Induction machines are widely used in the industry as one of the major actuators, such as water pumps, air compressors, and fans. It is necessary to monitor and diagnose these induction motors to prevent any sudden shut downs caused by premature failures. Numerous fault detection and isolation techniques for the diagnosis of induction machines have been proposed over the past few decades. Among these techniques, motor current signature analysis (MCSA) and vibration analysis are two of the most common signal-based condition monitoring methods. They are often adopted independently, but each method has its strengths and weaknesses. This research proposed a systemic method to integrate the information received from the vibration and current measurements. We applied the wavelet packet decomposition to extract the time-frequency features of the vibration and current measurements and used the support vector machines as classifiers for the initial decision-making. The significant features were identified, and the performances of several classifiers were compared. As a result, the decision-level sensor fusion based on the Sugeno fuzzy integral was proposed to integrate the vibration and current information to improve the accuracy of the diagnosis.
Rotary equipment driven by electromechanical systems such as an induction motor has been widely used in the industry because of its simple structure, low cost, and easy maintenance, and for this specific industry, the maintenance cost could ramp up to 60% of the goods produced [
Because most of the plant equipment is mechanical, vibration analysis has been adopted as one of the most often-used condition monitoring techniques [
Nevertheless, the vibration signal was easily contaminated by noises and disturbances, and the resonance of the equipment could therefore undermine the judgement of the diagnosis. To compensate the difficult identification of the electrical faults by the vibration analysis, the motor current signature analysis (MCSA) can attract much more attention. It measures the three-phase currents of the induction motor, and the Fourier spectrum of the current could reflect both the mechanical and electrical faults. In the definition of ISO 20958, the MCSA is one of the electrical signature analysis (ESA) methods. When the induction motor faults occur, they would cause the variation of the airgap during the radial rotor movement, influence the flux density, and change the three-phase stator currents. The fault-induced frequencies on the current spectrum would emerge as symmetric side lobes alongside the VFD frequency, a phenomenon called the frequency modulation [
Recently, it was reported that the diagnosis based on a single type of sensor could misjudge the machine’s condition. An in-service wind turbine train drive was originally misdiagnosed as bearing faults by the vibration analysis but was later identified as a mechanical imbalance by the current signature analysis [
In this study, we try to integrate the information received from the vibration and current signals. Five induction machine conditions including both mechanical and electrical faults were presented in the experiment. The vibration and current signals during the operation were measured, and the time-frequency features were extracted by applying statistical indexes to the WPD coefficients. The vibration-based diagnosis and current-based diagnosis were conducted, and the performances of multiple classifiers were compared. As a result, a decision-level sensor fusion diagnosis scheme was proposed to integrate both the vibration and current information to improve the accuracy of diagnosis.
Since the Fourier transform is insufficient when analysing the transient and nonlinear features generated by the induction motor faults, the wavelet analysis is used to capture the time-frequency characters of the vibration and current signals. By dilating and translating the mother wavelet, the time-frequency analysis could be realized. Wavelet analysis has a good frequency resolution at the low frequency range and a good time resolution at the high frequency range. The discrete form of the continuous wavelet transform can be represented as
Three-layer WPD.
Statistical features which are usually used for the induction motor fault diagnosis are extracted from WPD coefficients. The statistical indexes such as kurtosis (KU), skewness (SK), standard deviation (SD), root mean square (RMS), maximum value (MAX), and waveform factor (WF) were applied to the wavelet coefficients related to the specific fault characteristic frequencies. The indexes were reported as the most prominent conventional time-domain features which were applied for condition monitoring of typical rolling element bearings [
Statistical indexes.
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A support vector machine is a powerful machine learning technique for data classification. The concept is to calculate the hyperplane which separates two different classes of testing samples. Afterwards, the optimal hyperplane is used to find the maximum margin which separates two different classes of the closest data points [
The fuzzy integral considers the objective evidence supplied by each information source (called the h-function) and the expected worth of each subset of information sources (via a fuzzy measure) in its decision-making process [
The set generated by
The value of
The fuzzy integral is independently defined by Sugeno which is a nonlinear function defined in the fuzzy measure. The general form of the fuzzy integral is defined as [
A fusion strategy of vibration and current signature for the fault diagnosis of induction machines is illustrated in Figure
Flow chart of the proposed method.
The experiment consists of a TECO AEHF 3-phase induction motor (1 HP, low-voltage squirrel cage), a TECO A510 series variable frequency drive (VFD), and an AHB-5 hysteresis brake. Two Benstone 786A accelerometers with a sampling rate of 51,200 Hz were located in the vertical and horizontal directions with respect to the motor nondrive end, as shown in Figure
(a) Setup of the motor-driven rotary system. (b) Installation of accelerometers. a: accelerometer; b: 3-phase induction motor; c: coupling; d: hysteresis brake.
