System and method for extracting motor fault signatures using sparsely driven joint blind deconvolution and demodulation.

Abstract

A fault detection system is provided for extracting fault signatures from time-domain stator current signals of a motor under varying load operation by solving a joint blind deconvolution demodulation problem. The stator currents of the motor under varying operating conditions are modeled as stator currents under steady-state operating conditions affected by a system response vector and a load modulation vector. A proximal alternating linearization minimization method is used to solve the joint blind deconvolution demodulation problem, assuming that the spectrum of the desired signal is sparse. Motor fault detection is then performed using the recovered stator currents under steady-state operating conditions.

Description

Technical Field

[0001] The present invention relates to a system for extracting a fault signature of a motor operating under variable speed or variable load conditions based on motor current signature analysis.

Background Art

[0002] Motor faults such as bearing faults, eccentricity faults, and broken bar faults generate an asymmetric rotating magnetic flux in the air gap between the stator and the rotor, which consequently causes extra frequency components in the stator current. Therefore, when there is a motor fault, the frequency spectrum of the motor current will include not only the operating frequency components but also the fault signature frequency components. Depending on the type of fault, different faults will have different signatures. For example, in the case of an eccentricity fault, the frequency components can be expressed as f s ±mf r where, in the formula, f s is the power supply frequency, f r is the rotor frequency related to the rotational speed, and m = 0, 1, 2,....

[0003] Motor current signature analysis (MCSA) has been widely used for motor fault detection, aiming to extract fault signatures in the frequency domain. Over the past several decades, various MCSA-based methods have been developed to detect various types of motor faults. MCSA-based methods generally work well for motors operating in a steady state with a constant load and constant rotational speed. However, when a motor under test operates under fluctuating conditions, such as a variable load, the magnitude of the motor current will adaptively change to provide sufficient torque to drive the load. In such situations, fault signatures, which are generally much smaller in magnitude than the operating frequency components, can be obscured by the distorted frequency spectrum of the motor current due to the fluctuations in operation, or masked by noise and other systematic perturbations. This problem becomes more apparent in the early stages of fault manifestation. Therefore, it is desirable to develop advanced methods for recovering fault signatures from fluctuating motor currents. Recent research has investigated specific models of load fluctuations, such as phase modulation by sinusoidal loads. In situations where the load changes in a specific pattern, time-frequency analysis methods may be used by analyzing multiple time-domain segments. However, time-frequency analysis methods inherently involve a trade-off between time and frequency resolution. In recent years, minimum variance (MV) beamforming-based denoising techniques have been introduced into the field of motor fault detection to extract small fault signatures under fluctuating load conditions. While MV beamforming-based denoising is excellent at removing random noise, it cannot remove structural load fluctuations. Therefore, there is a need to develop novel methods and systems that can extract motor fault signatures while removing structural load fluctuations. [Overview of the project]

[0004] In this study, we propose a sparsity drive method for extracting fault signatures from time-domain stator current signals of motors under fluctuating load conditions by solving joint blind deconvolution and demodulation problems. Our literature contributes primarily to the following three aspects: First, we construct a physical model of the stator current, combining signal modulation with an unknown load signal and convolution with an unknown filter. Second, under appropriate assumptions, we pose the problem of recovering a steady-state stator signal with a fault signature as a joint deconvolution demodulation optimization problem. Third, assuming that the spectrum of the signal to be sought is sparse, we develop a proximal alternating linearization minimization method to solve the problem. We demonstrate the usefulness of our method for signals collected from actual two-pole induction motors under fluctuating load conditions.

[0005] Some embodiments of the present invention are based on the understanding that a fault detection system is provided for detecting faults in induction motors operating under variable operating conditions, such as variable load conditions, variable speed conditions, or combinations thereof.The fault detection system includes a sensor device connected to the power cable of an induction motor, the sensor device measuring the stator current of the induction motor under the fluctuating operating conditions via the power cable, and the fault detection system further includes a memory for storing a fault detection method implemented by a computer, and a signal processor for performing steps of the fault detection method implemented by the computer, the steps of forming a stator current vector by sampling the measured stator current to be used at a sampling frequency in a time series, reducing the noise of the stator current vector using a minimum variance (MV) beamforming method, formulating a joint-blind deconvolution demodulation optimization problem based on the stator current vector under steady-state operating conditions, the response vector of the induction motor, the modulation vector under fluctuating operating conditions, and the noise vector to satisfy the measured stator current vector having reduced noise, and the joint-blind The method includes the steps of solving a lined deconvolution demodulation optimization problem to estimate the stator current vector for steady-state operating conditions, the response vector for the induction motor, the modulation vector for fluctuating operating conditions, and the noise vector, and extracting fault signatures from a clean stator current estimate vector, the clean stator current estimate vector being generated using the estimated response vector and the estimated stator current vector, the step further including, if at least one of the fault signatures is greater than a threshold, generating a control command to the controller of the induction motor and transmitting the control command to cause the controller to reduce the operating speed of the induction motor to a safe level, and if at least one of the fault signatures is not greater than the threshold, generating a normal command indicating normal operation of the induction motor and transmitting it to the controller.

