Current Signature Analysis of Induction Motor Mechanical Faults by Wavelet Packet Decomposition

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003 1217 Current Signature Analysis of Induction Motor Mechanical Faults by Wavelet Packet Decomposition Zhongming Ye, Member, IEEE, Bin Wu, Senior Member, IEEE, and Alireza Sadeghian, Member, IEEE Abstract This paper presents a novel approach to induction motor current signature analysis based on wavelet packet decomposition (WPD) of the stator current. The novelty of the proposed method lies in the fact that by using WPD method the inherent nonstationary nature of stator current can be accurately considered. The key characteristics of the proposed method are its ability to provide feature representations of multiple frequency resolutions for faulty modes, ability to clearly differentiate between healthy and faulty conditions, and its applicability to nonstationary signals. Successful implementation of the system for two types of faults, i.e., rotor bar breakage and air-gap eccentricity is demonstrated here. The results are validated based on both simulation and experiments of a 5-hp induction motor. Index Terms Air-gap eccentricity, induction motor, mechanical fault, rotor bar, stator current signature analysis, wavelet packet decomposition (WPD). I. INTRODUCTION AS the backbone of modern industry, induction motors are virtually used in every industry. Online fault diagnostics of induction motors are very important to ensure safe operation, timely maintenance, increased operation reliability, and preventive rescue especially in high power applications. The induction motor faults are generally classified as either mechanical or insulation system faults. Common mechanical faults include rotor bar breakage, rotor end ring cracking, static and/or dynamic air-gap irregularities, stator winding faults, bent shaft, misalignment, and bearing gearbox failures. Statistical data show that the mechanical faults are responsible for more than 95% of all failures [1] [7]. There are different methods for the detection of mechanical faults. Typical examples as related to this may include detection of air-gap eccentricity, shaft and bearing faults by monitoring the vibration signal [6] or by analyzing the lubricating oil debris in the case of latter fault; and detection of stator winding faults means of searching coils that measure the leakage flux along the shaft [3]. Other diagnostic methods include acoustic noise analysis, temperature measurement, infrared measurement, radio frequency emission monitoring, partial discharge measurement and motor current signature analysis (MCSA) [1], [2], [7], [8]. Among all these methods, MCSA is Manuscript received January 7, 2002; revised December 11, 2002. Abstract published on the Internet September 17, 2003. Z. Ye was with the Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada. He is now with the Department of Electrical and Computer Engineering, Queen s University, Kingston, ON K7L 3N6, Canada (e-mail: zhongming.ye@ece.queensu.ca). B. Wu and A. Sadeghian are with Ryerson University, Toronto, ON M5B 2K3, Canada (e-mail: asadeghi@acs.ryerson.ca). Digital Object Identifier 10.1109/TIE.2003.819682 one of the most popular used methods because of the following reasons. Firstly, it is noninvasive. The stator current can be detected from the terminals. Secondly, it can be measured online therefore makes online detection possible. Thirdly, most of the mechanical and electrical faults can be detected by this method. The mechanism of MCSA can be explained as below. The occurrence of motor mechanical faults usually results in an asymmetry in the windings and eccentricity of air gap, which lead to a change in the air-gap space harmonics distribution. This abnormality exhibits itself in the spectrum of the stator current as unusual harmonics. The current spectrum can be obtained through fast Fourier transform (FFT) of the stator current under steady-state conditions. Fig. 1 and depict, respectively, the stator current waveform and spectrum around the fundamental component for a three-phase induction motor with two broken rotor bars. The low sideband harmonic component around 60 Hz is caused by the rotor bar breakage and it does not appear in a healthy motor [Fig. 1(c) and (d)]. The frequency of this component is given by where is the slip frequency of the induction motor and is the fundmanetal frequency. Fault detection and the diagnostic system of induction motors include at least two important parts: feature extraction and classification. The goal of feature extraction is to extract