Bearing fault diagnosis method and related device based on AC motor speed signal analysis

Abstract

A bearing fault diagnosis method and related device based on AC motor speed signal analysis includes: deducing the motor speed signal at the time of the fault based on the mechanical torque equation; performing signal noise reduction preprocessing on the collected speed signal using the variational mode decomposition algorithm (VMD) to obtain intrinsic mode functions with different bandwidths and center frequencies; determining the optimal center frequency and bandpass filter bandwidth using the correlation entropy index, and obtaining the fault characteristic frequency through spectral analysis. The present invention uses the correlation entropy method to calculate the degree of similarity between the sub-modes after variational mode decomposition and the original signal, determines the signal complexity by comparing the probability of multiple frequencies appearing in the time domain signal, and accurately selects the filter center frequency and bandwidth based on the criterion in information entropy theory that the smaller the entropy value, the more obvious the fault information.

Description

Technical Field

[0001] The present invention belongs to the technical field of AC motor bearing fault diagnosis, and in particular relates to a bearing fault diagnosis method and related devices based on AC motor speed signal analysis. Background Art

[0002] Mechanical equipment such as industrial robots and high-end CNC machine tools is continuously evolving toward heavier loads, increased intelligence, and higher speeds. This trend is also leading to increasingly complex and demanding service environments for these equipment. Minor local faults in these equipment can easily trigger a chain reaction, threatening their reliability and even causing significant economic losses and casualties. As core components of these equipment, AC motors are crucial for reliable operation and fault diagnosis. Bearing failures account for approximately 80% of AC motor failures. Fault diagnosis methods based on vibration signals require sensors installed inside the motor, near the bearings, to capture vibration signals for fault analysis. However, the presence of sensors increases motor manufacturing costs and increases the risk of motor failure. Non-invasive, sensorless fault diagnosis methods based on speed signals have recently attracted considerable research attention, as they eliminate the need for additional sensors and significantly reduce motor manufacturing costs. Traditional AC motor bearing fault diagnosis methods based on speed signals often employ resonance demodulation techniques to diagnose rolling bearing faults. The core of resonance demodulation technology is to select the optimal resonance frequency band for bandpass filtering. At present, it is impossible to accurately select the center frequency and bandwidth of the filter, resulting in low accuracy in bearing fault diagnosis. Summary of the Invention

[0003] The purpose of the present invention is to provide a bearing fault diagnosis method and related devices based on AC motor speed signal analysis to solve the problem that the center frequency and bandwidth of the filter cannot be accurately selected at this stage, resulting in low accuracy of bearing fault diagnosis.

[0004] To achieve the above object, the present invention adopts the following technical solutions:

[0005] In a first aspect, the present invention provides a bearing fault diagnosis method comprising:

[0006] Derivation of the motor speed signal at fault based on the mechanical torque equation;

[0007] The acquired speed signal is pre-processed for signal noise reduction using the variational mode decomposition (VMD) algorithm to obtain intrinsic mode functions with different bandwidths and center frequencies.

[0008] The correlation entropy index is used to determine the optimal center frequency and bandpass filter bandwidth, and the fault characteristic frequency is obtained by spectrum analysis.

[0009] Optionally, based on the fault frequencies of the inner ring, outer ring, cage, and rolling element of the motor bearing when the motor bearing fails, the rotational frequency of the motor speed at the time of the failure is derived from the mechanical torque equation:

[0010]

[0011] T L is the load torque, T0 is the electromagnetic torque in steady state, T c is the amplitude of the torque change caused by the bearing fault;

[0012] Changes in torque cause changes in speed:

[0013]

[0014] T(t) is the torque variation function, T m is the electromagnetic torque of the motor, J is the total mechanical inertia of the entire motor load;

[0015] Integrating both ends of equation (7) with respect to time t yields equation (8):

[0016]

[0017] Since in steady state: T m =T0, equation (8) yields equation (9):

[0018]

[0019] η is white noise with zero mean and infinite variance.

