Faulty bearing detection, classification and location in a three-phase induction motor based on Stockwell transform and support vector machine
Introduction
Induction motors are widely used motors for industrial and domestic applications. Most of them are exposed to various types of environments which cause heat, mechanical stress and corrosion depending on the application. These stresses lead to the development of incipient faults that are non-detectable in nature due to the low sensitivity of protection systems. Incipient faults do not directly affect the motor’s operation, however, in long run they can converge into major faults leading to complete shutdown which leads to catastrophic downtime with a high financial loss. Hence, early detection of incipient faults is important to prevent the same. Thus, effective condition monitoring and fault diagnosis mechanisms are needed to detect incipient faults at an early stage.
Bearing faults are the major contributor of faults with 40 [1] share in total motor faults. These faults include faults in outer-race, inner-race, broken cage and eroded balls etc. Bearing fault diagnosis has been studied using vibration and current data analysis. Vibration analysis is a commonly used approach for bearing fault detection and has been reviewed in [2], [3]. In vibration analysis, the additional requirement of vibration modules and transducers make it a costly solution. Motor current signature analysis (MCSA) is a cost-effective alternative that requires only current measurement. The relation between defect frequencies in the current spectrum and vibration spectrum can be obtained as reported by Schoen et al. [4]. In MCSA, Fourier transform provides spectral characteristics of the current signal in relation to defect frequency which is utilized to detect the bearing faults [5], [6], [7], [8]. In recent studies [9], [10], the features extracted from spectral characteristics are utilized to detect faults with multi-agent systems. In [11], the authors proposed a scheme based on Independent Component Analysis and FFT of the current signals. The features of FFT of current signal and Hilbert Huang Transform of vibration signals have been used together to perform bearing fault classification using a hierarchical classifier [12]. FFT is a widely used frequency domain tool for spectral analysis, however, it provides frequency information without time localization, which may not be effective in fault diagnosis.
The shortcoming of FFT is overcome by various advanced signal processing techniques with the multi-resolution capability in both time and frequency domain [13], [14], [15]. These include Short-time Fourier Transform (STFT), Wigner-Ville Distribution (WVD), Wavelet Transform, Hilbert-Huang Transform [16], [17], [18]. STFT and WVD are window based transforms which suffer from fixed window size limitation and existence of cross terms respectively. These limitations are overcome by Wavelet Transform (WT) where the window size is dependent on frequency; a wider window for low frequencies and vice versa. WT has been extensively explored for fault diagnosis of induction motors using vibration and current signals [19], [20].
In [21], Schmitt et al. proposed a bearing fault detection scheme based on information theoretic measures (relative entropy, Bhattacharyya distance and Lempel–Ziv complexity measure) based on Wavelet Packet Decomposition (WPD) of current signals which are fed to Artificial Neural Network (ANN) to classify inner and outer-race faults. Using Discrete Meyer wavelet as the mother wavelet, Zarei and Poshtan [22] used RMS values of coefficients extracted from WPD of current signals for bearing fault detection. The RMS values of components (defect frequency selective) extracted from WPD of current signals are used for detection of outer-race and cage faults in [23], [24].
Stockwell Transform (or S-Transform or ST) is a phase corrected version of Continuous Wavelet Transform (CWT) which magnifies the information in specific frequency bands with proper dilation and contraction of the Gaussian mother wavelet. The ST has found a number of application in distribution systems with renewable energy sources [25], [26], [27], [28], [29], [30] and in transformer protection [31]. The algorithm proposed by Singh and Shaik [32], [33] also illustrates the effectiveness of ST analysis in detecting the bearing faults. It has been shown that using the magnitude and phase information, bearing faults can be detected.
This paper presents an algorithm for detection, classification of various bearing faults such as outer-race, cage and ball faults and to locate defective bearings in three-phase induction motor. Defect in the bearing is detected by computing Total Harmonic Distortion of three-phase stator currents and with comparison with a preset threshold. Subsequent to fault detection, current signals are further decomposed with Stockwell Transform to extract the features in terms of magnitude and phase angle. The features used for SVM classifier are extracted based on the Fisher score and correlation technique. These selected features are fed to SVM for the purpose of classifying various defects in the bearing. The same features are fed to ANN in order to establish the superiority of SVM over ANN in terms of classification efficiency. It has been found successful in finding the location of defective bearings (fan-side or load-side). The performance of the algorithm has been established from the experimental data of defective bearings collected from the industry.
The rest of the paper has been organized in five sections. Section II explains the theoretical background of the proposed work. Section III details the experimental set-up used in the study. Section IV presents the proposed methodology for bearing fault detection and its location detection. Results are discussed in Section V. The paper is concluded in Section VI.
Section snippets
Bearing faults
Bearing defects induce vibrations in the machines, therefore causing predictable frequencies in the vibration spectrum. These vibrations affect the air–gap eccentricities which perturb flux density. It affects the stator current which can be captured in its spectrum. According to [4], the vibration and current frequencies can be related by the following equation,where, is the electrical frequency, and are the characteristic defect frequencies in current and
Experimental set-up
The experimental set-up comprises a 3-phase, 4-pole, 440 V, 50 Hz induction motor whose rotor is supported by two bearings, Type 6204 (fan-side) and Type 6205 (load-side) as shown in Fig. 3. The data acquisition system includes NI cDAQ9178 chassis, NI 9247 current module (50 Amp), NI 9205 voltage module and an interfacing software LabView 2012.
The defective bearings collected from the industry are batched into three categories i.e. bearings with ball fault, cage fault and outer-race fault as
Proposed methodology for bearing fault diagnosis
The stator currents are analyzed with the Fast Fourier Transform to detect fault followed by Stockwell Transform to classify various bearing defects and to locate the defective bearing. Detection of a faulty bearing is carried out by comparing Total Harmonic Distortion (THD) with that of a healthy bearing. Subsequent to fault detection, the current signals are analyzed with ST to extract possible features based on statistical properties of phase and magnitude plots of the ST matrix. These
Fault detection
The Fourier Transform of supply voltage and stator current signals (for healthy and bearing with ball defect) are presented in Fig. 6a and b respectively. Fig. 7a depicts the fault index computed for fault detection for healthy and bearing with ball fault. From this figure, it is evident that the fault index for ball fault is higher than that of a healthy bearing. Fig. 7b illustrates fault indexes of ball, cage and outer-race faults along with those of the healthy bearings. It can also
Conclusion
Detection, classification and location of faulty bearing in a three-phase induction motor is achieved by FFT and ST analysis of stator current signals with the help of SVM classifier. Fault detection is carried out by comparing a fault index with a predefined threshold which is computed based on THD of current and voltage signals. A set of features are selected from Stockwell Transform of current signals with the help of Fisher score ranking method and correlation techniques. These features are
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