features which are related to specific fault modes. Usually the features are obtained by processing the spectrum of stator current of the induction motors using FFT. Other possible methods include wavelet transform and short-time Fourier transform (STFT). The goal of classification is to classify faulty mode from normal mode and different fault modes. Artificial intelligence (AI), for instance, expert system and artificial neural network, are often used. Much work has been reported in the literature on AI-based fault detection and diagnostic systems [3], [4], [6] [8]. Most of the published methods are based on the features obtained by FFT spectrum. Unfortunately, not much work is reported on the feature extraction methods which can be very important for the performance of the whole diagnostic system. The task of distinguishing faulty conditions from normal conditions based on the resultant FFT spectrum can be done accurately as long as the signals are stationary, the induction motors are run around full-load condition, and the terminal voltages are sinusoidal. The stator current, however, is a nonstationary signal whose properties vary with the time-variant oper- (1) 0278-0046/03$17.00 2003 IEEE

1218 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003 (c) (d) Fig. 1. Stator current waveforms and spectrum around 60 Hz, for healthy and faulty induction motor at speed of 1749 r/min. Stator current waveform of a healthy induction motor. Corresponding spectrum around the fundamental frequency. (c) Stator current waveform for faulty induction motor with two broken rotor bars. (d) Corresponding spectrum around fundamental frequency. ating conditions of the motors such as fluctuations in load torque and power supply. To remedy the problems associated with time variations, STFT, which is a very useful time-frequency localization tool, is usually used. However, STFT is only applicable where the low-pass window function can be suitably chosen and well localized. To this end, a fixed-width window for all frequency components is usually used by this approach and, therefore, STFT cannot provide either multiple frequency resolution or temporal resolution [9], [10]. The importance of a study on new feature extraction methods also arises from the two requirements from the current industry applications. Firstly, most of the induction motors are powered from power electronics equipment, which generate a lot of harmonics. These harmonics make the FFT-based feature extraction difficult for online detection. Secondly, for offline detection and the diagnostic system of large induction motors, it is expensive to run the motor at full-load conditions. While the features obtained from light-load conditions normally cannot ensure an accurate classification. One method is to do the detection and diagnosis during startup. However, the FFT method is incapable for such transient signals. Only the wavelet-based method can be used in these cases. Wavelets are mathematical tools that have recently emerged for applications such as waveform representations and segmentations, time-frequency analysis, detection of irregularities, feature extractions, and compression of digital data. The popularity of wavelets is due to properties such as the dilation property that can be used to adjust the width of the frequency band along with the location of its center frequency, and the translation property that can be used to automatically zoom in and out in order to locate the positions of high-frequency and low-frequency changes. However, the data obtained from wavelet trans-

YE et al.: CURRENT SIGNATURE ANALYSIS OF INDUCTION MOTOR MECHANICAL FAULTS BY WPD 1219 form cannot be used for feature extraction unless by further FFT analysis, which increases the complexity of the algorithm. This paper proposes a new method for mechanical fault feature extraction of induction motors based on wavelet packet decomposition (WPD) of the stator current. Two important characteristics, time localization ability and multiresolution analysis, make WPD very attractive for the purposes of fault detection and diagnosis. The underlying idea of the proposed method is to use WPD to decompose the stator current into the time frequency spectrum, and then use the results to calculate and to choose proper feature coefficients which best represent the mechanical faults of the induction motor. The feature signatures for air-gap eccentricity fault as well as rotor bar breakage are investigated in this paper. II. WPD AND FEATURE COEFFICIENTS A. WPD For any given signal, the discrete wavelet transform is defined as