[0020] Optionally, when the motor bearing fails, the failure frequency of the bearing inner ring, outer ring, cage and rolling element:

[0021] Shaft rotation frequency: f r =n / 60(1)

[0022] Inner ring:

[0023] Outer ring:

[0024] Cage:

[0025] Rolling elements:

[0026] In the above formula, n is the rolling bearing speed rpm, N b is the number of rolling elements, α is the contact angle, d is the rolling element diameter, and D is the bearing pitch diameter.

[0027] Optionally, the collected speed signal is pre-processed for signal noise reduction using the variational mode decomposition algorithm VMD:

[0028] The VMD noise reduction process for the signal is as follows:

[0029] According to the extreme value principle and symmetry, the initial signal is decomposed into multiple intrinsic mode functions IMFs. Each IMF is expressed as:

[0030]

[0031]

[0032] In the above formula, Represents the phase, which is a non-decreasing function; A k (t) is x k (t) is the instantaneous amplitude, and A k (t)≥0;ω k (t) is the instantaneous frequency;

[0033] VMD is handled by solving the following constrained variational problem

[0034]

[0035]

[0036] The decomposed signal x k (t) consists of two parts: instantaneous frequency and carrier frequency;

[0037] (2) Assume that the test signal is composed of the original signal f and the noise signal η, denoted as f0, which is given by the following formula:

[0038] f0=f+η (12)

[0039] In formula (12), η is additive Gaussian white noise with a mean of 0;

[0040] Separate the signal f from the noisy signal f0 and use Tikhonov regularization to solve:

[0041]

[0042] In formula (13) Represents the distance between f and f0, which is used to measure the degree of approximation between two signals; Represents the L2 norm based on the gradient. Combining with the Lagrange equation, it is easy to get its solution in the frequency domain:

[0043]

[0044] In formula (14), The signal f(t) is obtained by Fourier transform. When ω=0, the signal f is obtained by performing a low-pass narrowband filter on the noisy signal f0, and the signal has a low-pass narrowband filter. Power spectrum, α represents the variance of white noise;

[0045] (3) Assuming there is a real-valued signal f(t), the Hilbert transform process is expressed as:

[0046]

[0047] In formula (15), H[·] represents Hilbert transform; * represents convolution.

[0048] The analytical expression of the real signal f(t) obtained by Hilbert transform is defined as:

[0049]

[0050] In formula (16), Indicates the amount of change in the time rotation of a complex signal; is the phase, A(t) represents the amplitude in the time domain;

[0051] VMD iteratively calculates the optimal solution of the variational equation and ultimately decomposes the signal data into intrinsic mode functions (IMFs) with different bandwidths and center frequencies.

[0052] Optional, spectrum analysis:

[0053] Multiple intrinsic mode functions (IMFs) are used for time-frequency analysis, using short-time Fourier transform with windowing function:

[0054] Assuming there is a non-stationary signal x(t), a sliding window w(t-τ), and τ reflects the position of the sliding window, the short-time Fourier transform STFT is obtained as follows:

[0055]

[0056] When the window function w(t-τ) is fixed, the frequency resolution Δf and time resolution Δt of the STFT are also fixed. The frequency resolution Δf and Δt are calculated by equations (18) and (19):

[0057]

[0058]

[0059] The frequency resolution Δf and time resolution Δt cannot reach arbitrarily small values ​​at the same time. They are constrained by the following relationship:

[0060]

[0061] Optionally, the cross-correlation function of the signals is defined as:

[0062]

[0063] After STFT analysis of the signal, its time-frequency distribution is expressed as:

[0064]

[0065] In formula (21), the matrix on the right is the time-frequency matrix obtained by STFT analysis, with rows and columns representing time distribution and frequency distribution respectively; M represents the number of frequency points, L represents the step size of the window function moving along the time axis;

[0066] The i-th frequency component f i The change of the amplitude along time is defined as: fi =(r i1 ,r i2 ,…,r iC ), then the single frequency component f i The related entropy of:

[0067]

[0068]

[0069] In formula (22), H si represents the maximum cross-correlation entropy of this signal sequence, where represents the cross-correlation coefficient spectrum of the signal sequence, P m,i is the probability of a certain signal frequency occurring, F is the frequency component Spectral distribution along the time axis;