Five conditions were applied to this experiment such as the normal condition, broken rotor bar, misalignment, inner ring fault, and outer ring fault. The broken rotor bar was created by making eight drilling holes in the rotor, as shown in Figure
Broken rotor bar (defect created by drilling).
Bearing failure: (a) inner ring; (b) outer ring.
Setup of laser alignment of the shaft.
The rotation speed of the motor could be adjusted by changing the output frequency of the VFD. In this experiment, the VFD frequency was set to 55 Hz, equivalent to a motor speed of 1650 rpm, and 50% of the nominal load was applied by the hysteresis brake. Hence, the actual rotation speed would be slower than 1650 rpm. The measured data included the three-phase voltage and current signals, the VFD output signal, and the signals from the two accelerometers. In each experiment, the raw data were acquired for 20 seconds. The actual rotation speed was fixed at 1618 rpm, equivalent to 26.97 Hz. The deep groove ball bearings of type 6204-T1 were used in this experiment, and their specification was as listed in [
Parameters of the experiment.
No. | VFD (Hz) | Rotation speed (Hz) | Resistance (%) | Failure mode | Current characteristic frequency (Hz) | Vibration characteristic frequency (Hz) |
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1 | 55 | 26.97 | 50 | Normal | 55 | 26.97 |
2 | 55 | 26.97 | 50 | Broken rotor bar | 57.13 | N/A |
3 | 55 | 26.97 | 50 | Misalignment | 82.5 | N/A |
4 | 55 | 26.97 | 50 | Inner ring fault | 188.3 | 133.3 |
5 | 55 | 26.97 | 50 | Outer ring fault | 137.43 | 82.43 |
The selection of the wavelet function and decomposition level depends on the previous literatures and the evaluation of wavelet coefficients. The mother wavelet and the decomposition level for the vibration and current signals were determined by the same procedure, respectively.
For the vibration signal analysis, the Daubechies and discrete Meyer wavelets were reported as the best wavelet functions in the previous literatures [
(a) Kurtosis factor and (b) crest factor of the vibration signal.
(a) Kurtosis factor and (b) crest factor of multiple-level WPD coefficients.
For the current signal analysis, a high frequency resolution wavelet function is required to emphasize the frequency characteristic of the signal. It was found that the dmey wavelet function has a better frequency resolution compared to db, sym, and coif wavelets [
(a) Kurtosis factor and (b) crest factor of the current signal.
The fault characteristic frequencies of the current signal were calculated as
For the vibration analysis, only the signals from the accelerometer in the vertical direction were considered. The time response, the frequency spectrum, and the time-frequency plot drawn by the WPD in the healthy, inner ring fault, and outer ring fault conditions are as shown in Figures
Vibration signal of the normal condition: (a) time-domain response; (b) FFT; (c) WPD.
Vibration signal of the inner ring fault: (a) time-domain response; (b) FFT; (c) WPD.
Vibration signal of the outer ring fault: (a) time-domain response; (b) FFT; (c) WPD.
The current frequencies generated by a broken rotor bar (
(a) Time response and (b) Fourier spectrum of the current signal under the normal condition.
To identify these frequencies successfully, the current signal was resampled at 1280 Hz, and 8th level decomposition of the WPD, which empirically adopted the discrete Meyer wavelet as the mother wavelet, was applied. The frequency bandwidth therefore was 2.5 Hz per node, and it could separate the characteristic frequency of each fault condition. Five sections of the wavelet coefficients related to
Wavelet coefficients related to (a)
(a) Time response and (b) Fourier spectrum of the current signal under the broken rotor bar condition.
Wavelet coefficients related to (a)
Recursive feature elimination methods (RFEs) [
Feature selection by the RFE.
Feature ranking | |||||||||
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Signal | #1 | #2 | #3 | #4 | #5 | #6 | #7 | #8 | #9 |
Vibration | SK | MAX | CF | KU | WF | VAR | RMS | SD | ME |
Current | SK | CF | WF | MAX | RMS | SD | ME | VAR | KU |
The SVM with linear kernel function was used to validate the result of feature selection by removing the least significant feature in sequence. Of the experiment data, 66.67% was used for training and the remaining 33.33% was used for testing. The classification accuracies of the vibration signal are listed in Table
Classification accuracies of the vibration signal (%).
Number of features | Normal | BRB | MIS | IRF | ORF | Average | Excluded features |
---|---|---|---|---|---|---|---|
9 | 33.33 | 55.56 | 38.89 | 100 | 100 | 65.56 | — |
8 | 33.33 | 55.56 | 38.89 | 100 | 100 | 65.56 | ME |
4 | 33.33 | 55.56 | 38.89 | 100 | 100 | 65.56 | ME, SD, RMS, VAR, WF |
3 | 11.11 | 61.11 | 27.78 | 100 | 100 | 60.00 | ME, SD, RMS, VAR, WF, KU |
On the contrary, the classification accuracy of the current signal in Table
Classification accuracies of the current signal (%).