[0006] According to some embodiments of the present invention, a computer-implemented method is provided for detecting a failure in an induction motor operating under fluctuating operating conditions, such as fluctuating load conditions, fluctuating speed conditions, or a combination thereof. The method comprises the steps of: measuring the stator current of the induction motor under the fluctuating operating conditions via a current sensor connected to the power cable of the induction motor; forming a stator current vector by sampling the measured stator current at a sampling frequency in a time series; reducing the noise of the stator current vector using a minimum variance (MV) beamforming method; formulating a joint-blind deconvolution demodulation optimization problem based on the stator current vector under steady-state operating conditions, the response vector of the induction motor, the modulation vector under fluctuating operating conditions, and a noise vector, to satisfy the measured stator current vector having reduced noise; and solving the joint-blind deconvolution demodulation optimization problem to satisfy the stator current vector under steady-state operating conditions, the induction motor The method includes the steps of estimating the response vector of the motor, the modulation vector of the fluctuating operating conditions, and the noise vector, and extracting fault signatures from a clean stator current estimate vector, the clean stator current estimate vector being generated using the estimated response vector and the estimated stator current vector, and further including the steps of generating a control command to the controller of the induction motor and transmitting the control command to cause the controller to reduce the operating speed of the induction motor to a safe level if at least one of the fault signatures is greater than a threshold, and generating and transmitting a normal command indicating normal operation of the induction motor to the controller if at least one of the fault signatures is not greater than the threshold.

[0007] The accompanying drawings are included for a further understanding of the present invention and are used to illustrate embodiments of the invention and to explain the principles of the invention together with the description. The drawings shown are not necessarily to scale and are generally focused on illustrating the principles of the embodiments of this disclosure. [Brief explanation of the drawing]

[0008] [Figure 1A] This is a schematic diagram showing a system for operating and monitoring an induction motor in the field, according to one embodiment of the invention. [Figure 1B] This is a schematic diagram showing a system for operating and monitoring an induction motor online (on the cloud) according to one embodiment of the invention. [Figure 2] This is a block diagram showing a fault detection process for an induction machine operating under variable operating conditions, according to an embodiment of the present invention. [Figure 3] This figure provides a detailed explanation of spectral analysis of stator current measured from an induction motor operating under variable conditions using a blind deconvolution decomposition method according to an embodiment of the present invention. [Figure 4] This figure shows an exemplary plot of the stator current in the time domain of an induction motor operating under fluctuating operating conditions, according to an embodiment of the present invention. [Figure 5] This is a schematic diagram showing the estimation of the induction motor system response vector and modulation vector of a motor system according to an embodiment of the present invention. [Figure 6A] This figure shows an exemplary plot of the stator current spectrum under one variable load condition (sinusoidal modulation) using Fourier transform and the proposed blind deconvolution decomposition spectral analysis method. [Figure 6B] This figure shows an exemplary plot of the stator current spectrum under one variable load condition (sinusoidal modulation) using Fourier transform and the proposed blind deconvolution decomposition spectral analysis method. [Figure 7A]This figure shows exemplary plots of stator current spectra under different fluctuating load conditions (rectangular modulation) using Fourier transform and the proposed blind deconvolution decomposition spectral analysis method. [Figure 7B] This figure shows exemplary plots of stator current spectra under different fluctuating load conditions (rectangular modulation) using Fourier transform and the proposed blind deconvolution decomposition spectral analysis method. [Figure 8A] This figure shows exemplary plots of stator current spectra under different fluctuating load conditions (random modulation) using Fourier transform and the proposed blind deconvolution decomposition spectral analysis method. [Figure 8B] This figure shows exemplary plots of stator current spectra under different fluctuating load conditions (random modulation) using Fourier transform and the proposed blind deconvolution decomposition spectral analysis method. [Modes for carrying out the invention]

[0009] Various embodiments of the present invention will be described below with reference to the figures. Note that the figures are not drawn to scale, and elements of similar structure or function are represented by the same reference numerals throughout the figures. Note that the figures are intended solely to facilitate the description of specific embodiments of the present invention. They are not intended to be an exhaustive description of the present invention or a limitation on the scope of the present invention. In addition, aspects described in relation to specific embodiments of the present invention are not necessarily limited to those embodiments and can be implemented in any other embodiment of the present invention.