[0070] Calculate the correlation entropy value of each frequency component and obtain the correlation entropy distribution of each frequency component in the full frequency band as shown in formula (24):

[0071] H sf =(H s1 ,H s2 ,…,H sM ) (twenty four)

[0072] If the frequency component If the change over time is smooth or regular, the correlation entropy value of the frequency component is small; if there are complex fluctuations within a certain period of time, the correlation entropy value is large; in bearing fault diagnosis, the correlation entropy is used to find the resonant frequency of the bearing, that is, the frequency component at the minimum correlation entropy value, as shown in formula (25).

[0073] H min =min(H sf) (25)

[0074] f rf =argmin(H sf ) (26)

[0075] Equations (25) and (26) can be used to obtain the minimum value of the correlation entropy and the frequency component f at the minimum value. rf , the subscript "rf" is the resonant frequency; after the resonant frequency is determined, it is used as the center frequency.

[0076] Optional, bandpass filter analysis based on correlation entropy:

[0077] The resonant frequency component f has been found in the frequency band using the correlation entropy theory. rf , which is used as the center frequency of the designed bandpass filter;

[0078] f cf =f rf (27)

[0079] In formula (27), f cf is the center frequency

[0080] First, calculate the correlation entropy values ​​under different window lengths, and then obtain the minimum value of the total correlation entropy. The corresponding window length is considered to be the optimal window length, which can be given by the following formula:

[0081] N W =2 k k=1,2,…,M (28)

[0082] Assuming that K correlation entropy analyses are performed under different window lengths, K correlation entropy values ​​will be obtained at the resonant frequency, which are recorded as:

[0083] H rf =(H rf,1 ,H rf,2 ,…,H rf,k ) (29)

[0084] Compare the correlation entropy values ​​at the resonant frequency components under different window lengths, and obtain the minimum value of the correlation entropy value at the resonant frequency. The corresponding window length is considered to be the optimal window length, which is obtained from formula (30):

[0085] N W * =argmin(H rf ) (30)

[0086] After obtaining the optimal window length N W * Afterwards, the window length N W * , sampling frequency fs Calculate the bandwidth parameters:

[0087] Δf=1.5·f s / N W * (31)

[0088] In formula (31), f s represents the system sampling frequency, Δf is the designed bandpass filter bandwidth, N W * is the optimal window length, and the constant 1.5 is described as the bandwidth parameter when designing the bandpass filter;

[0089] After the above signal processing, the signal is subjected to spectrum analysis, and the fault frequency that occurs when the bearing fails is clearly found in the frequency spectrum.

[0090] In a second aspect, the present invention provides a bearing fault diagnosis system based on AC motor speed signal analysis, comprising:

[0091] The speed signal acquisition module is used to derive the motor speed signal when a fault occurs based on the mechanical torque equation;

[0092] A processing module is used to perform signal noise reduction preprocessing on the collected speed signal using the variational mode decomposition algorithm VMD to obtain intrinsic mode functions with different bandwidths and center frequencies;

[0093] The analysis output module is used to determine the optimal center frequency and bandpass filter bandwidth using the correlation entropy index, and obtain the fault characteristic frequency through spectrum analysis.

[0094] In a third aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of a bearing fault diagnosis method based on analysis of an AC motor speed signal are implemented.

[0095] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of a bearing fault diagnosis method based on AC motor speed signal analysis.

[0096] Compared with the prior art, the present invention has the following technical effects:

[0097] The present invention discloses a bearing fault diagnosis method for analyzing the speed signal of an AC motor based on the correlation entropy index. The method adopts the correlation entropy method to calculate the similarity between the sub-modes after variational modal decomposition and the original signal. The complexity of the signal is judged by comparing the probability of occurrence of multiple frequencies in the time domain signal. According to the criterion in information entropy theory that the smaller the entropy value, the more obvious the fault information is, the accurate selection of the center frequency and bandwidth of the filter is achieved.

