A Comparative Study on Bearings Faults

Kalyan M. Bhavaraju et al. / International Journal of Engineering Science and Technology Vol. 2(5), 2010, 1001-1008

A Comparative Study on Bearings Faults Classification by Artificial Neural Networks and Self-Organizing Maps using Wavelets 

KALYAN M. BHAVARAJU*, P. K. KANKAR, SATISH C. SHARMA, AND S. P. HARSHA Vibration and Noise Control Laboratory Mechanical and Industrial Engineering Department Indian Institute of Technology Roorkee-247667 Abstract This paper presents a comparative study between soft computing techniques Artificial Neural networks (ANN) and Self-Organizing Maps (SOM) using continuous wavelet transform (CWT) for fault diagnosis of rolling element bearings. Six different base wavelets three real valued and three complex valued are considered. Out of these six wavelets, the base wavelet minimizing the Shannon Entropy is selected to extract statistical features from wavelet coefficients of raw vibration signals. Finally, bearing faults are classified using these statistical features as input to two soft computing techniques i.e. ANN and SOM. Complex Morlet wavelet is selected based on Shannon Entropy Criterion using proposed methodology. The test results show that the ANN identify the fault categories of rolling element bearing more accurately and has a better diagnosis performance compared to the SOM. Keywords: Continuous Wavelet Transforms, Shannon Entropy, Artificial Neural Networks, Self-Organizing Maps

NOMENCLATURE Symbol

Quantity

yk xpi wjk

Output vector ith input of the pth input vector Synaptic weight between hidden and output layer Scale number Energy probability distribution Shannon Entropy of nth scale ith wavelet coefficient of nth scale Energy of nth scale

n pi Sentropy(n)

Cn,i

E(n) 1. INTRODUCTION

Rolling element bearings are used in a wide variety of rotating machinery from small hand-held devices to heavy duty industrial systems and are primary cause of breakdowns in machines. Condition monitoring of rolling element bearings using vibration signature analysis is most commonly used to prevent breakdowns in machinery. To analyze vibration signals different techniques such as time, frequency and time-frequency domain are extensively used. The complex and non-stationary vibration signals with a large amount of noise make the bearing faults very difficult to detect by conventional time domain and frequency domain analysis which assumes that the analyzed signal to be strictly periodic. Therefore, development of method of conditioning the signal is necessary for features extraction. Samantha and Balushi [1] have presented a procedure for fault diagnosis of rolling element bearings through artificial neural network (ANN). The characteristic features of time-domain vibration signals of the rotating machinery with normal and defective bearings have been used as inputs to the ANN. Lei et al. [2] have proposed a method for intelligent fault diagnosis of rotating machinery based on wavelet packet transform (WPT), empirical mode decomposition (EMD), dimensionless parameters, a distance evaluation technique and radial basis function (RBF) network. The effectiveness of wavelet-based features for fault diagnosis of gears using

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support vector machines (SVM) and proximal support vector machines (PSVM) has been revealed by Saravanan et al. [3]. Yang et al. [4] have proposed a method of fault feature extraction for roller bearings based on intrinsic mode function (IMF) envelope spectrum. Li et al. [5] have shown that the feature vectors obtained by the FFT, wavelet transform, bi-spectrum, etc., can be used as fault features and the HMMs as the classifiers to recognize the faults of the speed-up and speed-down process in rotating machinery. Fault diagnosis of turbo-pump rotor based on support vector machines with parameter optimization by artificial immunization algorithm has been done by Yuan and Chu [6]. Various artificial intelligence techniques are used with wavelet transforms for fault detection in rotating machines [7-9]. In present work, a methodology is proposed for selection of most appropriate wavelet and to determine scale corresponding to characteristic defect frequency based on Minimum Shannon Entropy Criterion. To convert the complex vibration signals into simplified signals with more resolution in time and frequency domain, these raw signals are divided into 27 sub-signals. Six different wavelets are considered each with 27 sub-signals i.e. 128 scales. In order to select the best base wavelet for rolling element bearings fault diagnosis, Shannon Entropy for each wavelet is calculated. Statistical features are calculated from wavelet coefficients and fed as input to machine learning techniques i.e. Artificial Neural Network (ANN) and Self-Organizing Maps (SOM). The results show that the proposed methodology can extract useful features from the original data and dimension of original data can be reduced by removing irrelevant features. 2.

