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FAULT DIAGNOSIS OF LOW SPEED BEARING BASED ON ACOUSTIC EMISSION SIGNAL AND MULTI-CLASS RELEVANCE VECTOR MACHINE Achmad Widodo1, Jong-Duk Son1, Bo-Suk Yang1, Yong-Han Kim2, Andy C.C. Tan2, Joseph Mathew2 Dong-Sik Gu3, Byeong-Keun Choi3 1

School of Mechanical Engineering, Pukyong National University, San 100 Yongdang-dong, Nam-gu, Busan 608739, Korea. 2 CRC for Integrated Engineering Asset Management, Queensland University of Technology, 2 George St. Brisbane, QLD 4001, Australia. 3 Department of Mechanical and Aerospace Engineering, Gyeongsang National University, 445 Inpyeong-dong, Tongyeong City, Gyeongsang Nam-Do 650-160, Korea. [email protected]

Abstract This study presents fault diagnosis of low speed bearing using multi-class relevance vector machine (RVM) and support vector machine (SVM). A low speed test rig was developed to simulate various defects with shaft speeds as low as 10 rpm under several loading conditions. The data was acquired from the low speed bearing test rig using two acoustic emission (AE) sensors under constant loading (5 kN) with different speed (20 rpm and 80 rpm). The aim of this study is addressed to search the reliable method for low speed machine fault diagnosis. In this paper, two methods of multi-class fault diagnosis based on classification techniques using RVM and SVM are presented. In present study, component analysis was performed to extract the feature and to reduce the dimensionality of original data feature. Moreover, the classification for fault diagnosis was also conducted using original data feature without feature extraction. The result shows that multi-class RVM gives promising technique for fault diagnosis of low speed machine.

1. INTRODUCTION There are many industries equipped by low speed rotating machinery such as rolling machine in paper mill, steel pipe and mining industries. Also, low speed rotating machine can be found in wind turbine power plant. As rotating machinery, bearing is critical component and sometimes it must carry heavy loads and operate at high efficiency and reliability. Therefore, condition monitoring and fault diagnosis of low speed bearing is very useful to guarantee the effectiveness and reliability of this machine. Establishing intelligent system for faults detection of low speed rotating machine is a solution. To face this issue, the research area in machine learning has been applied to perform condition monitoring, faults detection and classification. The AE method is a high frequency analysis technique which was initially developed as a non-destructive testing (NDT) tool to detect crack growth in materials and structures. In the case of rolling element bearing, AE technique has been studied deeply by researcher with their own point of view. Yoshioka and Fujiwara have reported that AE parameters identified bearing defects before they appeared in the vibration acceleration range [1]. Morhain and Mba

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undertook an investigation to ascertain the most appropriate threshold level for AE count diagnosis in rolling element bearings [2]. Moreover, the research of low speed bearing monitoring also has been conducted using AE sensors. Another research was conducted by Miettinen and Patanity that show the use of AE technique in monitoring of faults in extremely low speed rotating rolling that vary from 0.5 to 5 rpm [3]. The result revealed that AE measurement was very sensitive and the fault was easily identified under laboratory scale. Jamaludin et al. investigated the applicability of AE for detecting early stage of bearing damage rotating at 1.12 rpm [4]. It was conclude that parameters such as amplitude and energy provided valuable information on the condition of a particular low speed rotating bearings. In present study, fault diagnosis of low speed bearings is presented using pattern classification method based on relevance vector machine (RVM) [5]. Previous study by Li and Li also has conducted bearings fault detection using AE sensor [6]. However, the bearings were rotated at high speed about 2200 rpm and linear discriminant function of classifier was applied for fault classification. Moreover, we employ component analysis that is aimed to support data preparation process.

2. METHODS 2.1 Component Analysis Component analysis is a technique of multivariate statistical analysis that can linearly or nonlinearly transforms an original set variables into a substantially smaller set variables. This technique has been widely applied to virtually every substantive area including cluster analysis, visualization of high-dimensionality data, regression, data compression and pattern recognition. In this research, component analysis is used to extract the optimal feature and to reduce the dimension of original features by means of principal component analysis (PCA) [7] and independent component analysis (ICA) [8]. This paper do not review the theory of component analysis, interested readers are suggested to refer to the mentioned papers. 2.2 Relevance Vector Machine Originally, RVM is derived and experimented on binary classification; it is desired to predict the posterior probability of membership of one of the classes given the input x. It follows the statistical convention and generalize the linear model by applying the logistic sigmoid function σ(y) = 1/(1+e-y) to y(x) and adopting the Bernoulli distribution for P(t|x), the likelihood is written as [5] N

P (t | x ) =

∏ σ { y (x

tn 1−tn n ; w )} [1 − σ { y ( x n ; w )}]

