Bengal Engineering and Science University, Shibpur, Howrah, India. AbstractâThe paper proposes a Rough-Set CWT based algorithm for multi-class fault ...
Fault Diagnosis of Induction Motor Using CWT and Rough-Set Theory Pratyay Konar1, Moumita Saha2, Dr. Jaya Sil2, Dr. Paramita Chattopadhyay1* 1 Department of Electrical Engineering, 2Department of Computer Science Bengal Engineering and Science University, Shibpur, Howrah, India diagnosis of induction motor [5]. The wavelet transform has certain inherent deficiencies like border distortion and energy leakage which generate a lot of small undesired spikes all over the frequency/scales making the results confusing and difficult to interpret [3]. For detecting different types of fault which spreads over a wide frequency range, large size samples are required to be analyzed. Since, computation of wavelet transform is somewhat time consuming it seems not suitable for large size data analysis. Another limitation of wavelet transform is that it cannot achieve fine resolutions in both time domain and frequency domain simultaneously due to the limitation of Heisenberg–Gabor inequality. Thus, although the wavelet transform has good time resolution in high frequency region, it often cannot separate those impacts, where time interval between them is very small [4]. For multi-class fault diagnosis problem an advanced signal processing method is required with a very good timefrequency resolution. Wavelet transform with its inherent deficiencies and limitations is still a very powerful signal processing tool, if applied properly. There are two types of wavelet transform Discrete Wavelet Transform (DWT) and Continuous Wavelet Transform (CWT). DWT has been extensively used by the previous researcher for motor fault detection [4, 5, 6] since it can be easily implemented using a set of successive filter banks. Whereas, there is very limited application of CWT in this area [8-11] especially in multiclass fault diagnosis problem. DWT results are associated with frequency bands following a dyadic scale fixed by the sampling frequency and number of decomposition levels previously selected. On the other hand CWT enables us to analyze the signal at any frequency determined by the scale [7]. The mother wavelet used in wavelet transform is contracted and dilated by changing the scale parameter. The variation in scale changes not only the characteristic center frequency of the wavelet, but also the window length. Therefore the scale is used instead of the frequency. Thus, wavelet coefficients are obtained corresponding to each scale. The whole time–frequency evolution of the signal components is obtained using CWT. CWT uses a set of non-orthogonal wavelet frames to provide highly redundant information and makes all information more visible that can be used for detecting faults. This redundancy requires a significant amount of computation time and resources. Thus, CWT analysis gains in “readability” and in ease of interpretation with a significant increase in amount of computation time and resources [8]. A wavelet function (or mother wavelet used to obtain the wavelet coefficients) has its own center frequency at each scale, inversely proportional to that frequency. A large scale
Abstract—The paper proposes a Rough-Set CWT based algorithm for multi-class fault diagnosis of induction motor. Use of powerful signal processing technique like CWT drastically reduces the hardware (sensor) requirement of the diagnostic system. Only axial vibration signal is enough to classify seven different types of motor faults. Moreover, successful application of Rough Set theory has enabled to select most relevant CWT scales and corresponding coefficients. Thus, the inherent deficiencies and limitations of CWT are eliminated. Consequently, the computational efficiency has also improved to a great extend. With reduction of attributes by 65%, the classification accuracy of the classifiers is very consistent even in presence of high level of noise and with a low frequency sampling frequency of 5120 Hz. Keywords—rough-set; continuous wavelet transform (CWT); vibration monitoring; fault diagnosis; induction motor;
I.