[0010] Figure 1A is a schematic diagram of a fault detection system 100 for controlling and monitoring an induction motor, according to one embodiment of the invention.

[0011] The induction motor (system) 200 includes a rotor assembly 102, a stator assembly 104, a main shaft 106, and two main bearings 108. In this example, the induction motor 200 is a squirrel-cage induction motor. The induction motor 200 is connected to a load device 210, such as a power fan or a transmission belt, mounted on the rotor shaft.

[0012] The controller 220 is powered by the power supply 230 and can be used to monitor and control the operation of the induction motor 200 in response to various inputs according to embodiments of the present invention. For example, the controller 220 connected to the induction motor 200 can control the speed of the induction motor based on inputs received from a fault detection system 100 configured to acquire data on the operating conditions of the induction motor 200 from a current sensor 150. According to a particular embodiment, the electrical signal from the current sensor 150 may be current from one or more of the multiple phases of the induction motor. More specifically, if the induction motor is a three-phase induction motor, the current sensor detects current data from the three phases of the three-phase induction motor. Although a particular embodiment of the present invention has been described in relation to a multiphase induction motor, other embodiments of the present invention are applicable to other multiphase electric machines.

[0013] Some embodiments of the present invention describe a system for fault detection in an electromachine such as an induction motor 200. The system configured for detection includes a fault detection system 100 for detecting the presence of a fault condition of the rotor 102, including an eccentric fault in the induction motor assembly. In one embodiment, the fault detection system 100 is implemented as a subsystem of the controller 220. In an alternative embodiment, the fault detection system 100 is implemented using a separate processor. The fault detection system 100 may also be a hardware circuit module operably connected to the controller 220. In some implementations, the fault detection system 100 and the controller 220 can share information. For example, the fault detection system 100 can reuse sensor data used by the controller to control the operation of the induction motor.

[0014] Furthermore, the fault detection system 100 includes a processor 110, a memory 120, and a fault detection program 121, the fault detection program 121 being stored in the memory 120 when the processor 110 executes instructions for the program. The fault detection system 100 further includes a sensor interface 130 configured to acquire signals from a current sensor 150. The interface 130 includes analog / digital (A / D) and A / D converters for data communication with the processor 110, the memory 120, the fault detection program, a user interface 140, and the current sensor 150. The processor 110 may consist of multiple processors, and the memory 120 may be a memory module containing multiple memories. The processor 110 is configured to execute the fault signature detection program 121 by using the sensor interface 130 to receive signals of the stator current and rotor current of the induction motor 200 via the current sensor 150 connected to the fault detection system 100.

[0015] The user interface 140 is configured to connect to a display unit and a keyboard, which are configured to show normal / fault status information of the induction motor 200 in response to the output of the fault detection module 200.

[0016] Figure 1B is a schematic diagram of a fault detection system operated by a user (operator) via a network 250 to control and monitor an induction motor, according to one embodiment of the invention. In this case, the fault detection system 100 may be located at the user / operator's location or may be included in the operating system of the induction motor located elsewhere. If the fault detection system 100 determines that a serious fault has occurred in the induction motor 200 based on the sensor signal of a current sensor 150 via the network (communication network) 250 during the operation of the induction motor 200, the fault detection system 100 may send a control signal indicating the level of the fault level that has occurred in the induction motor 200 to the controller 220 via the network 250, thereby causing the controller 220 to reduce the operating speed of the induction motor to a safe level or even stop the induction motor. For example, the controller 220 slows down or stops the operation of the induction motor 200 according to the control signal indicating the fault level of the fault determined by the fault detection system 100, based on a pre-programmed algorithm (not shown) stored in the controller 200's memory. The control signal can indicate the operational status of the induction machine 200. For example, the control signal can indicate the normal operation of the induction machine 200 or the level of a fault that has occurred in the induction machine 200. The controller 220 includes a display monitor system (not shown) and a user interface (not shown) configured for inputting control commands to the induction machine 200, so that the operator can control the operation of the induction machine 200 by inputting control commands to cause the induction machine 200 to slow down or stop its operation. Furthermore, when the controller 220 receives a control signal from the fault detection system 100, the display monitor system, which has a monitor and a graphical user interface (GUI), can display the operational status of the induction machine 200 on the monitor of the display monitor system, in which case the operational status indicates the normal operation of the induction machine 200 or the level of a fault detected by the fault detection system 100.