(1)

n =1

However, unlike the regression case, we cannot integrate the weights analytically, and so are denied the closed-form expression for either the weight posterior p(w|t,α) or the marginal likelihood P(t|α), with α a vector N+1 hyperparameters. The approximation procedure proposed by MacKay [9], which is based on Laplace’s method. While mentioning an extension to multi-class problem, the original formulation of RVM essentially treats the K multi-class problem as a series on n one-against-all binary classification problem. This would translate into training n binary classifiers independently. The likelihood in Eq. (1) is generalized to standard multinomial form: N

P (t | w ) =

K

∏∏ σ { y

tn k k ( x n ; w k )}

(2)

n =1 k =1

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where tnk is the indicator variable for observation n to be in class k; yk is the predictor for class k. Moreover, a true multi-class likelihood can be stated N

P (t | w ) =

K

∏∏ σ { y ; y , y ,..., y k

1

2

tn k K}

(3)

n =1 k =1

where the predictors of each class yk is coupled in the multinomial logit function (or softmax) σ ( y k ; y1 , y 2 ,..., y K ) =

e yk

(4)

(e y1 + e y2 + ... + e yK )

Interested readers who need detail explanation of this method are suggested to refer to the paper written by Zhang and Malik [10]. 2.3 Support Vector Machine The basic idea of applying SVM to pattern classification can be stated as follows: first, map the inputs vectors into one features space, possible in higher space, either linearly or nonlinearly, which is relevant with the kernel function. Then, within the feature space from the first step, seek an optimized linear division, that is, construct a hyperplane which separates two classes. However, this technique can also be extended to multi-class classification. A complete description about SVM is available in Ref. [11]. In the linear separable case, there exists a separating hyperplane whose function is w⋅x + b = 0 which implies

(5)

i = 1,…, N (6) yi(w⋅x + b = 0) ≥ 1, By minimizing ||w|| subject to this constrain, the SVM approach tries to find a unique separating hyperplane. Here ||w|| is the Euclidean norm of w, and the distance between the hyperplane and the nearest data points of each class is 2/||w||. By introducing Lagrange multipliers αi, the SVM training procedure amounts to solving a convex quadratic problem (QP). The solution is a unique globally optimized result, which has the following properties N

w=

∑α y x

(7)

i i i

i

Only if corresponding αi > 0, these xi are called support vectors. When SVM are trained, the decision function can be written as ⎛ f (x) = sign⎜ ⎜ ⎝

⎞

N

∑α y (x ⋅ x ) + b ⎟⎟⎠ i i

(8)

i

i =1

The method of low speed bearing fault diagnosis is presented in Figure 1. In this figure, AE signals are acquired from the developed test rig of low speed machinery fault simulator. The acquired signals are then preprocessed through enveloping technique to highlight the bearing characteristic frequencies. In addition, feature extraction is conducted by calculating statistical features and mean peak ratio (MPR) based on acquired signals. Peak finding is addressed to obtain the peaks of bearing characteristic frequency after enveloping process and then compared with calculated bearing frequencies. Frequency comparator is aimed to validate bearing characteristic frequency from enveloping process and the calculated one. Finally, fault diagnosis of low speed bearings is conducted by relevance vector machine (RVM).

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Bearing Characteristic Frequency Calculation

Acoustic Emission & Vibration Signal

Feature Calculation

Feature Extraction

Frequency Comparator

Enveloping

Mean Peak Ratio (MPR)

Peak Finding

Fault Diagnosis (RVM, SVM)

Figure 1. Block diagram of fault diagnosis scheme.

3. EXPERIMENT The low speed machinery fault simulator was developed to conduct research on low speed condition monitoring and fault diagnosis [12]. This test rig enables modelling of bearing and gearbox faults under different loading conditions; in particular, steady load, impact load, axial load and rumble at low speed as low as 10 rpm. At the driving end, the shaft is attached to a reduction gear box (10.1:1) through a coupling. The constant radial load can be applied close to the driven-end support for long period that is measured by load cell. AE sensor (type R3a from Physical Acoustic Corporations) with frequency range 25-530 kHz was attached on the top of the bearing housing using magnetic holder as shown in Figure. 2. Data acquisition process was used to record continuous AE waveform. A laptop computer connected to PCI board to form the Micro-DiSP system is capable of 18-bit, 10 MHz A/D conversion, on board processing. A total 15 waveforms were captured for each condition for spectral averaging.