the inner product of the wavelet function and the signal, that is, (2) Fig. 2. Wavelet packet filter bank decomposition and corresponding binary tree. h : low-pass filter; h : high-pass filter. Downsampling # operator. formation of the input sequence at scale can be described by [9], [10] where is the signal to be analyzed and is the discrete wavelet function. The original signal can be approximated with the wavelet functions and the wavelet coefficients where is the scale factor and is the displacement. The wavelets are derived from a so-called mother wavelet by the dilation and translation factors. The mother wavelet is normalized with zero average and meets the following admissibility condition Applying the wavelet transform to the original signal divides the signal into two parts, the high-frequency part and the lowfrequency part. The low-frequency part is called an approximation of the original signal. A series of approximations can be obtained by reiterating such decompositions. The difference of the approximations between two successive decompositions is called the details. The multiresolution analysis (MRA) is an algorithm based on the reiterative decomposition of the low-frequency parts only. The peeling-off process in MRA can also be defined as decomposing the approximation space into a subsequent approximation subspace and the corresponding detail subspace. The detail space related to the approxiamtion space, however, remains undecomposed. WPD is an extension of wavelet transformation achieved by means of generalizing the link between multiresolution approximation and wavelets. In WPD, both the approximation space and the detail space are decomposed further. The trans- (3) (4) where and represent low pass and high pass having a finite-impulse response of size. In Fig. 2, an example is shown for such a division using the conjugation mirror filter banks. The original space is divided into detail and approximation spaces by the low-pass filter and high-pass filter, respectively. The resultant detail space is further divided. The reiterative splitting of vector spaces is represented in a binary tree in Fig. 2, where the binary tree nodes are labeled by their Depth (a dilation factor) and node number (frequency factor), and the corresponding space is denoted as. It has been proven that there are more than different wavelet packet orthonormal bases included in a full wavelet packet binary tree of Depth [9]. Each of these packet has a limitted time support as well as frequency support. B. Feature Coefficients WPD adds redundancy to the transformation by expanding each packet repeatedly. The obtained time frequency representation is a matrix containing the wavelet packet coefficients for all Depths and Nodes. For a signal of length, the total number of Depths is. The maximum number of coefficients for one Depth is. At Depth 0, the coefficients are exactly the original signal. Most of the coefficinets are irrelevant to the mechanical faults to be detected. Further processing is required to make these data useful for the intelligent fault detection and diagnostics using AI techniques such as multilayer perceptron networks and adaptive neural fuzzy systems. (5)

1220 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003 Fig. 3. Approximation of the fourth-order Coiflet function. Fig. 5. Difference of the feature coefficients between faulty and normal conditions for different torques. At Depth 8. At Depth 9. the spectrum of the WPD. The Feature Coefficient for Node at Depth is defined in terms of WPD coefficients as (6) Fig. 4. Feature coefficients for a small three-phase induction motor with two broken rotor bars at different load conditions (torques), 16 sampling points per cycle for 1024 points. At Depth 8. At Depth 9. Owing to the frequency localization, the WPD coefficients of different harmonic components distribute at different Nodes of where is the number of WPD coefficients used for the calculation of the features at Depth and Node. For a given frequency component, the energy of the component is localized at a certain number of Nodes at a given Depth, and the strength of the energy depends on the amplitude of the frequency component [9]. In other words, this frequency component can be represented with the feature coefficients at these Nodes. A set of Nodes from different Depths can be selected to calculate the feature coefficients that best represent the frequency components caused by the faults of the induction motors. In the following section, the current signature extraction of rotor bar breakage and air-gap eccentricity is discussed.