[0098] The present invention uses the variational mode decomposition algorithm to perform signal noise reduction preprocessing on the collected speed signal, which can have a good suppression effect on the high-frequency noise of early bearing failures and greatly improve the signal-to-noise ratio of the signal. Finally, the use of the correlation entropy index proposed by the present invention has an excellent effect on determining the optimal center frequency and bandpass filter bandwidth, and can be well used for processing speed signals, ultimately significantly reducing the manufacturing cost of AC motors and improving the accuracy of fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 It is a flow chart of the present invention.

[0100] Figure 2 Motor rolling bearing fault diagnosis platform.

[0101] Figure 3 Time domain waveform of the original fault simulation signal.

[0102] Figure 4 Envelope spectrum of the original fault simulation signal.

[0103] Figure 5 VMD decomposition of the original fault signal.

[0104] Figure 6 The relationship between the correlation entropy value and frequency under different window lengths.

[0105] Figure 7 Envelope analysis results of the filtered signal.

[0106] Figure 8 Comparison of signal time domain waveforms before and after filtering. DETAILED DESCRIPTION

[0107] The present invention is further described below with reference to the accompanying drawings:

[0108] See also Figure 1 In a first aspect, the present invention provides a method for deriving a mathematical expression of a motor speed, comprising:

[0109] When the motor bearing fails, the failure frequency of the bearing inner ring, outer ring, cage and rolling element is:

[0110] Shaft rotation frequency: f r =n / 60 (1)

[0111] Inner ring:

[0112] Outer ring:

[0113] Cage:

[0114] Rolling elements:

[0115] In the above formula, n is the rolling bearing speed (rpm), N b is the number of rolling elements, α is the contact angle, d is the rolling element diameter, and D is the bearing pitch diameter.

[0116] The rotation frequency of the motor speed during the fault is derived from the mechanical torque equation:

[0117]

[0118] T L is the load torque, T0 is the electromagnetic torque in steady state, T c is the amplitude of the torque change caused by the bearing fault.

[0119] Changes in torque cause changes in speed:

[0120]

[0121] T(t) is the torque change function, T m is the motor electromagnetic torque, and J is the total mechanical inertia of the entire motor load.

[0122] Integrating both ends of equation (7) with respect to time t yields equation (8):

[0123]

[0124] Since in steady state: T m =T0, equation (8) can be converted to equation (9):

[0125]

[0126] η is white noise with zero mean and infinite variance.

[0127] It can be seen that the speed signal contains: a fault signal with a sinusoidal law and a noise component with an unknown frequency.

[0128] In the second aspect, the present invention designs a variational mode decomposition algorithm to perform signal noise reduction preprocessing on the collected speed signal, including:

[0129] The VMD noise reduction process for the signal is as follows:

[0130] (1) Based on the extreme value principle and symmetry, the initial signal is decomposed into multiple intrinsic mode functions (IMFs). Each IMF can be expressed as:

[0131]

[0132]

[0133] in, Represents the phase, which is a non-decreasing function. A k (t) is x k (t) is the instantaneous amplitude, and A k (t)≥0;ω k (t) is the instantaneous frequency.

[0134] The goal of VMD is to isolate a complex signal into a series of sub-signals (i.e., sub-modes) with a specific sparsity. This sparsity is reflected in the frequency bandwidth of the modes, that is, the spectrum of each mode is compact around its center frequency. This problem is addressed by solving the following constrained variational problem.

[0135]

[0136]

[0137] The decomposed signal x k (t) consists of two parts: instantaneous frequency and carrier frequency.

[0138] (2) Assuming that the test signal is composed of the original signal f and the noise signal η, denoted as f0, it can be given by the following formula:

[0139] f0=f+η (12)

[0140] In formula (12), η is additive Gaussian white noise with a mean of 0.

[0141] The classic solution to separate the signal f from the noisy signal f0 is to use Tikhonov regularization to obtain:

[0142]

[0143] In formula (13) Represents the distance between f and f0, which is used to measure the degree of approximation between two signals; Represents the L2 norm based on the gradient. Combining with the Lagrange equation, it is easy to get its solution in the frequency domain:

[0144]

[0145] In formula (14), The signal f(t) is obtained by Fourier transform. When ω=0, the signal f is obtained by performing a low-pass narrowband filter on the noisy signal f0, and the signal has a low-pass narrowband filter. Power spectrum, α represents the variance of white noise.