Figure 2. Location of AE sensor and accelerometer. The bearing used in this study is a cylindrical roller bearing, SKF NF307, with the inner ring and outer ring are separable. The test bearing enables an easy access to the raceway for seeded defects and to observe the surface condition. The faults of crack and spall was simulated by a hair-line scratching using diamond bit and grinding using air-speed grinding tool, respectively. All type seeded defect bearings used in this study (Figure 4) are listed as follows: inner-race crack (IFC1), inner race spall (IF1), outer-race crack (OFC1), outer-race spall (OF1), small spall on roller (BF1), medium spall on roller (BF2). In addition, the normal bearing was also experimented for benchmarking. Totally, we have 6 classes of faulty bearings and one normal condition for fault diagnosis simulation. In this study, measurement has involved acoustic emission sensor. The AE technique has been successfully applied in bearing defect detection in the high frequency range over 100 kHz [4,13]. In this experiment, the signals were acquired using acoustic emission sensor with a sampling frequency of 500 kHz for 10 second.

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(a)

(b)

(c)

(d) (e) (f) Figure 4. Seeded defects on the bearing: (a) IFC1, (b) IF1, (c) OFC1, (d) OF1, (e) BF1, (f) BF2.

4. FEATURE EXTRACTION AND SIGNAL PROCESSING The time series signal can be used to perform fault diagnosis by analysing acoustic signal obtained from the experiment. Statistical methods have been widely used that can able to present the physical meaning of time data series. For instance, the use of overall root-means-square (RMS) and crest factor (ratio of peak value to RMS) has been applied for detection of localized defects [14]. Moreover, probability density has also popularly been used for bearing defect detection [15]. In present study, statistical method is employed to investigate the characteristic of the system by calculating 14 statistical feature parameters in time and frequency domain presented as follows: mean, RMS, shape factor, skewness, kurtosis, crest factor, entropy error, entropy estimation, histogram lower and upper, peak value, RMS frequency, frequency center and root variance frequency. To detect rolling element bearing failures, we also performed envelope analysis to show bearing characteristics frequencies by isolating other unwanted signals. Envelope analysis typically refers to sequence of the following procedures: (1) Band-pass filtering (BPF), (2) Signal rectification, (3) Hilbert transform of low-pass filtering, and (4) Power spectrum. The purpose of BPF is to reject the low-frequency high-amplitude signals to eliminate random-noise outside the pass-band. In the present study, we employed six band-pass setting for enveloping: BPF1: 5-15 kHz, BPF2: 15-25 kHz, BPF3: 25-35 kHz, BPF4: 35-55 kHz, BPF5: 55-75 kHz, BPF6: 75-100 kHz. From the enveloping process, six features called mean-peak ratio [16] are calculated using the following equations. n

∑ (P mPRO = 20 log10

j

− As )

j =1

(9)

As

n

∑ (P mPRI = 20 log10

j =1

n

j

− As ) +

∑ ( Ps

i

− As )

j =1

(10)

As

where b

As =

∑S

k

k =a

(11)

(b − a)

Figure 7 shows the envelope spectra of an outer-race defective bearing with a hair line scratch (OFC1) at a rotating speed of 80 rpm. It shows the six envelope spectra of AE data using 5

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six different band-pass filter ranges BPF1~ BPF6 as mentioned in previous section. The vertical dot-lines in the figures indicate the BPFO (4.76*80/60 = 6.35 Hz) and its harmonics. From the AE result shown in Figure 7, although the BPFO and its harmonics are clearly visible in all band pass filter range, BPF5 and BPF6 shows the most significant result with relatively high mPRO, 46.77 and 40.75, respectively. A high mPRO indicates higher peak values over the average spectrum. -8

4

-7

HPF[5-15]kHz

x 10

←13.53

2

mPRO=18.84

3

←34.03

0

10 -6

Power spectrum (µV2rms)

1

←27.12 ←28.37 ←5.72 ←11.32 ←22.71 ←39.760.5 ←4.41 ←17.05

1

5

←13.59

1.5

2

0

HPF[15-25]kHz

x 10

mPRO=6.22

20

30

0

40

10

20

30

40

HPF[35-55]kHz x 10 5 ←0.54 mPRO=30.89 4

mPRO=26.76

4 ←0.54

0 -6

HPF[25-35]kHz

x 10

←12.87 ←19.25 25.69 27.12 ←← 39.70 ← ←38.50 27.72 ← ←27.42

←6.44

3

3

2

2

← ←2.156.44 ← 1 2.15 ← ←1.61 2.68 3.22 ← ←25.69 1.07 ←6.44←12.81 ←38.50 ←← ←19.25 ←3.22 ←32.13 13.59 ← ←12.87 1.61

1 0

0

10 -7

2

20

30

0

40

1

←6.44

10 -8

HPF[55-75]kHz

x 10

0 x 10

20

←25.69 30

40

HPF[75-100]kHz

mPRO=46.77

mPRO=40.75 0.8

1.5

0.6

←6.44

1

←19.25 ←25.69 ←12.81 ←38.50 ←32.13

0.5 0.54 2.15 ← ← 1.61 1.07 ← 0 ← 0

10 20 30 Frequency (Hz)

