x ; , (9) where f (xi; 1, 2) is the probability density function (pdf). For Weibull negative log-likelihood function and normal negative log-likelihood function, the pdfs are computed as follows

Weibull pdf, f(xi;,) = -|xi|-1exp[-(|xi|/)] (10)

where and are the shape and the scale parameters respectively.

Normal pdf, f(xi;,) = { }2i 2-(x -) 21 exp 2 (11) where and are the mean and the standard deviation respectively.

III. FAULT DIAGNOSIS USING NEURAL NETWORKS An ANN is composed of nodes arranged in input, hidden

and output layers, with all the nodes in each layer having weighted inter-connections with all the nodes in the succeeding layer. Nodes in the hidden and output layers consist of artificial processing units called neurons. After training, neural network can recognize various conditions or states of a complex system. The number of nodes in the input layer is equal to the number of input features. Feed-forward neural network with back propagation training algorithms are used in the study. In the context of classification problems, networks with two layers of weights and sigmoid activation function for neurons in the hidden layer can approximate any decision boundary to arbitrary accuracy [15]. Hence, architecture with single hidden layer is selected. The number of neurons in the hidden layer is decided using a trial and error method. Starting from two, the number of neurons is increased by one in each trial until the required accuracy is achieved with quick convergence. Since there are four classes to discriminate, four neurons are used in the output layer, where each output represents a condition of the bearing.

The input features are normalized in the range of -1.0 and 1.0 for negative log-likelihood values, and in the range of 0.0 to 1.0 for other features. Log sigmoid and tan sigmoid activation functions are used for neurons in the hidden layer and the output layer, respectively. The weights and biases of the network are initially selected randomly. The stopping criteria used for training process is the achievement of one of the conditions namely mean square error of 10-10, gradient of 10-10 or 100 epochs. The network is trained using different back propagation algorithms and it is observed that LM algorithm converges quickly. Hence, this algorithm is used for training.

Sensitivity analysis is performed to understand the effect of each input feature on the ANN output. Irrelevant input features identified using this analysis can be removed, which in turn reduce the size of the network, the complexity and the training time. Moreover, the inclusion of irrelevant input variables can reduce the accuracy of forecast through added noise or systematic bias. Sensitivity based pruning method [16] is used to evaluate the effect of removing an input variable from the fully connected network. A sensitivity measure of feature i, Si is calculated by assessing the change in training error when the input feature i is replaced with the mean value of that feature. After the network is trained, the sensitivity measure for each input feature can be calculated as

Si = MSE ( xi ) MSE (x) (12)

where MSE (x) is the mean square error (MSE) of the ANN and MSE ( xi ) is the MSE after replacing the input feature i with its average value.

IV. EXPERIMENT DATA Vibration signals provided by the CWRU bearing data

center [17], collected from a 2 HP motor fixed in a test stand is used for investigations in this paper. The motor is connected to


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a dynamometer and torque sensor by a self-aligning coupling. The bearing at the drive end of the motor supporting the motor shaft is tested at a load of 1 HP. Load is applied using dynamometer. Speed and horsepower data are collected using transducer/encoder. Single point faults are introduced into the test bearings using electron-discharge machining with a fault diameter of 0.18 mm and a depth of 0.28 mm. Vibration data is acquired using accelerometers, which are attached to the housing with magnetic bases. Digital data is sampled at 12,000 samples per second and recorded using a 16 channel DAT recorder. The speed of the shaft is measured as 1772 rpm. SKF 6205 series deep groove ball bearings are used for the analysis. The specifications of the bearing are: ball diameter = 7.94 mm; pitch diameter = 39.04 mm; number of balls = 9; and contact angle = 0.

The time domain vibration signals considered for the analysis are collected for four different conditions of the bearing: (i) normal, (ii) rolling element fault, (iii) outer race fault, and (iv) inner race fault. The vibration signature for a normal bearing is shown in Fig.1a. Vibration fault signals for bearings with faults located in rolling element, outer race and inner race are shown in Figs. 1b, 1c and 1d, respectively.

V. RESULTS AND DISCUSSION The vibration data for each condition with 120000 samples

is used in the study for fault diagnosis. The signals are split into 20 non-overlapping segments each. The length of the segments is chosen carefully to contain enough information to capture

localized features of the signal such that the computation time is minimum. The data segments are preprocessed to extract the features. Hence, 20 sets of 10 normalized features are obtained for each of the four conditions of the bearing, out of which 12 sets selected in random are used to train the network and the remaining 8 sets are used for testing. During training, the first, second, third and fourth outputs are set to denote the normal, defective rolling element, defective outer race and defective inner race conditions, respectively of the bearing.

The features extracted from the vibration signals are shown graphically in Fig. 2. The separations between normal and defective cases are maximum in the plots of Wnl and Nnl. The plots of Pv, RMS value and SD show a narrow separation between normal and rolling element defective cases. In the plots of the other five normalized features, there is no separation between normal and rolling element defective cases. Separation between normal and defective inner race is maximum for the plot of Kv.