[0146] (3) Assuming there is a real-valued signal f(t), the Hilbert transform process can be expressed as:

[0147]

[0148] In formula (15), H[·] represents Hilbert transform; * represents convolution.

[0149] The analytical expression of the real signal f(t) obtained by Hilbert transform is defined as:

[0150]

[0151] In formula (16), Indicates the amount of change in the time rotation of a complex signal; is the phase, and A(t) represents the amplitude in the time domain.

[0152] VMD mainly calculates the optimal solution of the variational equation through iteration, and finally decomposes the signal data into intrinsic mode functions (IMFs) with different bandwidths and center frequencies.

[0153] In a third aspect, the present invention designs a method for determining the optimal center frequency and bandpass filter bandwidth using a correlation entropy index, including:

[0154] A short-time Fourier transform (STFT) with a windowing function is used.

[0155] Assuming there is a non-stationary signal x(t) and a sliding window w(t-τ) (τ reflects the position of the sliding window), the STFT can be obtained as follows:

[0156]

[0157] The analysis result of formula (17) reflects the spectrum characteristics of the signal x(t) in a finite interval (sometimes the window width is absolute) at time t = τ, which can also be regarded as the complex exponential function w(t = τ)·e with the envelope of the time function x(t) -j2πft The correlation value of , that is, it is a function of time shift τ and frequency f.

[0158] If the window function w(t-τ) is fixed, the frequency resolution Δf and time resolution Δt of the STFT are also fixed. The frequency resolution Δf and Δt can be calculated using equations (18) and (19):

[0159]

[0160]

[0161] Constrained by the Heisenbeg uncertainty principle, the frequency resolution Δf and the time resolution Δt cannot reach arbitrarily small values ​​at the same time. They are constrained by the following relationship:

[0162]

[0163] After STFT analysis of the signal, its time-frequency distribution can be expressed as:

[0164]

[0165] In formula (21), the matrix on the right is the time-frequency matrix obtained by STFT analysis, with rows and columns representing time distribution and frequency distribution, respectively. M represents the number of frequency points, L represents the step size of the window function moving along the time axis.

[0166] The i-th frequency component f i The change of the amplitude along time can be defined as: fi =(r i1 ,r i2 ,…,r iC ), then the single frequency component f i The related entropy of:

[0167]

[0168]

[0169] In formula (22), H si represents the maximum cross-correlation entropy of the signal sequence, where represents the cross-correlation coefficient spectrum of the signal sequence, P m,i is the probability of a certain signal frequency occurring, F is the frequency component The spectrum distribution along the time axis reveals the changes of the frequency component along the time axis.

[0170] The cross-correlation function of the signal is defined as:

[0171]

[0172] Calculate the correlation entropy value of each frequency component and obtain the correlation entropy distribution of each frequency component in the full frequency band as shown in formula (24):

[0173] H sf =(H s1 ,H s2 ,…,H sM) (twenty four)

[0174] If the frequency component If the change over time is smooth or regular, the correlation entropy value of the frequency component is small; if there are complex fluctuations within a certain period of time, the correlation entropy value is large. Therefore, in bearing fault diagnosis, the correlation entropy can be used to find the resonant frequency of the bearing, that is, the frequency component at which the correlation entropy value is minimum, as shown in Equation (25).

[0175] H min =min(H sf ) (25)

[0176] f rf =argmin(H sf ) (26)

[0177] Equations (25) and (26) can be used to obtain the minimum value of the correlation entropy and the frequency component f at the minimum value. rf (The subscript "rf" stands for resonance frequency.) Once the resonance frequency is determined, it can be used as the center frequency and as a reference for designing the parameters of the adaptive filter.

[0178] The resonant frequency component f has been found in the frequency band using the correlation entropy theory. rf , which is used as the center frequency of the designed bandpass filter.