[0017] In some cases, the calibration of the current sensor 150 can be performed based on a sensor calibration program (not shown) stored in the memory of the fault detection system 100. In some cases, the network 250 may be an optical fiber network, a wireless network, or an Internet network, or may be a data communication network composed of at least two combinations of an optical fiber network, a wireless network, and an Internet network.

[0018] This configuration can be a maintenance system managed by a user / client who operates the induction machine system 20 installed separately from the location of the induction machine. For example, this system configuration can be used for a power generation system operated by a user and a train system for controlling an induction motor that drives a train. In some cases, when the fault detection system 100 detects that the location of the induction machine is far from the location of the fault detection system, data communication between the location of the induction machine and the location of the fault detection system is performed via the network. The network 250 may be an optical fiber network, a wireless network, or an Internet network, or may be a data communication network composed of at least two combinations of an optical fiber network, a wireless network, and an Internet network.

[0019] Furthermore, the fault detection system is included as part of the user's maintenance system. When the fault level (e.g., eccentricity) determined for the induction machine is above the critical threshold level, the fault detection system generates a control command and transmits a control signal of the control command to the controller 220 of the induction machine 200 via the network 250 using the sensor interface / control interface 130 to decelerate or stop the operation of the induction machine 200.

[0020] Figure 2 is a block diagram of a fault detection process for an induction machine operating under fluctuating operating conditions, according to an embodiment of the present invention. When the motor 200 is operating under a fluctuating load 210, the motor current is monitored using the sensor interface 130 by continuously measuring the stator current using the current sensor 150. Through the motor current monitoring process 410, the time-domain current 415 is measured and saved at regular time intervals for spectral analysis 420 using the proposed blind deconvolution-resolved spectral analysis method, resulting in a frequency-domain spectrum 425 corresponding to a constant operating condition, with the effects of the fluctuating load removed. Based on the frequency-domain spectrum, fault signatures at a constant frequency, for example, frequency components of approximately 30 Hz and approximately 90 Hz for an eccentric fault when the operating frequency is 60 Hz, are extracted. In this case, the magnitude of the fault signature is used to determine the presence or absence of a fault (440). If the magnitude of the fault component of the fault signature is greater than a certain value (threshold amplitude), for example, about 1 / 100 (-40dB) of the operating frequency component at 60Hz, the fault detection system determines that a fault has been detected, and then a control command (control signal) 450 is sent to the control circuit of the induction motor controller to decelerate or stop the motor for safety purposes. Furthermore, the control command can indicate various fault types, various fault levels, and fault locations based on the detected frequency component and the magnitude of the fault signature signal. For example, if the current intensity on the bearing fault signature frequency increases, a bearing fault is detected. Otherwise, the fault detection system continues to monitor the stator current. In some cases, if the fault detection system does not detect a fault based on the threshold, the fault detection system generates a normal command indicating the normal operation of the induction motor and sends it to the controller's display, causing the display's GUI to display a sign / text indicating the normal operation status on the display.

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[0032] To make our method robust to noise, we preprocess the measurements using denoising by minimum dispersion (MV) beamforming. In the minimum dispersion beamforming method, the time-domain stator current for the test is segmented into multiple overlapping time series with a fixed time shift. Each sequence is treated as an independent measurement of a virtual current sensor. Since the time difference between adjacent sequences is identical, these virtual sensors form a linear virtual sensor array. The spectral analysis problem is then transformed into a beamforming problem of a linear array in the frequency domain. The minimum dispersion beamforming method minimizes the noise dispersion of the spectrum at each frequency, with respect to the weights of the frequency components of the separate sequences. Therefore, while this is effective in reducing noise in the measured current signal, it cannot remove structured artifacts caused by fluctuating loads.

