Motor bearing fault diagnosis method based on wavelet ridge line and variational mode decomposition

Abstract

The invention discloses a motor bearing fault diagnosis method based on a wavelet ridge line and variational mode decomposition, and the method employs the wavelet ridge line technology to carry out the time-frequency analysis of a signal, can capture the transient characteristics of the signal, and is higher in sensitivity and accuracy especially when a non-stationary signal is processed. Variational mode decomposition is a self-adaptive signal decomposition method, and complex signals can be decomposed into a series of intrinsic mode functions (IMFs) with physical significance, so that characteristic frequency components related to bearing faults are effectively separated. By combining the two technologies, the fault of the motor bearing can be more accurately diagnosed under a complex working condition, and the robustness and reliability of fault detection are remarkably improved.

Description

Technical Field

[0001] The invention relates to the field of motor bearing fault diagnosis, and in particular to a motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition. Background Art

[0002] Bearings are core components in motors. Their main function is to support the rotation of the shaft and guide the rotation of the shaft while reducing friction and energy loss. Once they fail, they will cause vibration, noise and torque reduction. In severe cases, they will cause damage to other parts of the motor and may even cause failure or shutdown of the entire equipment. Therefore, accurate and timely diagnosis of motor bearing failures is of great significance to ensure the safety and efficiency of industrial production. Motor bearing fault diagnosis usually involves complex signal processing and analysis techniques, because bearings are affected by many factors during operation, such as mechanical vibration, noise interference and load changes, which makes it difficult to extract and identify fault features from the signal.

[0003] Traditional bearing fault diagnosis methods rely on frequency domain analysis and time domain analysis techniques, such as fast Fourier transform (FFT) and envelope analysis, etc. However, these methods have limitations in processing nonlinear and non-stationary signals and may not be able to effectively extract the weak features of bearing faults. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that it is difficult to determine the parameters of traditional variational modal decomposition, and to propose a motor bearing fault diagnosis method based on wavelet ridge and variational modal decomposition.

[0005] The specific technical solutions provided by the present invention are as follows:

[0006] A motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition comprises the following steps:

[0007] S1. Collect the vibration signal and sound signal of the bearing during operation through the acceleration sensor installed on the motor bearing and the microphone sensor near the motor;

[0008] S2. Use filtering technology to pre-process the collected vibration signals and sound signals, remove noise and interference signals, and highlight the signal components within the fault characteristic frequency range;

[0009] S3. Using wavelet ridge extraction technology to extract the wavelet ridges of the bearing vibration signal from the wavelet time-frequency signal, and determining the number of variational mode decompositions K according to the number of wavelet ridges;

[0010] S4. The preprocessed signal is input into the variational mode decomposition algorithm (wavelet ridge-variational mode decomposition). According to the variational mode decomposition number K determined by the wavelet ridge extraction algorithm, the complex vibration signal is decomposed into a set of intrinsic mode functions (IMFs), thereby separating the signal components related to the bearing fault and suppressing the irrelevant interference components;

[0011] S5. Input the extracted vibration and sound characteristic parameters into the support vector machine (SVM) fault diagnosis model to identify different types of bearing faults and output the diagnosis results.

[0012] Further, in step S1, the vibration sensor is installed on the platform directly above the motor, and the microphone sensor is installed as close to the bearing as possible, 2 to 5 cm away from the bearing position.

[0013] Furthermore, in step S2, a bandpass filter is used to process the collected vibration signal. The bandpass filter is set in a characteristic frequency range that may be involved in the bearing fault to remove low-frequency trend items and high-frequency noise.