Initially, all the 10 time domain features explained above are used to train the neural network. Using the trial and error method, the optimum number of hidden nodes is obtained as 11. The network is able to detect the normal and three defective states of the bearing with 100% success during training and testing. Fig. 3 shows the sensitivity diagram of each output about the mean square. From the sensitivity diagram, it can be observed that Nnl is the feature with the most significant contribution towards output nodes 1 and 2. Similarly, Kv is a significant feature for nodes 3 and 4.

Figure 1. Vibration signal of the bearing a) normal, b) rolling element fault, c) outer race fault, d) inner race fault.

0 0.1 0.2 0.3 0.4 0.50.25

0.15

0.05

0

0.05

0.15

0.25

Ampl

itude

Time (Second) 0 0.1 0.2 0.3 0.4 0.5

1

0.5

0

0.5

1

Ampl

itude

Time (s) (a) (b)

0 0.1 0.2 0.3 0.4 0.58

4

0

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8

Time, (s)

Ampl

itude

0 0.1 0.2 0.3 0.4 0.5

3

2

1

0

1

2

3

Time, (s)

Ampl

itude

(c) (d)


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Figure 2. Time-domain features of vibration signals.

Figure 3. Sensitivity diagram of the outputs of ANN a) node 1, b) node 2, c) node 3, d) node 4.

0

0.5

1

Pv RM

S

SD

0

0.5

1Kv Cr

f

Clf

0

0.5

1

Imf

0 10 200

0.5

1

Shf

Signal Segment

0 10 201

0

1

Wnl

Signal Segment

normal defective outer race

0 10 20

Nnl

Signal Segment

defective inner race defective rolling elment

1 2 3 4 5 6 7 8 9 100

0.05

0.10

0.14

Feature

Sens

itivity

1. Pv2. RMS3. SD4. Kv5. Crf6. Clf7. Imf8. Shf9. Wnl10.Nnl

1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

Feature

Sens

itivity


(a) (b)

1 2 3 4 5 6 7 8 9 100

0.0001

0.0002

0.0003

0.0004

0.0005

Feature

Sens

itivity


1 2 3 4 5 6 7 8 9 100

0.005

0.01

0.015

0.02

0.025

Feature

Sens

itivity


(c) (d)


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The procedure is repeated by removing the eight less significant input features and reducing the size of the network. This will result in the reduction of complexity and training time. Nnl and Kv are used as input features. The optimum number of neurons in the hidden layer is obtained as 14. Fig. 4 and 5 shows the learning curve and sensitivity diagram of the network respectively. Fig. 6 shows the target and actual values of output nodes. It can be observed that the network performs fault diagnosis with the same accuracy of 100% even after pruning 8 input channels.

Performances of various time-domain features are studied for comparison. The effect of input features on the training speed of neural network is shown in Table I. It can be observed that the number of epoches required for training is minimum for the network with Nnl and Kv as input features. Since only two input features are used in this case, the number of neurons in the hidden layer is also less. Hence, complexity and training time are less for this network.

An optimization study has been carried out to find the best ANN training algorithm in this context. LM, resilient propagation (RP) [18], scaled conjugate gradient (SCG) [19] and Powell-Beale conjugate gradient (PBCG) [20] are the training algorithms considered for the study. Table II shows the

0 2 4 6 8 10 12 140

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

epochs

Mea

n Sq

uare

Erro

r

Figure 4. Learning curve of the ANN with Kv and Nnl as input.

1 2 3 40

0.3

0.5

Output

Sens

itivity

KvNnl

Figure 5. Sensitivity diagram of the ANN with Kv and Nnl as input features.

Figure 6. Target and actual output values of ANN with Kv and Nnl as input features a) node 1, b) node 2, c) node 3, d) node 4.

0 20 40 60 800.2

0

0.2

0.4

0.6

0.8

1

Data Sequence Number

Targ

ets/

net o

utpu

ts

outputtarget

training testing

0 10 20 30 40 50 60 70 800.2

0

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0.4

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Targ

ets/

net o

utpu

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outputtarget

training testing

(a) (b)

0 10 20 30 40 50 60 70 800.2

0

0.2

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Targ

ets/

net o

utpu

ts

outputtarget

training testing

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Targ

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training testing

(c) (d)


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TABLE I. EFFECT OF INPUT FEATURES ON FAULT DIAGNOSIS

Input features No. of neurons in hidden layer Average no.

of epochs Pv,RMS,SD,Kv,Crf Clf,Imf,Shf,Wnl,Nnl 11 20

Kv, Nnl 10 14 Pv, RMS, SD, Kv, Crf, Clf, Imf, Shf 8 23

RMS, SD 10 19

TABLE II. EFFECT OF TRAINING ALGORITHMS ON FAULT DIAGNOSIS

Training algorithm Average no. of epochsLevenberg-Marquardt, LM 14 Resilient propagation, RP 29 scaled conjugate gradient, SCG 90 Powell-Beale conjugate gradient, PBCG 28

average number of epochs required for training. The study reveals that LM algorithm has converged to the optimum solution more efficiently compared to the other algorithms under consideration.