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[0038] Using the initialization of the obtained optimization variables, the estimated values ​​of the variables are obtained by the following optimization problem representing joint blind deconvolution and demodulation. Similar problems have been solved using alternating minimization methods from the perspective of blind deconvolution.

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[0040] Figures 6A and 6B are exemplary plots of the stator current spectrum under one variable load condition (sinusoidal modulation), using the Fourier transform and the proposed blind deconvolution-resolved spectral analysis method, respectively.

[0041] These plots show, as expected, that MV beamforming successfully denoising the signal. This is because MV beamforming effectively destroys noise by averaging the random phase components of the noise while actively adding structured periodic signal sections. However, as expected, MV beamforming cannot remove artifacts caused by load variations, since these artifacts are structured. The proposed method is effective in removing the effects of load variations. The eccentric fault signature corresponds to the rotor frequency f r When the frequency is 30Hz, it can be clearly observed around 30Hz and 90Hz, which is consistent with MSCA-based fault detection models.

[0042] Figures 7A and 7B are exemplary plots of stator current spectra under different fluctuating load conditions (rectangular modulation), obtained using the Fourier transform and the proposed blind deconvolution-resolved spectral analysis method, respectively. Similarly, the proposed method significantly reduced the effects of modulation caused by the fluctuating load.

[0043] Figures 8A and 8B are exemplary plots of stator current spectra under different fluctuating load conditions (random modulation), obtained using the Fourier transform and the proposed blind deconvolution decomposition spectral analysis method, respectively. The proposed algorithm reduces the effects of modulation from the time-domain plot. In the frequency-domain plot, the proposed method is effective in reducing the effects of random convolution and modulation as well as noise, and can maintain eccentric fault signatures at approximately 30 Hz and 90 Hz, respectively.

[0044] The embodiments described above of the present invention can be implemented in any of a number of ways. For example, the embodiments may be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or set of processors, whether provided on a single computer or distributed across multiple computers. Such a processor may be implemented as an integrated circuit with one or more processors within an integrated circuit component. However, the processor may be implemented using circuitry in any suitable format.

[0045] Furthermore, embodiments of the present invention may also be implemented as methods, one example of which has already been shown. The operations performed as part of such methods may be ordered in any suitable manner. Thus, embodiments may be configured in which the operations are performed in an order different from the example sequence, which, although shown as a series of operations in the exemplary embodiments, may include performing several operations simultaneously.

[0046] When terms indicating order, such as "first," "second," etc., are used in a claim to modify a claim element, they do not imply any priority, precedence, or order of one claim element over another, nor do they imply any temporal order in which the actions of the method are performed. Rather, they are merely used as labels to distinguish a claim element having a specific name from another element having the same name (but using terms indicating order).

[0047] While the present invention has been described as an example of a preferred embodiment, it should be understood that various other adaptations and modifications are possible within the spirit and scope of the invention.

[0048] Therefore, the purpose of the attached claims is to cover all such changes and modifications that fall within the true spirit and scope of the invention.

Claims

1. A fault detection system for detecting a fault in an induction motor operating under variable operating conditions, such as variable load conditions, variable speed conditions, or combinations thereof, The fault detection system includes a sensor device connected to the power cable of the induction motor, the sensor device measures the stator current of the induction motor under the fluctuating operating conditions via the power cable, and the fault detection system further includes: A memory that stores fault detection methods implemented by a computer, The computer includes a signal processor that performs the steps of the fault detection method implemented by the computer, the steps of which include: The steps include: forming a stator current vector by sampling the measured stator current used at a sampling frequency in accordance with the time series; A step of reducing the noise in the stator current vector using a minimum dispersion (MV) beamforming method, The steps include: formulating a joint-blind deconvolution demodulation optimization problem based on the stator current vector under steady-state operating conditions, the response vector of the induction motor, the modulation vector under fluctuating operating conditions, and the noise vector, so as to satisfy the measured stator current vector having reduced noise; The steps include: estimating the stator current vector under steady-state operating conditions, the response vector of the induction motor, the modulation vector under fluctuating operating conditions, and the noise vector by solving the joint-blind deconvolution demodulation optimization problem; The step includes extracting a fault signature from a clean stator current estimate vector, the clean stator current estimate vector being generated by using the estimated response vector and the estimated stator current vector, and the step further includes, A fault detection system comprising the steps of: generating a control command for the induction motor controller and transmitting the control command to the controller to reduce the operating speed of the induction motor to a safe level if at least one of the fault signatures is greater than a threshold; and generating a normal command indicating normal operation of the induction motor and transmitting it to the controller if at least one of the fault signatures is not greater than a threshold.