[0179] f cf =f rf (27)

[0180] In formula (27), f cf is the center frequency

[0181] Calculate the correlation entropy values ​​under different window lengths, and then obtain the minimum value of the total correlation entropy. The corresponding window length is considered to be the optimal window length. The window length can be given by the following formula:

[0182] N W =2 k k=1,2,…,M (28)

[0183] Assuming that K correlation entropy analyses are performed under different window lengths, K correlation entropy values ​​will be obtained at the resonant frequency, which can be recorded as:

[0184] H rf =(H rf,1 ,H rf,2 ,…,H rf,k ) (29)

[0185] By comparing the correlation entropy values ​​at the resonant frequency components under different window lengths, the minimum value of the correlation entropy value at the resonant frequency can be obtained. The corresponding window length is considered to be the optimal window length, which can be obtained by the following formula:

[0186] N W * =argmin(H rf ) (30)

[0187] After obtaining the optimal window length N W * Afterwards, the window length N W * , sampling frequency f s The bandwidth parameters can be calculated:

[0188] Δf=1.5·f s / N W * (31)

[0189] In formula (31), f s represents the system sampling frequency, Δf is the designed bandpass filter bandwidth, N W * is the optimal window length, and the constant 1.5 is described as the bandwidth parameter when designing the bandpass filter.

[0190] After the above signal processing, the signal is subjected to spectrum analysis, and the fault frequency that occurs when the bearing fails can be clearly found in the frequency spectrum.

[0191] In another embodiment of the present invention, a bearing fault diagnosis system based on AC motor speed signal analysis is provided, which can be used to implement the above-mentioned bearing fault diagnosis method based on AC motor speed signal analysis. Specifically, the bearing fault diagnosis system based on AC motor speed signal analysis includes:

[0192] The speed signal acquisition module is used to derive the motor speed signal when a fault occurs based on the mechanical torque equation;

[0193] A processing module is used to perform signal noise reduction preprocessing on the collected speed signal using the variational mode decomposition algorithm VMD to obtain intrinsic mode functions with different bandwidths and center frequencies;

[0194] The analysis output module is used to determine the optimal center frequency and bandpass filter bandwidth using the correlation entropy index, and obtain the fault characteristic frequency through spectrum analysis.

[0195] The module division in the embodiments of the present invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in various embodiments of the present invention may be integrated into a single processor, exist physically as separate modules, or two or more modules may be integrated into a single module. The integrated modules may be implemented in either hardware or software functional modules.

[0196] In another embodiment of the present invention, a computer device is provided, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the bearing fault diagnosis method based on AC motor speed signal analysis.

[0197] In another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device for storing programs and data. It is understandable that the computer-readable storage medium here can include both built-in storage media in the computer device and, of course, extended storage media supported by the computer device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space. These instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the steps of the bearing fault diagnosis method based on AC motor speed signal analysis in the above embodiment.

[0198] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0199] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0200] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0201] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0202] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A bearing fault diagnosis method based on AC motor speed signal analysis is characterized in that: include: Derivation of the motor speed signal at fault based on the mechanical torque equation; The acquired speed signal is pre-processed for signal noise reduction using the variational mode decomposition (VMD) algorithm to obtain intrinsic mode functions with different bandwidths and center frequencies. The correlation entropy index is used to determine the optimal center frequency and bandpass filter bandwidth, and the fault characteristic frequency is obtained by spectrum analysis; Based on the fault frequencies of the inner ring, outer ring, cage and rolling element of the motor bearing when the motor bearing fails, the rotation frequency of the motor speed when the fault occurs is derived from the mechanical torque equation: T L is the load torque, T0 is the electromagnetic torque in steady state, T c is the amplitude of the torque change caused by the bearing fault; Changes in torque cause changes in speed: T(t) is the torque change function, T m is the electromagnetic torque of the motor, J is the total mechanical inertia of the entire motor load; Integrating both ends of equation (7) with respect to time t yields equation (8): Since in steady state: T m =T0, equation (8) yields equation (9): η is white noise with zero mean and infinite variance; Spectrum Analysis: Multiple intrinsic mode functions (IMFs) are used for time-frequency analysis, using short-time Fourier transform with windowing function: Assuming there is a non-stationary signal x(t), a sliding window w(t-τ), and τ reflects the position of the sliding window, the short-time Fourier transform STFT is obtained as follows: When the window function w(t-τ) is fixed, the frequency resolution Δf and time resolution Δt of the STFT are also fixed. The frequency resolution Δf and Δt are calculated by equations (18) and (19): The frequency resolution Δf and time resolution Δt cannot reach arbitrarily small values ​​at the same time. They are constrained by the following relationship:

2. The bearing fault diagnosis method based on AC motor speed signal analysis according to claim 1 is characterized in that: When the motor bearing fails, the failure frequency of the bearing inner ring, outer ring, cage and rolling element is: Shaft rotation frequency: f r =n / 60(1) Inner ring: Outer ring: Cage: Rolling elements: In the above formula, n is the rolling bearing speed rpm, N b is the number of rolling elements, α is the contact angle, d is the rolling element diameter, and D is the bearing pitch diameter.

3. The bearing fault diagnosis method based on AC motor speed signal analysis according to claim 1 is characterized in that: The collected speed signal is preprocessed for signal noise reduction using the variational mode decomposition algorithm VMD: The VMD noise reduction process for the signal is as follows: According to the extreme value principle and symmetry, the initial signal is decomposed into multiple intrinsic mode functions IMFs. Each IMF is expressed as: In the above formula, Represents the phase, which is a non-decreasing function; A k (t) is x k (t) is the instantaneous amplitude, and A k (t)≥0;ω k (t) is the instantaneous frequency; VMD is handled by solving the following constrained variational problem The decomposed signal x k (t) consists of two parts: instantaneous frequency and carrier frequency; (2) Assume that the test signal is composed of the original signal f and the noise signal η, denoted as f0, which is given by the following formula: f0=f+η (12) In formula (12), η is additive Gaussian white noise with a mean of 0; Separate the signal f from the noisy signal f0 and use Tikhonov regularization to solve: In formula (13) Represents the distance between f and f0, which is used to measure the degree of approximation between two signals; Represents the L2 norm based on the gradient. Combining with the Lagrange equation, it is easy to get its solution in the frequency domain: In formula (14), The signal f(t) is obtained by Fourier transform. When ω=0, the signal f is obtained by performing a low-pass narrowband filter on the noisy signal f0, and the signal has a low-pass narrowband filter. Power spectrum, α represents the variance of white noise; (3) Assuming there is a real-valued signal f(t), the Hilbert transform process is expressed as: In formula (15), H[·] represents Hilbert transform; * represents convolution; The analytical expression of the real signal f(t) obtained by Hilbert transform is defined as: In formula (16), Indicates the amount of change in the time rotation of a complex signal; is the phase, A(t) represents the time domain amplitude; VMD iteratively calculates the optimal solution of the variational equation and ultimately decomposes the signal data into intrinsic mode functions (IMFs) with different bandwidths and center frequencies.

4. The bearing fault diagnosis method based on AC motor speed signal analysis according to claim 1 is characterized in that: The cross-correlation function of the signal is defined as: After STFT analysis of the signal, its time-frequency distribution is expressed as: In formula (21), the matrix on the right is the time-frequency matrix obtained by STFT analysis, with rows and columns representing time distribution and frequency distribution respectively; M represents the number of frequency points, L represents the step size of the window function moving along the time axis; The i-th frequency component f i The change of the amplitude along time is defined as: X fi =(r i1 ,r i2 ,…,r iC ), then the single frequency component f i The related entropy of: In formula (22), H si represents the maximum cross-correlation entropy of this signal sequence, where represents the cross-correlation coefficient spectrum of the signal sequence, P m,i is the probability of a certain signal frequency occurring, F is the frequency component Spectral distribution along the time axis; Calculate the correlation entropy value of each frequency component and obtain the correlation entropy distribution of each frequency component in the full frequency band as shown in formula (24): H sf =(H s1 ,H s2 ,…,H sM ) (24) If the frequency component If the change over time is smooth or regular, the correlation entropy value of the frequency component is small; if there are complex fluctuations within a certain period of time, the correlation entropy value is large. In bearing fault diagnosis, the correlation entropy is used to find the resonant frequency of the bearing, that is, the frequency component at the minimum correlation entropy value, as shown in formula (25). H min =min(H sf ) (25) f rf =argmin(H sf ) (26) Equations (25) and (26) can be used to obtain the minimum value of the correlation entropy and the frequency component f at the minimum value. rf , the subscript "rf" is the resonant frequency; after the resonant frequency is determined, it is used as the center frequency.