VI. CONCLUSIONS A neural network approach for automated fault diagnosis of

rolling element bearing from vibration data has been introduced in this paper. The time domain parameters; normal negativelog-likelihood value and kurtosis value, are used as input features. The proposed procedure uses ANN classifier and requires data measured from only one measurement point. The signal is not preprocessed before the feature extraction. The algorithm uses less number of input features resulting in faster training. The effectiveness of the algorithm has been illustrated using bearing vibration data and results showed 100% success rate in the recognition of different bearing conditions for fault diagnosis. The results of the study show the potential suitability of the procedure for automatic fault detection and diagnosis of complex systems in industry.

ACKNOWLEDGMENT The authors would like to thank Professor K.A. Loparo of

Case Western Reserve University for providing access to the bearing vibration dataset.

REFERENCES [1] S. Braun, B. Datner, Analysis of roller/ball bearing vibrations, Analysis

of roller/ball bearing vibrations, ASME J of Mechanical Design, vol. 101(1), 1979, pp. 118125.

[2] G. K. Chaturvedi, D. W. Thomas, Bearing fault detection using adaptive noise cancellation, ASME J of Mechanical Design, vol. 104(2), 1982, pp. 280-289.

[3] C. J. Li, J. Ma, B. Hwang, Bearing condition monitoring by pattern recognition based on bicoherence analysis of vibrations, Proceedings of the Institution of Mechanical Engineers, J of Mechanical Engg. Science, vol. 210(c3), 1996, pp. 277-285.

[4] P. D. McFadden, J. D. Smith, Vibration monitoring of rolling element bearings by the high frequency resonance technique - a review, Tribology International, vol. 17(1), 1984, pp. 3-10.

[5] A. C. Braccesi, M. Carfagni, P. Rissone, Using force signals to monitor mechanical systems, Mechanical Systems and Signal Processing, vol. 3(2), 1989, pp. 111-122.

[6] A. C. McCormick, A. K. Nandi, Classification of the rotating machine condition using artificial neural networks, Proceedings of Institution of Mechanical Engineers, Part C, vol. 211, 1997, pp. 439-450.

[7] A. C. McCormick, A. K. Nandi, Real time classification of rotating shaft loading conditions using artificial neural networks, IEEE Transactions on Neural Networks, vol. 8, 1997, pp. 748-756.

[8] B. A. Paya, I.L. Esat, M.N.M. Badi, Artificial neural network based fault diagnosis of rotating machinery using wavelet transforms as a preprocessor, Mechanical Systems and Signal Processing, vol. 11(5), 1997, pp. 751-765.

[9] Y. Lei, Z. He, Y. Zi, Q Hu, Fault diagnosis of rotating machinery based on a new hybrid clustering algorithm, International J of Advanced Manufacturing Technology, vol. 35, 2008, pp. 968-977.

[10] B. Samanta, K. R. Al-balushi, Artificial neural network based fault diagnostics of rolling element bearings using time-domain features, Mechanical Systems and Signal Processing, vol. 17(2), 2003, pp. 317-328.

[11] B. Li, G. Goddu, M. Chow, Detection of common bearing faults using frequency-domain vibration signals and a neural network based approach, Proceedings of the American Control Conference, Philadelphia, Pennsylvania, June 1998, pp. 2032-2036.

[12] D. M. Yang, A. F. Stronach, P. MacConnell, Third-order spectral techniques for the diagnosis of motor bearing condition using artificial neural networks, Mechanical Systems and Signal Processing, vol. 16(23), 2002, pp. 391-411.

[13] B. S. Yang, T. Han, J. L. An, ART-KOHONEN neural network for fault diagnosis of rotating machinery, Mechanical Systems and Signal Processing, vol. 18, 2004, pp. 645-657.

[14] S. Abbasion, A. Rafsanjani, A. Farshidianfar, N. Irani, Rolling element bearings multi-fault classification based on the wavelet denoising and support vector machine, Mechanical Systems and Signal Processing, vol. 21, 2007, pp. 2933-2945.

[15] C. Bishop, Neural networks for pattern recognition, Oxford University Press, New York, 1995.

[16] T. I. Laine, K. W. Bauer, Feature selection assessment and comparison using two saliency measures in an Elman recurrent neural network, Proceedings of the International Joint Conference on Neural Networks, IEEE Press, vol. 4, July 2003, pp. 2807- 2812.

[17] Case Western Reserve University, Bearing data centre, last accessed 26/04/2008 URL:http://www.eecs.cwru.edu/laboratory/bearing

[18] M. Riedmiller, H. Braun, A direct adaptive method for faster backpropagation learning: the RPROP algorithm, Proceedings of the IEEE Int. Conf. On Neural Networks, San Francisco, CA, March 28, 1993, pp.586-591.

[19] M. F. Moller, A scaled conjugate gradient algorithm for fast supervised learning, Neural Networks, vol. 6, 1993, pp. 525-533.

[20] H. B. Demuth, M. Beale, Neural Network Toolbox for Use with MATLAB, Users Guide, The MathWorks Inc., Natick, MA, USA, 2004.

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