INTRODUCTION
Real world data is often vague and redundant, creating a lot of problem for powerful machine learning technique to take decision accurately. This limits applicability of intelligent techniques to real world problems. The price of the computing equipment has dropped drastically over the past decade while the human experts have remained steadily expensive. In addition, a system that learns automatically from the historical data, works faster than human expert [1]. Data dimensionality, on the other hand is an obstacle for both training and run time phases of machine learning especially to real world applications, where the exact parameter of a relations are not necessarily known. Many more attribute than needed are used to ensure all the necessary information is present which increases complexity of the system. Data mining is the process of analyzing data-set from different perspective and summarizing it into useful information or knowledge. Large dimensional data consists of redundant as well as important information, which are extracted using different data mining algorithms. Technically, data mining is the process of finding correlation or patterns in large relational database and then making crucial decisions depending upon the information acquired. Different computational tools such as Rough-set theory, Fuzzy-set theory, Fuzzy-rough set and genetic algorithm are utilized to develop the data mining algorithms. There has been a substantial amount of research over the past 15 years on the development of condition monitoring of induction motors using various signal processing technique [2,6]. By reviewing the past work it is noted that the wavelet transform has emerged as one of the most popular and widely used time-frequency analysis method in the area of fault
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corresponds to a low frequency, giving global information of the signal. Small scales correspond to high frequencies, providing detail signal information. According to Heisenberg inequality the bandwidth-time product ǻtǻf is constant and lower bounded. Decreasing the scale, i.e. a shorter window, will increase the time resolution ǻt, resulting in a decreasing frequency resolution ǻf. This implies that the frequency resolution ǻf is proportional to the frequency, i.e. wavelet analysis has a constant relative frequency resolution [7]. Therefore one of the key problems using the CWT technique for extraction of features is the selection of proper scales. The selection of mother wavelet and scales that offers the optimum results is a challenging task. Selection of the CWT scales by visual observation can be carried out to find the optimum wavelet scales. But visual observation is always prone to human error and involves the loss of information [12]. The scales selected by visual observation might emphasize one aspect of the original data; but other aspects are inevitably lost. Thus, it is absolutely necessary to use some dimensionality reduction technique to find the most relevant scales which can correlate the wavelet coefficients obtained to that of the original signal. On the other hand it is known that some background noise might creep while recording the vibration signals, due to the effects of the other vibration sources and the external environment. This noise signal is typically assumed to be a white noise signal. Thus, the complex and non-stationary vibration signals in the presence of large amount of noise make the fault detection a bit challenging, especially at the early stage. Keeping the above view points in minds, in the present work an attempt has been made to apply rough set based data mining technique to solve the problem of dimensionality reduction and feature selection complexity, associated with continuous wavelet transform (CWT) based multi-class fault detection in induction motor. Only axial frame vibration signal has been analyzed for this purpose. The investigation has also considered the different level of noisy signals. II.
DIMENSIONALITY REDUCTION AND ROUGH SET
Real-world data-sets are often vague and redundant, creating problems to take decision accurately. Rough-set theory has been used in many applications [13] for dimensionality reduction and selection of the most relevant features that are predictive of class outcome. Dimensionality reduction comprises of selection of the most relevant features that are predictive of the class outcome and rejection of the irrelevant features with minimum information loss [13]. The computation efficiency of a classification problem depends on selection of number of attributes used to build the classifier. Dimensionality reduction can be performed by applying the concept of rough set theory. Rough Set theory was introduced by Z. Pawlak (1982) as a mathematical approach to handle vagueness. Rough Set is a formal approximation of a crisp set (i.e., conventional set) in terms of a pair of sets which give the lower and the upper approximation of the original set [14].
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A. Information and Desision System An information system is a data table represented by S = (U, R). S consisting of data universe U and set of attributes, R known as condition attribute. The attribute a (in R) characterizes each of the data elements x (in U) [14]. Decision System is the information system represented by: S = (U, R ∪ {D}); where, D
∉ R known as decision attribute.
B. Indiscernibility Relation Indiscernibility Relation IND(P) [14] is an equivalence relation defined below:
IND( P ) = {(e, f ) ∈ U × U , ∀a ∈ R, a(e) = a( f ) where, e and f are indiscernible objects. C. Lower Approximation In U/R, the objects which are positively classified, called lower approximation [15] of the set X and written as:
R( X ) = {x ∈U ,[ x]R ⊆ X } D. Upper Approximation The R −upper approximation [16] is the union of all equivalence classes in [X]R which have non-empty intersection with the target set X. Mathematically, it is written as : R ( X ) = { x ∈ U , [ x] R ∩ X ≠ ∅
E. Positive Region The positive region [16] of a target set X is defined below:
POS R (Q ) = U X ∈U / Q R ( X ) where, Q is the decision attribute. F. Dependency An important issue in data analysis is discovering dependencies between the attributes. Intuitively, a set of attributes D depends totally on a set of condition attributes R, denoted by: C D D depends on R to a degree k (0 k 1) as given below:
k = γ ( R, D) = ( POS R D / U The higher the dependency the more significant the attribute is. The lower and upper approximation of Rough Set is represented in Fig 1.