YE et al.: CURRENT SIGNATURE ANALYSIS OF INDUCTION MOTOR MECHANICAL FAULTS BY WPD 1221 TABLE I MEANS OF THE COEFFICIENTS FOR ROTOR BAR BREAKAGE FOR DIFFERENT LOAD CONDITIONS (c) (d) Fig. 6. Feature coefficients for air-gap eccentricity at various loading conditions. Circles: normal conditions; squares: faulty conditions with air-gap eccentricity (simulation results). Node 14 of Depth 8. Node 16 of Depth 8. (c) Node 32 of Depth 9. (d) Node 8 of Depth 7. III. FEATURE COEFFICIENTS FOR DETECTION OF BROKEN ROTOR BARS AND AIR-GAP ECCENTRICITY Dynamic simulations for a 7.5-hp induction motor (parameters are given in Appendix A) with and without mechanical faults can be accomplished using the Winding Function Method (WFM) [11] [13] that is a convenient and a fast method for simulation of the mechanical faults, such as rotor bar breakage, end ring crack, shaft alignment, etc. The parameters of the equivalent circuits representing the rotor and stator can be deterimined from the dimensions of the rotor and stator using the WFM. Any mechanical fault will lead to the change of the parameters of the equivalent circuits. Two mechanical fault modes, i.e.,

1222 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003 TABLE II MEAN AND STANDARD DEVIATION OF THE FEATURE COEFFICIENTS FOR AIR-GAP ECCENTRICITY FOR DIFFERENT LOAD CONDITIONS Fig. 7. Experiment setup. Induction motor and generator: 5 hp, 60 Hz, 208 V, 1750 r/min. rotor bar breakage and air-gap eccentricity are simulated with this method. Although detection and diagnostics of mechanical and electrical faults of induction motors can be done with full load applied. However, the following practical conditions have to be under consideration: For an online fault detection system, it is expected the system can also work when the motor is not run in rated torque. For offline diagnostics system, it is expensive to build a test bench for full-load operation for large power motors. Therefore, a system which can perform diagnostics under reduced load torque is better. Therefore, the conditions for the full range of the torque will be investigated, that is, from 0% to 110% of rated torque. Using WPD, the WPD coefficients of the stator current at steady state can be obtained. The feature coefficients can be calculated for all Depths and Node numbers according to (5). In this paper, fourth-order biorthogonal wavelet Coiflets [11] are used in the WPD. The approximation of the wavelet is plotted in Fig. 3. The Coiflets are one family of compactly supported wavelets with highest number of vanishing moments for a given th order Coiflet, the support width and the vanishing moment for the wavelet function is and the scaling function is, respectively. support width [11]. For an is A. Rotor Bar Breakage Rotor bar breakage is one of the most common motor faults. Several factors may contribute to this fault, such as, hot spots, sparking and thermal unbalance, chemical contamination, and moisture abrasion of the rotor materials. As a rotor bar is broken, a sideband component next to the fundamental frequency increases in the spectrum of the stator current. Using the WPD analysis and (6), the feature coefficients for different load torques are calculated. The mesh plots of the feature coefficients of the stator current at Depths 8 and 9 are given in Fig. 4. This presents the simulation case where two (out of the 44) rotor bars of a three-phase induction motor are broken. The stator current waveform is sampled with 16 points per cycle for a window of 64 cycles. The large amplitude of the coefficients around Node 32, Depth 8, and Node 64, Depth 9, are corresponding to the fundamental component of the stator current. As the torque increases, the fundamental component of the stator current increases which, in turn, leads to the increase of the corresponding feature coefficients. At Depth 8, the feature coefficients plot in Fig. 5 exhibits local peaks at the proximity of Node 32. This implies a low sideband frequency component in the stator current which corre- Fig. 8. Feature coefficients for three-phase induction motor with two broken rotor bars at different load conditions (torques), 16 sampling points per cycle for 1024 points. The y axis is exactly the experiment sequence number; the larger this number, the larger the torque. At Depth 8. At Depth 9. sponds to the broken rotor bar fault. As the torque increases, the node number, which represents the local peak, decreases. Since the node number is propotional to the frequency, this indicates that the sideband component of the rotor bar breakage decreases as the slip speed increases. For light-load conditions, the slip speed is too small, and according to (1), the sideband component is very close to the fundamental component. Therefore, the feature coefficients are too close to the fundamental to be distinguished at this Depth. A similar observation can be made for