2. The fault detection system according to claim 1, wherein the signal processor performs noise reduction of the stator current using a minimum variance (MV) beamforming method before calculation.

3. The fault detection system according to claim 1, wherein the controller's monitor displays a fault operation sign in response to the reception of the control command.

4. The fault detection system according to claim 1, wherein the control command indicates the fault level and location of the fault that occurred in the induction motor.

5. The fault detection system according to claim 1, wherein, under the aforementioned fluctuating operating conditions, the electromagnetic torque is approximated by the stator current or rotor current of the induction motor.

6. The fault detection system according to claim 5, wherein the half-width of the modulation signal relating to the electromagnetic torque is set to approximately half the operating frequency of the induction motor.

7. The fault detection system according to claim 1, wherein the stator current vector under the steady-state operating conditions is initialized as a linear combination of harmonics of the operating frequency of the induction motor.

8. The fault detection system according to claim 1, wherein the fault signature is determined by running a spectral analysis program on the clean stator current estimation vector.

9. The aforementioned solution is, A step of initializing the response vector and the modulation vector, The fault detection system according to claim 1, further comprising the step of repeatedly updating the stator current vector, the response vector, and the modulation vector until the updates converge.

10. The fault detection system according to claim 1, wherein, under the aforementioned fluctuating operating conditions, the electromagnetic torque is approximated by the stator current and rotor current of the induction motor.

11. A computer-implemented method for detecting a failure in an induction motor operating under variable load conditions, variable speed conditions, or variable operating conditions representing a combination thereof, The steps include: measuring the stator current of the induction motor under the fluctuating operating conditions via a current sensor connected to the power cable of the induction motor; The steps include: forming a stator current vector by sampling the measured stator current used at a sampling frequency in accordance with the time series; A step of reducing the noise in the stator current vector using a minimum dispersion (MV) beamforming method, The steps include: formulating a joint-blind deconvolution demodulation optimization problem based on the stator current vector under steady-state operating conditions, the response vector of the induction motor, the modulation vector under fluctuating operating conditions, and the noise vector, so as to satisfy the measured stator current vector having reduced noise; The steps include: estimating the stator current vector under steady-state operating conditions, the response vector of the induction motor, the modulation vector under fluctuating operating conditions, and the noise vector by solving the joint-blind deconvolution demodulation optimization problem; The method includes the step of extracting a fault signature from a clean stator current estimate vector, wherein the clean stator current estimate vector is generated by using the estimated response vector and the estimated stator current vector, and the method further includes the step of extracting a fault signature from a clean stator current estimate vector, the clean stator current estimate vector being generated by using the estimated response vector and the estimated stator current vector, and the method further includes A method comprising the steps of: if at least one of the fault signatures is greater than a threshold, generating a control command for the controller of the induction motor and transmitting the control command to cause the controller to reduce the operating speed of the induction motor to a safe level; and if at least one of the fault signatures is not greater than a threshold, generating a normal command indicating normal operation of the induction motor and transmitting it to the controller.

12. The method according to claim 11, further comprising removing noise from the stator current using a minimum dispersion (MV) beamforming method before calculation.

13. The method according to claim 11, wherein the controller's monitor displays a fault operation sign on the controller's display in response to the reception of the control command.

14. The method according to claim 11, wherein the control command indicates the fault level and location of the fault in the induction motor.

15. The method according to claim 11, wherein, under the aforementioned fluctuating operating conditions, the electromagnetic torque is approximated by the stator current or rotor current of the induction motor.

16. The method according to claim 15, wherein the half-width of the modulation signal relating to the electromagnetic torque is set to about half the operating frequency of the induction motor.

17. The method according to claim 11, wherein the stator current vector under the steady-state operating conditions is initialized as a linear combination of harmonics of the operating frequency of the induction motor.

18. The method according to claim 11, wherein the fault signature is determined by running a spectral analysis program on the clean stator current estimation vector.

19. The aforementioned solution is, A step of initializing the response vector and the modulation vector, The method according to claim 11, further comprising the step of repeatedly updating the stator current vector, the response vector, and the modulation vector until the update converges.

20. The method according to claim 11, wherein, under the aforementioned fluctuating operating conditions, the electromagnetic torque is approximated by the stator current and rotor current of the induction motor.

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