0.4 0.2

←25.69 32.13 38.50 ←19.25 ← ←

←12.81 2.686.56 1.07 ←← 0.54 0 ← ← 0 10 20 30 Frequency (Hz)

40

40

Figure 7. Envelope spectra from OFC1 bearing at 80 rpm. Totally, 20 features are calculated from 14 statistical features and 6 features of mean-peak ratio. The 20 features are too many for performing fault diagnosis; it can be burden and degrade the performance of classifier. Therefore, feature extraction and reduction using component analysis is proposed in this study. Component analysis through ICA, PCA and their kernel is expected can highlight the salient feature among conditions of the machine and reduce the dimension of original features. Feature reduction is performed by calculating eigenvalue of covariance matrix in the component analysis [17], then the features which correlated to highest eigenvalue are selected as data input for classification.

5. RESULTS AND DISCUSSION In this study, classification techniques through SVM and RVM are employed for simulating fault diagnosis. SVM based multi-class classification is applied to perform classification process using one-against-one [18]. Sequential minimal optimization (SMO) proposed by Platt [19] is used to solve the SVM classification problem. RBF kernel (K= exp(– ||x – xj||2 /2γ 2) is used as kernel function of SVM to map the input data into feature space. To select proper kernel parameters (C, γ ), we used cross-validation technique to obtain good performance of classification and to avoid overfitting or underfitting problem. Furthermore, RVM employs multinomial logistic regression for multi-class classification. To solve the standard multinomial form, the components of weights wk in Eq. (2) are estimated from the training data, and then the Newton’s method is employed to perform maximum likelihood estimation of wk. A clear description of this method is presented by Zhang and Malik [10].

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Table 2 shows the classification performance using original features with SVM. In this case, all classification results are bad, even failed. Testing errors are high although SVM has been performed using RBF kernel with optimized kernel parameters by cross-validation. Employing multi-class RVM for this case gives better performance, but they still have bad performance (Table 3). The percentage of minimum errors of RVM is 20.4%. The existence of irrelative features in data input are suspected to be a reason why the classification performances are bad. Therefore, implementation of feature extraction and reduction by component analysis is suggested to increase the performance of classification. Table 2 Classification result of original data using SVM Signal RBF Kernel parameters (C, γ) Testing error, % AE, 20 rpm, 5 kN (1, 0.125) 87.5 AE, 80 rpm, 5 kN (1, 0.125) 85.5

#SV 48 45

Table 3 Classification result of original data using RVM Signal Testing error, % #SV AE, 20 rpm, 5 kN 73.5 127 AE, 80 rpm, 5 kN 20.4 87 Tables 4 and 5 present the result of fault diagnosis based on AE signals using SVM and RVM, respectively. SVM classification technique and ICA feature extraction reach success with testing error 2.04% for AE signal from bearing at rotating speed 80 rpm. Another success is also obtained from SVM classification and ICA with testing error 11.2% for input data from AE signal at rotating speed 20 rpm. In this case, performance of PCA feature extraction is bad in producing data input for SVM. Uncorrelated features from PCA are not satisfied to make input data as linear as possible for determining hyperplane in SVM. Table 4 SVM classification result of AE signal AE Data 20 rpm, 5kN 80 rpm, 5kN

Component analysis ICA PCA ICA PCA

RBF kernel parameters (C, γ) (128, 2) (1, 0.125) (4, 4) (1, 0.125)

Testing error, %

# SV

11.2 85.7 2.04 85.7

42 48 39 48

Table 5 RVM classification result of AE signal Component Data Testing error (%) # RV analysis ICA 16.3 25 20 rpm, 5kN PCA 6.1 28 ICA 44 2.04 80 rpm, 5kN PCA 4.08 42 In the case of fault diagnosis based on RVM, ICA and PCA feature extraction, accuracies are better than SVM technique. Extracted feature by ICA from AE signal at rotating speed 80 rpm give 2.04% testing error. This accuracy is similar to SVM with same data. It can be said that RVM is able to be competed with SVM technique. In addition, the performance of RVM and PCA feature extraction outperforms SVM and PCA techniques. The results are excellent with 6.1% and 4.08% for PCA feature extraction of AE signal at rotating speed 20 rpm and 80

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rpm, respectively. These results are promising for establishing intelligent fault diagnosis of low speed bearing based on RVM classification technique.

6. CONCLUSION In this paper, the study of fault diagnosis of low speed bearing based on AE signal has been presented. Fault diagnosis is conducted using classification technique through relevance vector machine (RVM) and support vector machine (SVM). The classification process gives a comparative study between RVM and SVM in fault diagnosis of low speed bearing. In this study, RVM outperform SVM based on experimental work.

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[18] [19]

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