YE et al.: CURRENT SIGNATURE ANALYSIS OF INDUCTION MOTOR MECHANICAL FAULTS BY WPD 1223 (c) (d) Fig. 9. Feature coefficients at Depth 10 for rotor bar breakage. Circles: healthy conditions; squares: faulty conditions. Node 60. Node 61. (c) Node 62. (d) Node 63. the feature coefficients at Depth 9 as shown in Fig. 4. The difference of the feature coefficients between the normal and fault conditions are denoted as where and are the feature coefficients for normal and faulty conditions, respectively. Fig. 5 illustrates the feautre coefficient differences at Depths 8 and 9 in a contour form. In the contour plot, the dark area represents a large difference value, while the light area represents a small difference. As can be seen in Fig. 5, the nodes with large differences of feature coefficients appear in three lines: the fundamental components (Node 32, Depth 8 and Node 64, Depth 9), the left sideband components shifting toward the low nodes as the torque increases, and the right sideband components shifting toward high nodes as the torque increases. The feature coefficients on the left-half side correspond to component in the frequency domain and the right-half-side features correspond to the component. (7) The obvious differences of the feature coefficients for the sideband components indicate that these feature coefficients can be used for the applications of detection and diagnosis of the rotor bar fault. However, it is noted that for light-load conditions, the differences of the feature coefficients between faulty and healthy are not very obvious and the nodes are too close to the fundamental component. Therefore, it is difficult to perform a fault diagnosis for these conditions using the stator current. Table I surmmarizes the mean values of the feature coefficients for both faulty and healthy modes of operation of an induction motor with a synchronous frequency of 60 Hz. Three different load conditions, i.e., light, medium, and heavy are considered, where they refer the torque of 0% 30% of the full load, 30% 70% of the full load, and 70% 110% of the full load, respectively. Each of the statistics mean is estimated from about 20 samples. Table I shows that normal and faulty conditions can be clearly distinguished based on the statistical properities of the feature coefficients. Further investigations reveal that the feature coefficients for normal conditions approximately follow a normal distribution,

1224 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003 Fig. 10. Feature coefficients at Depth 9 for rotor bar breakage. Circles: healthy conditions; squares: faulty conditions. Node 30. Node 31. while for faulty conditions, the statistic characteristics vary with the load conditions. Table I shows that for different load conditions, the feature coefficients that best describe the difference between the faulty and normal conditions are located at different Nodes and Depths. For example, for light-load conditions, feature coefficients at Depth 10 are better than those at Depth 8, and the feature coefficients at Nodes 62 and 63 of Depth 10 are better than those at Nodes 60 and 61 of the same Depth. According to the results obtained from Table I, small node numbers should be chosen to detect faults at heavy-load conditions, whereas large node numbers should be used for light-load conditions. B. Air-Gap Eccentricity Air-gap eccentricity is another typical fault related to induction motors. One of the traditional methods to detect the air-gap eccentricity is to monitor the behavior of the motor stator current at the sideband of the fundamental component, that is, where is the rotation frequency, is the number of pole pairs, and is the slip frequency. Feature coefficients related to air-gap eccentricity are also analyzed here in a similar fashion to those of rotor bar breakage. It is observed that the large difference between the feature coefficients of normal and faulty motors appear around: Nodes 31, 32, and 33 at Depth 10; Nodes 15, 16, 17 at Depth 9; and Nodes 7 and 8 at Depth 8. Fig. 6 and depicts feature coefficients of Nodes 14 and 16 (whose frequency is half the fundamental frequency) at Depth 9 for both normal and faulty conditions. The solid lines in these figures are obtained from the feature coefficients using a linear polynormal fit. The feature coefficients of Node 16 tend to decrease with the increase of the slip speed or load torque, while the feature coefficients of Node 14 have another tendency. According to (8), the frequency of the sideband component next to the fundamental component tends to decrease as the slip increases. Hence, the feature