MACHINE LEARNING TECHNIQUES

Machine learning is an approach of using examples (data) to synthesize programs. In the particular case when the examples are input/output pairs, it is called Supervised Learning. In a case, where there are no output values and the learning task is to gain some understanding of the process that generated the data, this type of learning is said to be unsupervised. Various machine learning techniques such as Artificial Neural Network (ANN), Support vector machines and Self-Organizing Maps (SOM) etc. may be used for fault diagnosis [10, 11]. In the present study, a supervised machine learning technique ANN and SOM as an unsupervised machine learning technique are considered. Pattern recognition and classification using machine learning techniques are described here. 2.1 Artificial Neural Network Artificial Neural Network is an interconnected group of artificial neurons. These neurons use a mathematical or computational model for information processing. ANN is an adaptive system that changes its structure based on information that flows through the network [10]. A single neuron consists of synapses, adder and activation function. Bias is an external parameter of neural network. Model of a neuron can be represented by following mathematical model. p

yk   ( wki xi  wk 0 ) i 1

(1)

Input vector comprising of ‘p’ inputs multiplied by their respective synaptic weights, and sum off all weighted inputs. A threshold (bias) is used with constant input. Activation function converts output into a limited range output. Intelligence of neural network lies in the weights between neurons. Back Propagation (BP) algorithm is most widely used as learning algorithm for calculating synaptic weights. 2.2 Self-Organizing Maps Self-organizing maps are special class of ANN and are based on competitive learning. In self-organizing maps, the neurons are placed at the nodes of a lattice that is usually one or two dimensional. The neurons become selectively tuned to various input patterns or classes of input patterns in the course of a competitive learning process. The location of neuron so tuned (winning neurons) becomes ordered with respect to each other in such a way that a meaningful co-ordinate system for different input features is created over the lattice. A SOM is therefore characterized by the formation of a topographic map of the input patterns in which the spatial locations of the neurons in the lattice are indicative of intrinsic statistical features contained in the input patterns, hence self-organizing map. The type of SOM used in the present study is Kohonen model as shown in Fig. 1.

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Two dimensional array of postsynaptic neurons Winning neuron Bundle of synaptic connections

Input

Fig. 1 Kohonen Model of SOM.

3. EXPERIMENTAL SETUP The problem of predicting the degradation of working conditions of bearings before they reach the alarm or failure threshold is extremely important in industries to fully utilize the machine production capacity and to reduce the plant downtime. In the present study, an experimental test rig (Fig. 2) is used and vibration response for healthy bearing and bearing with faults are obtained. The rig is connected to a data acquisition system through proper instrumentation. Data acquisition and analysis system consists of VibraQuest software and data acquisition hardware. VibraQuest software is designed in LabVIEW for quick data acquisition, review, and storage. Hardware consists of 16 analog input channels, for simultaneous sampling. PCI bus ensures high-speed data acquisition (102.4k Samples/sec). A remote optical sensor with a visible red LED light source is used to measure rotor speed. Piezoelectric accelerometers (IMI 603C01) are used for picking up the vibration signals from various stations on the rig. These accelerometers are having measurement range as ±490m/s2. Table-1 shows dimensions of the Ball Bearings taken for the study. Piezo-electric accelerometers are used for picking up the vibration signals from various stations on the rig.

Fig. 2

Experimental setup: (1) Digital encoder; (2) Variable speed control; (3) Motor; (4) Enclosure; (5) Flexible coupling; (6) Accelerometer; (7) Bearing housing; (8) Tested bearing; (9) Rotor; (10) Load disc; (11) Base; (12) Alignment adjustor; (13) Magnetic load system; (14) Gearbox

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TABLE 1 PARAMETERS OF BEARING

Parameter Outer race diameter Inner race diameter Ball diameter Ball number Contact angle Radial Clearance

Value 28.262 mm 18.738 mm 4.762 mm 8 0° 10 µm

As a first step, the machine was run with healthy bearing to establish the base-line data. Then data are collected for different fault conditions. Various faults considered in bearing components are as shown in Fig. 3. A variety of faults on bearings are simulated on the rig at different rotor speed 250, 500, 1000, 1500 and 2000 rpm. Following five bearing conditions are considered for the study: 1. Healthy bearings (HB) 2. Bearing with spall on inner race (BSIR) 3. Bearing with spall on outer race (BSOR) 4. Bearing with spall on ball (BSB) 5. Combined bearing component defects (CBD) Spall

Spall

(a) Outer Race with spall

4.