5. The bearing fault diagnosis method based on AC motor speed signal analysis according to claim 4 is characterized in that: Bandpass filter analysis based on correlation entropy: The resonant frequency component f has been found in the frequency band using the correlation entropy theory. rf , which is used as the center frequency of the designed bandpass filter; f cf =f rf (27) In formula (27), f cf is the center frequency First, calculate the correlation entropy values ​​under different window lengths, and then obtain the minimum value of the total correlation entropy. The corresponding window length is considered to be the optimal window length, which is given by the following formula: N W =2 k k=1,2,…,M(28) Assuming that K correlation entropy analyses are performed under different window lengths, K correlation entropy values ​​will be obtained at the resonant frequency, which are recorded as: H rf =(H rf,1 ,H rf,2 ,…,H rf,k ) (29) Compare the correlation entropy values ​​at the resonant frequency components under different window lengths, and obtain the minimum value of the correlation entropy value at the resonant frequency. The corresponding window length is considered to be the optimal window length, which is obtained from formula (30): N W * =argmin(H rf ) (30) After obtaining the optimal window length N W * Afterwards, the window length N W * , sampling frequency f s Calculate the bandwidth parameters: Δf=1.5·f s / N W * (31) In formula (31), f s represents the system sampling frequency, Δf is the designed bandpass filter bandwidth, N W * is the optimal window length, and the constant 1.5 is described as the bandwidth parameter when designing the bandpass filter; After the above signal processing, the signal is subjected to spectrum analysis, and the fault frequency that occurs when the bearing fails is clearly found in the frequency spectrum.

6. Bearing fault diagnosis system based on AC motor speed signal analysis, characterized in that: include: The speed signal acquisition module is used to derive the motor speed signal when a fault occurs based on the mechanical torque equation; A processing module is used to perform signal noise reduction preprocessing on the collected speed signal using the variational mode decomposition algorithm VMD to obtain intrinsic mode functions with different bandwidths and center frequencies; The analysis output module is used to determine the optimal center frequency and bandpass filter bandwidth using the correlation entropy index, and obtain the fault characteristic frequency through spectrum analysis; Based on the fault frequencies of the inner ring, outer ring, cage and rolling element of the motor bearing when the motor bearing fails, the rotation frequency of the motor speed when the fault occurs is derived from the mechanical torque equation: T L is the load torque, T0 is the electromagnetic torque in steady state, T c is the amplitude of the torque change caused by the bearing fault; Changes in torque cause changes in speed: T(t) is the torque change function, T m is the electromagnetic torque of the motor, J is the total mechanical inertia of the entire motor load; Integrating both ends of equation (7) with respect to time t yields equation (8): Since in steady state: T m =T0, equation (8) yields equation (9): η is white noise with zero mean and infinite variance; Spectrum Analysis: Multiple intrinsic mode functions (IMFs) are used for time-frequency analysis, using short-time Fourier transform with windowing function: Assuming there is a non-stationary signal x(t), a sliding window w(t-τ), and τ reflects the position of the sliding window, the short-time Fourier transform STFT is obtained as follows: When the window function w(t-τ) is fixed, the frequency resolution Δf and time resolution Δt of the STFT are also fixed. The frequency resolution Δf and Δt are calculated by equations (18) and (19): The frequency resolution Δf and time resolution Δt cannot reach arbitrarily small values ​​at the same time. They are constrained by the following relationship:

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the bearing fault diagnosis method based on AC motor speed signal analysis as described in any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the bearing fault diagnosis method based on AC motor speed signal analysis as described in any one of claims 1 to 5 are implemented.

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