coefficients (8) TABLE III MEAN VALUES OF THE FEATURE COEFFICIENTS FOR ROTOR BAR BREAKAGE shift from Node 16 to 14 as load increases. Similar observations can be made for the feature coefficients illustrated in Fig. 6(c) and (d). The feature coefficients of Nodes 7, 8, and 9 at Depth 8, Nodes 14, 15, 16, 17, and 18 at Depth 9, and Nodes 30, 31, 32, 33, and 34 at Depth 10 can be used for detection of air-gap eccentricity. Table II shows the mean and standard deviation for the feature coefficients for normal and faulty conditions, respectively. It can be observed that the mean values for normal conditions are much smaller than those of the faulty conditions. IV. EXPERIMENT VERIFICATION A. Experiment Layout Experiments on a three-phase 5-hp 208-V 60-Hz induction motor (parameters are given in Appendix B) are carried out for normal and faulty conditions (one broken rotor bar, two broken rotor bars, and air-gap eccentricity). The rated speed of the induction motor is 1750 r/min. The induction motors used have an aluminum rotor with 28 rotor bars. The layout of the circuit for the experiment is shown in Fig. 7. Two identical induction motors are installed on the same bench where one is used as a motor and the other as a generator. The shafts of the two machines are in the same axial direction. A delta-connected capacitor bank is connected to the output terminals of the generator to provide a self-excitation current.

YE et al.: CURRENT SIGNATURE ANALYSIS OF INDUCTION MOTOR MECHANICAL FAULTS BY WPD 1225 (c) (d) Fig. 11. Feature coefficients at Depth 10 for rotor bar breakage. Solid lines: normal conditions; dashed lines: conditions of one broken rotor bars; dotted lines: two broken rotor bar conditions. Node 60. Node 61. (c) Node 62. (d) Node 63. B. Rotor Bar Breakage In order to emulate a real rotor bar breakage, first, a hole in the middle of a rotor bar is drilled, so that it is electrically broken. Since in real situations nearby rotor bars are more likely to be broken than remote ones, a second bar which is physically next to the first broken bar is damaged in a similar fashion to create the two broken rotor bar condition. Using the WPD analysis and (6), the feature coefficients for different load torques are caluclated. The mesh plots of the feature coefficients,, of the stator current at Depths 8 and 9 are given in Fig. 8. This experiment presents the case where two (out of the 28) rotor bars are broken, and the stator current waveform is sampled with 16 points per cycle for a window of 64 cycles. The large amplitude of the coefficients around Node 32, Depth 8, and Node 64, Depth 9, corresponds to the fundamental component of the stator current. As the torque increases, the fundamental component of the stator current increases which, in turn, leads to the increase of the corresponding feature coefficients. In Fig. 9, feature coefficients obtained by analyzing the stator current of the induction motor at Depth 10 are plotted for healthy conditions and faulty conditions with two broken rotor bars. As can be observed, distinguishable differences exist between healthy and faulty conditions. For healthy motors, the feature coefficients are constantly small for all load conditions compared to those of the faulty motors, while for faulty conditions, the feature coefficients are changing with the load torque. In Fig. 9, the solid lines are linearly fitted to the feature coefficients. The notable difference in shapes of the lines at different nodes corresponds to the variation tendency of the feature coefficients at a specific node when load changes. For instance, at Node 60, which corresponds to large slip frequency, the feature coefficients increase as the load or slip increases. The feature coefficients are, therefore, fit for detecting the fault at heavy-load conditions. On the contrary, the features at Node 63 are fit for light-load conditions, and for medium-load conditions, the proper Nodes for the fault detection are 62 and 61. The feature coefficients at Nodes 31 and 32 of Depth 9 are given in

1226 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003 Fig. 12. Feature coefficients at Depth 9 for rotor bar breakage. Solid lines: normal conditions; dashed lines: conditions of one broken rotor bar; dotted line: two broken rotor bar conditions. Node 30. Node 31. (c) Fig. 13. Feature coefficients for air-gap eccentricity. Circles: healthy conditions; squares: faulty conditions. Node 15 of Depth 9. Node 16 of Depth 9. (c) Node 32 of Depth 10. (d) Node 8 of Depth 8. (d)