(b) Inner Race with spall Fig. 3 Bearing Components with faults induced in them

(c) Ball with spall

MINIMUM SHANNON ENTROPY CRITERION

Total six different wavelets have been considered for the present study. An appropriate wavelet is the base wavelet which minimizes the Shannon entropy of the corresponding wavelet coefficients. Energy content of signal at nth scale is given by ∑ , (2) where ‘m’ is the number of wavelet coefficients and Cn,i is the ith wavelet coefficient of nth scale. The Shannon Entropy of wavelet coefficients is given as . ∑ (3) Where pi is the energy probability distribution of the wavelet coefficients, defined as

,

(4)

1, and in the case of pi = 0 for some i, the value of . is taken as zero. With∑ The following steps explain the methodology developed for selecting a base wavelet based on the “Minimum Shannon Entropy criterion” for the vibration signals under study: 1) Total 150 vibration signals are obtained by considering healthy and faulty bearing conditions. 2) To convert the complex vibration signals into simplified signals with more resolution in time and frequency domain, these raw signals are divided into 27 sub-signals i.e. 128 scales in seventh level of decomposition. 3) For healthy and faulty bearings, continuous wavelet coefficients (CWC) of vibration signals are calculated using six different mother wavelets in which three from real valued as Meyer, Coiflet5, Symlet2 wavelets and other three are complex valued as complex Gaussian, complex Morlet and Shannon wavelets. 4) The Shannon Entropy of CWC is calculated for each of 30 segmented signals at different rotor speed 250, 500, 1000, 1500 and 2000 rpm and loading conditions using healthy and faulty bearings. The average of the Shannon Entropy in the 30 segmented signals is calculated for five bearing conditions i.e. BSB, BSIR, CBD, HB and BSOR. 5) Sum of the mentioned average of the five bearing conditions is determined for each scale (27). 6) The total Shannon Entropy for each wavelet is calculated by adding “Sum of the mentioned average” of all the scales. 7) The wavelet having Minimum Shannon Entropy is considered for fault diagnosis of rolling element bearing.

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The flowchart for above mentioned methodology is shown in Fig. 4. Shannon Entropy calculated for Complex Morlet wavelet is found minimum. Hence, Complex Morlet wavelet is considered to extract features for fault diagnosis. For healthy and faulty bearings, Fig. 5 shows the plots between Shannon Entropy and scale number at rotor speed 2000 rpm with no loader using Complex Morlet wavelet. Entropy plots for faults in Ball, Inner race and outer race are as shown in Fig. 5(a), Fig. 5(b) and Fig. 5(e) respectively. From this it is concluded that fault in inner race gives minimum entropy as compare to fault in ball or outer race, which indicates that inner race defect has more affect on machine vibrations. While for combined bearing component defects, Fig. 5(c) shows that Shannon entropy value is less. For healthy bearing, it is observed that Shannon entropy value is more as compare to bearing containing some faults as shown in Fig. 5(d). Fig. 5 clearly indicates that Minimum Shannon Entropy criterion applied in this study can be effectively used for fault diagnosis of rotor bearing system. 30 sample signals for BSB 3 Real Valued Wavelets

30 sample signals for BSIR

30 sample signals for CBD

3 Complex Valued Wavelets

Signal Decomposition using Wavelet Transform

Raw Vibration Signals

30 sample signals for HB

Shannon Entropy (n)

Fig. 4 Flowchart for wavelet selection criteria 30 sample signals for BSOR

Average ‘n’ of BSB

Average ‘n’ of BSIR

Average ‘n’ of CBD

Average ‘n’ of HB

Average ‘n’ of BSOR

S = Sum of the calculated Average in bearing conditions in each scale

T = total of S corresponding to all scales

Select wavelet which minimizes “T”

Fig. 5 Rotor running at speed of 2000 rpm with no loader (a) BSB (b) BSIR (c) CBD (d) HB (e) BSOR

5.