Figure 1: Lower and Upper Approximation of Rough Set [13]
2013 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)
Rough set theory is used for reduct computation by making use of attribute frequency information in discernibility matrix. A reduct is the minimal attribute set preserving classification power of original dataset. Finding a reduct is similar to feature selection problem. Feature selection problem is defined as finding a minimum subset that satisfies a certain criterion. For reduct problem, the criterion is preserving classification quality of original dataset in term of positive region [17]. Two objects are discernible if their values are different in at least one attribute. Skowron and Rauszer suggested a matrix representation for storing the sets of attributes that discern pairs of objects, called a discernibility matrix [18]. III.
CONTINUOUS WAVELET TRANSFORM
Wavelet analysis is similar to Fourier analysis in the sense that it breaks a signal down into its constituent parts for analysis. The Fourier transform breaks the signal into a series of sine waves of different frequencies; the wavelet transform breaks the signal into its ‘wavelets’, scaled and shifted versions of the ‘mother wavelet’. Recently, several research papers have concentrated on Continuous Wavelet Transform (CWT) based fault diagnosis method. The continuous wavelet transform (CWT) is defined as the sum over all time of the signal multiplied by scaled, shifted versions of the wavelet function Ȍ [9]. Lψ f ( s,τ ) = ³ f (t )Ψs*,τ (t )dt
f(t) is decomposed into a set of basis function ȥ(t), called wavelets generated from a single basic wavelet ȥ(t), the so called mother wavelet, by scaling and translation: Ψ s ,τ (t ) =
§ t −τ · Ψ¨ ¸ s © s ¹
1
‘s’ is a scale factor, ‘IJ’ is the translation factor and the factor 1
s 2 is for energy normalization across the different scale. Scaling a wavelet simply means stretching (or compressing) it. IV.
frequency was set to 50 Hz. The experiments were done for different loading conditions varying from no-load to full-load. Six types of faulty motors were considered consisting of motors with faulted bearings, stator fault, voltage unbalance and three motors with rotor related faults (Bowed Rotor, Broken Rotor Bar, Rotor Unbalance). These faults were selected based on surveys conducted by IEEE and EPRI on medium-sized induction machines [19][20][21]. Fig 3 shows the percentage occurrence of different types of faults in induction motor.
CWT IN FAULT CLASSIFICATION OF INDUCTION MOTOR
The schematic representation of the proposed scheme is presented in Fig 2. .
Figure 3: Survey result of IEEE & EPRI of Induction Motor Faults
The loading was applied using a belt drive system. With the belt in place, a constant load was applied to the system by means of a magnetic clutch (brake). Load was varied from 0.510 in-lbs of torque. Adjustment of the load was done by rotating a ring from a position “0” to “5”. A setting of “0” means no-load and a setting of “5” means maximum load. The recorded data were decomposed using CWT. The parameters for wavelet transform are proper selection of mother wavelet and corresponding scales. In this investigation ‘morlet’ wavelet was used as mother wavelet for all CWT operations and implemented in MATLAB 7.1 using wavelet toolbox. ‘morlet’ wavelet was selected to obtain improved frequency resolution since the frequency can be determined via more time points and ‘morlet’ wavelet has more cycles compared to other wavelets. Since the selection of scales is a challenging task in CWT all scales corresponding to the pseudo-frequency range from (0~2560) Hz was selected and the optimum scale selection was attempted using rough set theory. The typical time-domain signal and the corresponding CWT scalogram plot for healthy motor are shown in Fig 4 and Fig 5 respectively.
Figure 2: The schematic representation of the proposed scheme
The axial frame vibration for the healthy and faulty motors was recorded at a sampling frequency of 5120 Hz and supply
Figure 4: Time domain signal of healthy motor
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Figure 5: CWT scalogram of healthy motor
Figure 9: CWT scalogram of motor with voltage unbalance
The typical CWT scalogram plots for different faulty motors are shown in Fig 6-11.