Number of features | Normal | BRB | MIS | IRF | ORF | Average | Excluded features |
---|---|---|---|---|---|---|---|
9 | 66.67 | 100 | 55.56 | 61.11 | 66.67 | 70.00 | — |
8 | 77.78 | 100 | 72.22 | 61.11 | 61.11 | 74.44 | KU |
7 | 72.22 | 100 | 72.22 | 61.11 | 61.11 | 73.33 | KU, VAR |
6 | 66.67 | 100 | 66.67 | 61.11 | 61.11 | 71.11 | KU, VAR, ME |
5 | 66.67 | 100 | 72.22 | 55.56 | 61.11 | 71.11 | KU, VAR, ME, SD |
4 | 55.56 | 100 | 72.22 | 55.56 | 66.67 | 70.00 | KU, VAR, ME, SD, RMS |
In addition to the linear kernel function, Gaussian kernel and polynomial kernel have been used to implement the kernel SVM. A third-order polynomial is used for the polynomial kernel, while the parameters C and
Classification accuracy of the vibration signal by different SVM kernels (%).
SVM kernel | Normal | BRB | MIS | IRF | ORF | Average |
---|---|---|---|---|---|---|
Linear | 33.33 | 55.56 | 38.89 | 100 | 100 | 65.56 |
Polynomial | 77.78 | 11.11 | 72.22 | 100 | 66.67 | 65.56 |
Gaussian | 38.89 | 16.67 | 77.78 | 100 | 100 | 66.67 |
Classification accuracy of the current signal by different SVM kernels (%).
SVM kernel | Normal | BRB | MIS | IRF | ORF | Average |
---|---|---|---|---|---|---|
Linear | 77.78 | 100 | 72.22 | 61.11 | 61.11 | 74.44 |
Polynomial | 61.11 | 100 | 33.33 | 38.89 | 55.56 | 57.78 |
Gaussian | 61.11 | 100 | 33.33 | 55.56 | 66.67 | 63.33 |
It could be seen that the Gaussian kernel has the highest accuracy of 66.67% for the vibration signal, but it is merely about 1% higher than that of the linear kernel. Besides, the linear kernel has the highest accuracy of 74.44% for the current signal. Hence, the linear SVM was selected to analyse both the vibration and current signals for consistency.
K-nearest neighbours (KNN) and artificial neural network (ANN) were implemented in addition to the linear kernel SVM [
Classification accuracy of the vibration signal by different classifiers (%).
Classifier | Normal | BRB | MIS | IRF | ORF | Average |
---|---|---|---|---|---|---|
SVM | 33.33 | 55.56 | 38.89 | 100 | 100 | 65.56 |
KNN | 61.11 | 27.78 | 55.56 | 100 | 100 | 68.89 |
ANN | 22.22 | 55.56 | 72.22 | 100 | 100 | 69.99 |
Classification accuracy of the current signal by different classifiers (%).
Classifier | Normal | BRB | MIS | IRF | ORF | Average |
---|---|---|---|---|---|---|
SVM | 77.78 | 100 | 72.22 | 61.11 | 61.11 | 74.44 |
KNN | 77.78 | 100 | 44.44 | 33.33 | 55.56 | 62.22 |
ANN | 72.22 | 100 | 22.22 | 50 | 22.22 | 53.33 |
From the aforementioned discussion, it could be concluded that the analyses based on the vibration and current signals have their strengths and weaknesses. The vibration analysis identified the inner ring and outer ring defects accurately, while the current analysis was most sensitive to the broken rotor bar. Both of them have a low classification rate regarding the misalignment and the normal condition. Therefore, a decision-level data fusion scheme based on the fuzzy integrals was proposed to integrate the information from both the vibration and current signals to produce higher classification accuracy than any individual data source, as shown in Figure
In this scheme, the previous vibration and current analysis, which included the feature extraction and classification, remains. The classification results obtained from each SVM classifier and the distance to the hyperplane of each faulty category are used to fuse two data sources. The distance to the hyperplane of each faulty category was calculated and is shown in Figure
Distance of the SVM with (a) vibration data and (b) current data.
The first step of data fusion is to define the membership degree which could be used as a set function to calculate the fuzzy integral. The membership degree represents the degree of accuracy. The value of subset
The second step of data fusion is to determine the fuzzy measure values based on the results of the SVM. The fuzzy measure could be defined as the degree of reliability of the classification result. By looking at the first raw data in Tables
Definition of fuzzy measures.