FEATURE EXTRACTION AND FAULTS CLASSIFICATION

Complex Morlet wavelet is selected as best base wavelet among the other wavelets considered from the proposed methodology. The CWC of all the 150 signals with Complex Morlet as a base wavelet are calculated at seventh level of decomposition (27 scales). When applying wavelet transform to a signal, if the Shannon Entropy measure of a particular scale is minimum

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then we can say that a major defect frequency component exists in the scale. In the present study out of 27 scales considered, the scale having the minimum Shannon Entropy is selected, and the statistical features of the CWC corresponding to the selected scale are calculated. The statistical features that are considered in the present study are 1) Kurtosis: A statistical measure used to describe the distribution of observed data around the mean. Kurtosis is defined as the degree to which a statistical frequency curve is peaked.(5) x x 3 n 1 n n 1 Kurtosis s n 1 n 2 n 3 n 2 n 3 2) Skewness: Skewness characterizes the degree of asymmetry of a distribution around its mean. Skewness can come in the form of negative or positive skewness. x x n Skewness s n 1 n 2 3) Standard Deviation: Standard deviation is measure of energy content in the vibration signal. Standard Deviation

∑

(6)

∑

(7)

These statistical features are fed as input to the machine learning algorithms ANN and SOM for faults classification. The following steps give an overview of the methodology presented in this study for bearing faults diagnosis. 1) In this study, healthy bearings, bearing with spall in outer race, inner race, ball and bearing with combined component defects are considered. Vibration signals in time domain are obtained both in horizontal and vertical directions for each bearing condition at different rotor speed 250, 500, 1000, 1500 and 2000 rpm under loader and no loader condition. 2) Continuous Wavelet Coefficients (CWC) of the vibration signals are calculated at the seventh level of decomposition (27 scales for each sample). These coefficients are calculated for all six mother wavelets, considered in this study. 3) Shannon Entropy of CWC can be calculated thereafter. 4) Complex Morlet wavelet is considered for the fault diagnosis among the six mother wavelets based on minimum Shannon Entropy Criterion. 5) Statistical Features like Kurtosis, Skewness and Standard Deviation are calculated from the wavelet coefficients corresponding to scales having the minimum Shannon Entropy. 6) These three statistical features are calculated for each horizontal and vertical response. So, total six statistical features along with loader condition and rotor speed are fed as input to the machine learning algorithms ANN, SOM for faults classification. 6.

RESULTS AND DISCUSSIONS

In the present study, training and testing of the classifiers ANN and SOM has been carried out. The results on a test set in a multi-class prediction are displayed as a two dimensional confusion matrix with a row and column for each class [12]. Each matrix element shows the number of test examples for which the actual class is the row and the predicted class is the column. A sample training/testing vector is shown in Table 2. Total 75 instances and 8 features are used for the study including statistical features for each of the horizontal and vertical response, number of loader and rotor speed used. TABLE 2 SAMPLE INPUT VECTOR FOR ANN/SOM Horizontal Response Skewness Standard Deviation 10.83371 2.219912 0.00022 11.07509 2.328135 0.002189 6.465513 1.50172 0.000543 5.105068 1.251012 9.59E-05 6.461471 1.54027 0.000284 11.52051 2.097072 0.000249 11.93591 2.410487 0.000198

Amplitude of Features

Kurtosis

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Kurtosis 44.70497 22.66564 16.52251 54.83589 5.805013 7.707975 7.281817

Features Vertical Response Skewness Standard Deviation 4.753333 0.000702 3.398547 0.001975 2.751154 0.00444 4.1949 0.000118 1.464965 0.000217 1.741795 0.000371 1.735277 0.000209

Loader

Speed

Class

0 0 0 1 1 1 1

1000 1500 2000 1000 1500 2000 1000

BSB BSB BSB BSIR BSIR BSIR CBD

1006


4.630504 5.553487 7.704414 6.118728 4.282953 14.40096 6.202332 5.107758

1.210162 1.400872 1.519889 1.480516 1.093893 2.558341 1.447155 1.28273

0.000193 0.000348 0.000105 0.000204 0.000264 0.0002 0.000246 0.000466

13.42329 10.68352 6.478991 4.864674 5.511267 31.59812 25.01716 8.521063

2.375881 2.191045 1.578542 1.254669 1.36593 4.54973 3.508182 2.24933

0.000467 0.001183 0.000399 0.000205 0.000297 0.001268 0.00568 0.030608

1 1 2 2 2 2 2 2

1500 2000 1000 1500 2000 1000 1500 2000

CBD CBD HB HB HB BSOR BSOR BSOR

Table 3 and 4 show the test results as confusion matrices for each of the two techniques i.e. ANN and SOM. Total 75 numbers of instances are obtained in which 15 cases are considered with each of BSB, BSIR, CBD, HB and BSOR respectively. From the Table 3, it is inferred that ANN has correctly predicted 13, 14, 15, 15 and 14 instances, while Table 4 shows that SOM has classified 13, 10, 12, 8 and 13 instances. TABLE 3 CONFUSION MATRIX FOR ANN