Figure 10: CWT scalogram of motor with faulted bearing Figure 6: CWT scalogram of motor with bowed rotor
Figure 11: CWT scalogram of motor with stator fault Figure 7: CWT scalogram of motor with broken rotor bar
Figure 8: CWT scalogram of motor with unbalanced rotor
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From the scalogram plots it is seen that at low frequency range below 400 Hz distinct characteristic features are not noticed that can be used to discriminate different types of faulty motors from each other or from the motor at healthy condition. Whereas, for the frequency range above 400 Hz distinct characteristic features are observed. This may be used for detecting and discriminating different types of fault. The motors with voltage unbalance and rotor related faults (Bowed Rotor, Broken Rotor Bar and Unbalance Rotor) are difficult to diagnose by visual inspection since they have many common frequency components present. However, by visual inspection scale range varying from 1-8 can be selected to account for all frequency components in the frequency range (400 – 2560) Hz to discriminate and diagnose various motor faults.
2013 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)
V.
FEATURE EXTRACTION AND FEATURE SELECTION USING ROUGH SET
Statistical features were extracted from the CWT coefficients. Total 875 datasets (25 samples x 5 motor load x 7 motor class) from both healthy and faulty motors at five different loading conditions denoted by brake positions ‘0’‘1’-‘2’-‘3’-‘4’ were obtained. The number of data-points was set to 800 for all the samples. 23 scales were selected from wavelet scale range varying from 1 to 84 (1:1:8 10:2:16 20:4:36 44:8:84) to account for all the frequency components. Eight statistical features: Mean, Root Mean Square (RMS), variance, standard deviation, crest, Kurtosis and Entropy values were evaluated from the CWT coefficients for every sample for all loading conditions and treated as attributes. The features were extracted from the CWT coefficients for every scale separately. Thus, in total 184 attributes (8 features x 23 scales) were obtained for each sample. The schematic representation of the algorithm is shown in Fig 12.
attributes selected by visual inspection and furnished in TableI. It is important to observe that reduction of attributes by 65% has very little effect on the classification accuracy. Moreover, if the accuracy levels of 64 attributes obtained from reduct-set and visual observation are compared, it is clear that the performance of the 64 Reduct-Set is more stable and consistent even with a very high level of noisy data. TABLE I. Sl No. Original 2 3 4 5 6 7 TABLE II.
NO OF ATTRIBUTES AND CLASSIFICATION ACCURACY Reduct Set 184 87 82 64 27 5 2
% accuracy Cross Validate
It is very likely that all 184 attributes of the original decision system are not required to determine the class label. Different attributes has different weights and evaluating the most important attributes among them is the main objective of the dimensionality reduction method. The dataset with class label so obtained is discretized and prepared for dimensionality reduction using rough-set. The steps are narrated below: 1. Input the data objects along with class label. 2. Check for discernible objects, i.e, find the attributes which are different for two data objects from different class labels. 3. Evaluate the frequency of each attribute in the set of discernible objects. 4. Sort the attributes according to the decreasing order of frequency of attributes. 5. Fix a threshold and evaluate the reduct set by selecting the attribute having frequency greater than threshold. 6. Output the reduct set. VI.
RESULTS AND ANALYSIS
The cross-validation accuracy of the reduct sets are compared and tabulated in TABLE I. The classification accuracy is judged by three types of classifiers: Multilayer Perceptron (MLP), Radial Basis Function (RBF) and support Vector Machine (SVM) for unknown test sets and two different levels of noisy data. The results are compared with
RBF
SVM
99.08 % 96.45 % 96.34 % 96.11 % 93.82 % 68.00 % 34.04 %
99.54 % 92.34 % 92.68 % 92.22 % 93.82 % 70.05 % 31.08 %
96.34 % 94.85 % 95.08 % 95.31 % 94.05 % 64.80 % 32.91 %
CLASSIFICATION PERFORMANCE FOR UNKNOWN TEST DATA USING MLP AS A CLASSIFIER
Classifier MLP
Figure 12: Schematic representation of the algorithm
MLP
Unknown Test Data Data with 15 dB Noise Data with 10 dB Noise Training Time (in Sec)
184 Attribute Scale 1-84 99.08
64 Attribute Scale 2-9 99.08
82 Reduct From 184 96.34
64 Reduct From 84 96.11
27 Reduct From 184 93.82
99.08
99.20
97.94
98.28
96.57
98.17
95.20
96.57
96.57
95.31
94.97
73.60
92.68
91.54
86.74
339
49
74
48
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Figure 13: Graphical representation of performance of MLP TABLE III.