YE et al.: CURRENT SIGNATURE ANALYSIS OF INDUCTION MOTOR MECHANICAL FAULTS BY WPD 1227 TABLE IV MEAN VALUES OF THE FEATURE COEFFICIENTS FOR AIR-GAP ECCENTRICITY TABLE V 7.5-hp 220-V 60-Hz INDUCTION MOTOR Fig. 10. The statistics of the feature coefficients at some of the Depths and Nodes are given in Table III. The differences of the feature coefficients between normal and faulty conditions are clearly demonstrated. It is further found that the feature coefficients are related to the number of broken rotor bars. The feature coefficients for serious faulty conditions are larger than those of slight faulty conditions or normal conditions. For example, the feature coefficients for two broken bars are larger than for one broken rotor bar, and the feature coefficients for one broken rotor bar are larger than for normal conditions. In Figs. 11 and 12, the feature coefficients with zero, one, and two broken rotor bars are plotted versus slip frequency for normal and faulty conditions. C. Air-Gap Eccentricity The same motor generator set is used for the air-gap eccentricity experiment. The induction motor is intentionally placed out of axis with the generator to make a slight air-gap eccentricity. The displacement is about 1 mm. The feature coefficients at Nodes 15 and 16 of Depth 9, Node 32 of Depth 10, and Node 8 of Depth 8 are plotted in Fig. 13. The statistic characteristics of the feature coefficients at some of the Depths and Nodes are given in Table IV for two eccentricity conditions: one is for about 1-mm displacement and the other is for 1.5-mm displacement. The differences of the feature coefficients between normal and air-gap eccentricity are clearly demonstrated. As can be observed, compared to the traditional FFT-based method, the WPD-based feature extraction method provides multiresolution presentation with which the features for lightload conditions can be easier to identify. Although the FFT analysis for steady-state current is accurate, the multiresolution presentation facilitates the training of the artificial-neuralnetwork-based classification network and, therefore, improves the performance of the fault detection and diagnostics. For the transient signal, the WPD is inherently superior to the FFT-based method because of its time localization ability. V. CONCLUSION New feature coefficients for induction motor mechanical faults are obtained by WPD of the stator current. The feature coefficients differentiate the healthy and faulty conditions with an obvious difference. They can be used for the purpose of online noninvasive detection and diagnosis of such mechanical faults. One of the major advantages of this method is that it can be used for nonstationary signal analysis. As is well known, induction motors are commonly used together with the power electronics drives. The traditional FFT-based MCSA method is TABLE VI 5-hp 208-V 60-Hz INDUCTION MOTOR subject to not only the harmonics disturbance, but also frequent dynamics of the drives. This method can be used for such applications. Another advantage is that the feature coefficients obtained using the proposed method are of multiple frequency resolutions. The same frequency component can be represented with different frequency resolution. It is advantageous for fault detection and diagnosis. This method can also be extended to other MCSA-based fault detection applications. See Table V. See Table VI. APPENDIX A APPENDIX B REFERENCES [1] H. Toliyat and T. Lipo, Transient analysis of cage induction machines under stator, rotor bar and end ring faults, IEEE Trans. Energy Conversion, vol. 10, pp. 241 247, June 1995. [2] M. Elkasabgy, A. Eastam, and G. Dawson, Detection of broken bars in the cage rotor on an induction machine, IEEE Trans. Ind. Applicat., vol. 28, pp. 165 171, Jan./Feb. 1992. [3] G. Kliman et al., Noninvasive detection of broken bars in operating induction motors, IEEE Trans. Energy Conversion, vol. 3, pp. 874 879, Dec. 1988. [4] A. H. Bonnett and G. C. Soukup, Rotor failures in squirrel cage induction motors, IEEE Trans. Ind. Applicat., vol. 22, pp. 1165 1173, Nov./Dec. 1986. [5] A. H. Bonnett et al., Cause and analysis of stator and rotor failures in three-phase squirrel cage induction motors, IEEE Trans. Ind. Applicat., vol. 28, pp. 921 937, July/Aug. 1992. [6] D. Dorrell, W. Thomson, and S. Roach, Analysis of air gap flux, current and vibration signals as function of the combination of static and dynamic air gap eccentricity in 3-phase induction motors, IEEE Trans. Ind. Applicat., vol. 33, pp. 24 34, Jan./Feb. 1996. [7] M. E. Benbouzid et al., Induction motor asymmetrical faults detection using advanced signal processing techniques, IEEE Trans. Energy Conversion, vol. 14, pp. 147 152, June 1999. [8] T. Breen et al., New developments in noninvasive online motor diagnostics, in Proc. IEEE PCIC, 1996, pp. 231 236. [9] S. Mallat, A Wavelet Tour of Signal Processing. San Diego, CA: Academic, 1998. [10] I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992.