BSB

BSIR

CBD

HB

BSOR

13 0 0 0 0

0 14 0 0 1

1 0 15 0 0

0 1 0 15 0

1 0 0 0 14

Classified as BSB BSIR CBD HB BSOR

TABLE 4 CONFUSION MATRIX FOR SOM

BSB

BSIR

CBD

HB

BSOR

13 3 1 3 0

0 10 0 1 1

0 0 12 0 1

0 1 0 8 0

2 1 2 3 13

Classified as BSB BSIR CBD HB BSOR

Table 5 shows accuracy associated with each technique for faults classification. For this study, classification accuracy and Kappa statistic shows that ANN is a better classifier than SOM. The correctly classified instances for ANN and SOM are 94.6667% and 74.6667% respectively. TABLE 5 EVALUATION OF THE SUCCESS OF NUMERIC PREDICTION

Parameters

7.

ANN

SOM

Correctly Classified Instances

71(94.6667%)

56(74.6667%)

Incorrectly Classified Instances

4(5.3333%)

19(25.3333%)

Kappa statistic

0.9333

0.68

Total Number of Instances

75

75

CONCLUSION

This study presents a methodology for detection of bearing faults by classifying them using two soft computing techniques, namely, ANN and SOM. Methodology incorporates most appropriate wavelet selection based on Minimum Shannon Entropy criterion. Complex Morlet wavelet is considered for the fault diagnosis among the six mother wavelets considered. The responses observed for different fault condition of bearing shows that minimum Shannon entropy is obtained for bearings with inner race fault. The classification accuracy obtained for ANN is 94.6667% which is better than SOM (74.6667%). The results show the potential application of these

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soft computing techniques for developing effective maintenance strategies to prevent catastrophic failure and reduce operating cost. REFERENCES [1]

B. Samantha and K.R. Al. Balushi. Artificial Neural Networks based fault diagnostics of rolling element bearings using time domain features, Mechanical Systems and Signal Processing 17: 317-328 (2003). [2] Y. Lei, Z. He and Y. Zi. Application of an intelligent classification method to mechanical fault diagnosis, Expert Systems with Applications 36: 9941-9948 (2009). [3] N. Saravanan, V.N.S Kumar Siddabattuni, and K.I. Ramachandran. A comparative study on classification of features by SVM and PSVM extracted using Morlet Wavelet for fault diagnosis, Expert systems with applications 35: 1351-1366 (2008). [4] Yu Yang, Dejie Yu and Junsheng Cheng. A fault diagnosis approach for roller bearing based on IMF envelope spectrum and SVM, Measurement 40: 943-950 (2007). [5] Z. Li, Z. Wu, Y. He, and C. Fulei. Hidden Markov model-based fault diagnostics method in speed-up and speed-down process for rotating machinery, Mechanical Systems and Signal Processing 19: 329-339 (2005). [6] S. Yuan and F. Chu. Fault diagnosis based on support vector machines with parameter optimization by artificial immunization algorithm, Mechanical Systems and Signal Processing 21: 1318–1330 (2007). [7] Guang-Ming Xian and Bi-Qing Zeng. An intelligent fault diagnosis method based on wavelet packet analysis and hybrid support vector machine, Expert Systems with Applications 22: 1048-1060 (2009). [8] B.A. Paya and I.I. Esat. Artificial neural networks based fault diagnostics of rotating machinery using wavelet transforms as a preprocessor, Mechanical Systems and Signal Processing 11: 751–765 (1997). [9] N. Mehala and R. Dahiya. Rotor Faults Detection in Induction Motor by Wavelet Analysis, International Journal of Engineering Science and Technology 1(3): 90-99 (2009). [10] Simon Haykin, Neural Networks A Comprehensive Foundation, Pearson Prentice Hall publications. Ontario, Canada, 2005. [11] N. Cristianini and N.J. Shawe-Taylor, An Introduction to Support Vector Machines, Cambridge University Press, Cambridge, 2000. [12] Ian H. Witten and Eibe Frank, Data mining practical machine learning tools and techniques, Morgan Kaufmann Publishers, San Francisco, CA, 2005.

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