Classifier faults | SVM I (vibration signal) | SVM II (current signal) |
---|---|---|
Normal | 0.33 | 0.78 |
BRB | 0.5 | 1 |
Misalignment | 0.39 | 0.72 |
Inner ring fault | 1 | 0.5 |
Outer ring fault | 1 | 0.5 |
Once the fuzzy measure and membership degree are defined, the values of fuzzy integrals can be calculated using equation (
Diagnosis results of fuzzy integrals.
Fault | SVM classifier | Membership degree | Initial diagnosis | Fuzzy integrals |
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Normal (N) | 1 | 0.7784 | N | 0.7784 (N) |
2 | 0.9539 | E | ||
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Broken rotor bar (BRB) | 1 | 0.9756 | BRB | 0.9756 (BRB) |
2 | 0.9715 | N | ||
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Misalignment (E) | 1 | 0.8869 | E | 0.8869 (E) |
2 | 0.9896 | N | ||
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Inner ring fault (I) | 1 | 0.9894 | O | 0.9923 (I) |
2 | 0.9923 | I | ||
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Outer ring fault (O) | 1 | 0.9029 | N | 0.9476 (O) |
2 | 0.9476 | O |
Classification accuracy of the fusion scheme.
Faulty condition of the motor | ||||||
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Normal | BRB | MIS | IRF | ORF | ||
Results of prediction | Normal | 15 | 0 | 0 | 0 | 0 |
BRB | 1 | 18 | 1 | 0 | 0 | |
MIS | 0 | 0 | 15 | 0 | 0 | |
IRF | 0 | 0 | 2 | 18 | 0 | |
ORF | 2 | 0 | 0 | 0 | 18 | |
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Accuracy (%) | 83.33 | 100 | 83.33 | 100 | 100 | |
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Total accuracy (%) | 93.33 |
This research has discussed the diagnosis of the induction motor from two different perspectives: vibration and current analysis. In general, both the vibration-based and current-based diagnoses have their strengths and weaknesses. For the vibration-based diagnosis, the data acquisition of multiple accelerometers from various locations could help identify the fault location accurately, but this would increase the overall cost on the hardware and software. The diagnosis accuracy is significantly affected by the noise, input disturbance, and resonance. To receive the most accurate measurement of the vibration signal, the accelerometers must be fixed to the shaft holder intrusively. However, most practices attach the accelerometers to the equipment’s surface and hence hinder the transmission of the high-frequency vibration. Simply put, the current transducers used in the current-based diagnosis are nonintrusive and could be installed on the power source, thus preventing the sensors from being damaged by the hazardous environment. Nonetheless, the motor loading must be large enough to make the fault characteristic frequency significant on the current spectrum. To overcome the deficiency of vibration-based and current-based diagnoses, this research proposed a sensor fusion scheme to integrate the information of vibration and current signals. The contributions of this research are listed as follows: The commonly used statistical indexes were applied to the WPD coefficients related to the specific bandwidths, such as the resonant frequency of the vibration signal and the fault characteristic frequencies of the current signal, to generate features for the support vector machines. Through the feature selection process, it was found that skewness, maximum value, crest factor, and kurtosis of the WPD coefficients are the most significant features for the vibration analysis, while skewness, crest factor, waveform factor, maximum value, root mean square, standard deviation, mean, and variance of the WPD coefficients are the most significant features for the current analysis. Both mechanical and electrical faults were reproduced in the experiment. Five conditions including the healthy condition, broken rotor bar, coupling misalignment, inner ring fault, and outer ring fault were considered. The WPD coefficients of vibration and current signals showed distinct patterns with regard to different conditions. It was found that the vibration-based diagnosis has a better performance regarding the mechanical faults, while the current-based diagnosis is more sensitive to the electrical faults. The performances of k-nearest neighbours, artificial neural network, and support vector machines of different kernels were compared. It was shown that the artificial neural network had the best classification accuracy in the vibration analysis, but its edge over the other classifiers was small. On the contrary, the linear kernel support vector machine outperformed the other classifiers in the current analysis. The Sugeno fuzzy integral was adopted to perform the decision-level data fusion of the vibration and current signals. The distance to the SVM hyperplane of each faulty category was used to define the membership degree, and the fuzzy measure between the vibration and current analysis was determined by the classification accuracy of the linear kernel SVM. The fusion result indicated that integrating the information from the vibration-based and the current-based diagnosis at the decision level could well improve the accuracy of the overall diagnosis.
Future development of this diagnosis architecture could include more electrical faults of the induction motor, such as the faults induced by the converter, inverter, and variable frequency drive.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was financially supported by the “Center for Cyber-Physical System Innovation” from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan. Part of the funding also came from the Ministry of Science and Technology (MOST) in Taiwan under Grant no. MOST 107-2221-E-011-139.