1228 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003 [11] L. Xiaogang and H. Toliyat, Multiple coupling circuit modeling of induction machines, IEEE Trans. Ind. Applicat., vol. 31, pp. 311 318, Mar./Apr. 1995. [12] H. Toliyat, A method for dynamic simulation of air gap eccentricity in induction machines, IEEE Trans. Ind. Applicat., vol. 32, pp. 910 918, July 1996. [13], Simulation and detection of dynamic air gap eccentricity in salient pole synchronous machines, IEEE Trans. Ind. Applicat., vol. 35, pp. 86 93, Jan./Feb. 1999. Zhongming Ye (M 01) was born in Jiangsu, China. He received the B.S. degree from Xi an Jiaotong University, Xi an, China, in 1992, the M.S. degree from Shanghai Jiao Tong University, Shanghai, China, in 1995, and the Ph.D. degree from Zhejiang University, Hangzhou, China, in 1998, all in electrical engineering. From 1998 to 1999, he was with the Department of Electrical and Electronics Engineering, University of Hong Kong, Hong Kong. From 1999 to 2001, he was with the Department of Electrical and Computer Engineering, Ryerson University, Toronto, ON, Canada. Since 2001, he has been with the Department of Electrical and Computer Engineering, Queen s University, Kingston, ON, Canada. His research interests include high-frequency power conversion, high-frequency ac power distribution systems, electrical machine fault diagnostics, power quality, artificial intelligence, neural networks, and fuzzy logic. Bin Wu (S 89 M 92 SM 99) received the M.A.Sc. and Ph.D. degrees in electrical and computer engineering from the University of Toronto, Toronto, ON, Canada, in 1989 and 1993, respectively. After being with Rockwell Automation Canada as a Senior Engineer, he joined Ryerson University, Toronto, ON, Canada, where he is currently a Professor in the Department of Electrical and Computer Engineering. His research interests include high-power converter topologies, motor drives, and application of advanced control in power electronic systems. Dr. Wu is the recipient of the Gold Medal of the Governor General of Canada, the Premier s Research Excellence Award, and the NSERC Synergy Award for Innovation. He is a Registered Professional Engineer in the Province of Ontario, Canada. Alireza Sadeghian (S 94 M 00) was born in Tehran, Iran. He received the B.A.Sc. (Hons.) degree in electrical engineering from Tehran Polytechnic University, Tehran, Iran, in 1989, and the M.A.Sc. and Ph.D. degrees in electrical and computer engineering from the University of Toronto, Toronto, ON, Canada, in 1994 and 1999, respectively. In l999, he joined the Department of Mathematics, Physics and Computer Science, Ryerson University, Toronto, ON, Canada, as an Assistant Professor. His research interests include knowledge-based expert systems, artificial neural networks, fuzzy logic systems, adaptive neuro-fuzzy networks, and nonlinear modeling.