C LASSIFICATION PERFORMANCE FOR UNKNOWN TEST DATA USING RBF AS A CLASSIFIER
% accuracy
184 Attribute Scale 1-84
64 Attribute Scale 1-8
82 Reduct From 184
64 Reduct From 184
27 Reduct From 184
Cross Validate
99.54
99.42
92.68
92.22
93.82
Unknown Test Data Data with 15 dB Noise Data with 10 dB Noise
99.20
99.20
94.17
94.51
93.82
98.62
97.25
93.37
93.14
90.85
94.05
74.62
89.48
88.8
81.02
Classifier RBF
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accelerometer probe is used for recording the axial frame vibration at a low sampling frequency of 5120 Hz. The performance of the proposed method is very encouraging and consistent even in presence of high level of noise as compared to other research papers presented in TABLE V. The previous research works have used three accelerometer probes along with three current probes. Thus, the proposed scheme provides a better alternative for multi-class diagnosis of induction motor with drastic reduction in instrumentation and computational time. TABLE V. Figure 14: Graphical representation of performance of RBF TABLE IV.
PAPER
CLASSIFICATION PERFORMANCE FOR UNKNOWN TEST DATA USING SVM (c=0.2, g=0.8) AS A CLASSIFIER
Classifier SVM % accuracy Cross Validate Unknown Test Data Data with 15 dB Noise Data with 10 dB Noise Training Time (in Sec)
[22]
184 Attribute Scale 1-84 96.34
64 Attribute Scale 1-8 98.28
82 Reduct From 184 95.08
64 Reduct From 184 95.31
27 Reduct From 184 94.05
96.34
98.62
97.48
97.48
96.68
96.45
94.85
96.34
96.80
96.22
[23]
93.14
72.22
93.37
94.28
88.00
Tri-Axial Vibration
2.1
0.47
0.99
0.42
0.22
Tri-Axial Vibration & 3 ph Current 12800 Hz
Tri-Axial Vibration & 3 ph Current 12800 Hz
[25]
VII. CONCLUSIONS In this paper a Rough Set-CWT based approach is established as a very powerful technique for multi-class classification of induction motor. Only axial frame vibration was found sufficient for detection of faults. Rough Set is successfully used for dimensionality reduction and feature selection. The optimum scales and attributes are efficiently selected using rough set. Consequently, the computation efficiency has improved due to selection of the most relevant features. 19 scales are found important using rough set out of the original 23 scales and consequently the computation time of CWT has reduced from 4.04 sec to 3.05 sec., With reduct set of 64 attributes, which is 65% less than the original set, the average reduction of training time is 85% for MLP classifier. Only one
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FEATURE EXTRATION & SELECTION 126 Features Time Domain
Tri-Axial Vibration & 3 ph Current
PCA+GA Features Selected 27 18 Features Time Domain
Normal condition Bearing looseness Bearing damage Rotor unbalance
12800 Hz
Present work Axial Vibration 5120 Hz
78 Features Time & Frequency Domain ICA, PCA Features Selected 24-27 78 Features Time & Frequency domain ICA + PCA Features Selected 20-27 184 Features CWT Rough-Set Features Selected 64
VIII.
TYPES OF MOTORS
Normal condition Broken Rotor Bar Bowed Rotor Faulty Bearing Rotor Unbalance Eccentricity Phase Unbalance
GA Features Selected 6 [24]
Figure 15: Graphical representation of performance of SVM
TABLE TYPE STYLES CLASSFIER ACCURACY
ART KNN 98.89 %
Decision tree and SVM 99.67 %
Normal condition Broken Rotor Bar Bowed Rotor Faulty Bearing Rotor Unbalance Eccentricity Phase Unbalance
SVM 100 %
Normal condition Broken Rotor Bar Bowed Rotor Faulty Bearing Rotor Unbalance Eccentricity Phase Unbalance
SVM 100 %
Normal condition Broken Rotor Bar Bowed Rotor Rotor Unbalance Faulty Bearing Voltage Unbalance Stator Fault
MLP 96.11 % RBF 92.22 % SVM 95.31 %
ACKNOWLEDGMENT
The authors are thankful to Council of Scientific and Industrial Research (CSIR) for their support for continuation of this project. The authors are also thankful to AICTE and TEQIP-I (BESU, Shibpur unit), Govt. of India for their financial support toward the project.
2013 IEEE Symposium on Computational Intelligence in Control and Automation (CICA)
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