[0014] Furthermore, in step S3, the wavelet ridge extraction technique can be mainly divided into three steps:

[0015] S31. Calculate the wavelet ridge: The analytical form of the real wavelet ψ(t) is Then the analytical wavelet transform of the asymptotic signal s(t) is as follows:

[0016]

[0017] in,

[0018] The integral value of the above formula depends on the stationary point t s , and satisfy Φ′ a,b (t) = 0 and Φ′ a ' ,b (t s )≠0, these continuous stationary points form the wavelet ridge R={(a,b)∈Ω,t s (a,b)=b};

[0019] S32. Wavelet curve fitting: The wavelet curve is a curve passing through the point (a r (b0),b0), and satisfies t s The set of all points (a, b) where (a, b) = b0, that is, C = {(a, b)∈R 2 ; a>0,t s The (a,b)=b0} wavelet curve is completely composed of the phase function of the analytical wavelet Sure;

[0020] S33. Wavelet ridge extraction: By multiplying the real symmetric window function g(t) by the complex sine wave Construct an approximate analytical wavelet Where ω0 is the center frequency (angular frequency) of ψ(t), and Let the wavelet coefficient of the signal s(t) with respect to the wavelet ψ(t) be W s (a,b), then we have

[0021]

[0022] Among all the wavelet coefficients at time b, the ridge point of the wavelet (a r (b), the wavelet coefficient mode at b) is the largest when the instantaneous frequency f of the signal s(t) at time t s (t) and instantaneous amplitude A s (t) For example:

[0023]

[0024] Furthermore, in step S4, the vibration signal is decomposed using a variational mode decomposition method, and the specific steps are as follows:

[0025] S41. Define the variational problem, which is a functional problem of minimizing the sum of the bandwidths of each mode, as follows:

[0026]

[0027] Among them, [(δ(t)+j / (πt))*u k (t)] is to find the analytical signal of the original signal, Indicates that the spectrum is shifted to the baseband, {u k (t)} represents the K IMF components obtained by VMD decomposition, {ω k (t)} represents the center frequency of each IMF component, represents partial derivative, and j represents the imaginary unit.

[0028] S42. Solve the Lagrangian function: Use the augmented Lagrangian method to transform the above constrained variational problem into an unconstrained variational problem, and then use the alternating multiplier method to solve u k,n+1 ,ω k , After that, it looks like this:

[0029]

[0030] Among them, k represents the serial number of the mode, n represents the number of iterations, and ∧ represents Fourier transform; in the process of iterative solution of the variational model, the frequency center and bandwidth of each IMF component are continuously updated until the iteration stop condition is met as shown below:

[0031]

[0032] Furthermore, in step S5, the vibration and sound are fused at the feature level using a support vector machine algorithm to form an acoustic-vibration feature vector which is input into a support vector machine for fault diagnosis model training.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The motor bearing fault diagnosis based on wavelet ridges and variational mode decomposition proposed in the present invention can effectively separate the signal components related to the motor bearing fault, significantly improving the accuracy and reliability of fault diagnosis. Compared with traditional signal processing methods, the present invention can more sensitively capture early fault characteristics when dealing with complex and changeable working conditions. The multi-level signal preprocessing method adopted by the present invention, including filtering technology and wavelet ridge extraction, can effectively remove noise and interference in the signal, highlight the signal components within the fault characteristic frequency range, thereby improving the robustness of the fault diagnosis system in practical applications. The present invention simultaneously utilizes two information sources, vibration signals and sound signals, and realizes comprehensive monitoring of the operating status of motor bearings through the fusion analysis of multi-dimensional data. This multi-source information fusion technology improves the comprehensiveness and accuracy of fault diagnosis and is suitable for a wider range of industrial application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the steps of the present invention;

[0036] Figure 2 This is the result graph of wavelet ridge extraction;

[0037] Figure 3 It is the variational mode decomposition result diagram;

[0038] Figure 4 This is the fault diagnosis result diagram of support vector machine. DETAILED DESCRIPTION

[0039] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0040] like Figure 1 As shown, the present invention proposes a motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition. The specific implementation steps in the embodiment are as follows:

[0041] S1. In this embodiment, a vibration sensor and a microphone sensor are used to monitor the vibration signal and sound signal generated by the motor during operation. The vibration sensor is installed on the platform directly above the motor, and the microphone sensor is installed 2 to 5 cm away from the bearing;

[0042] S2. In this embodiment, a 10Hz-10kHz bandpass filter is used to preprocess the collected vibration signal and sound signal to remove high-frequency noise interference;

[0043] S3. In this embodiment, the wavelet ridge line of the bearing vibration signal is extracted from the wavelet time-frequency diagram based on the wavelet ridge line extraction algorithm, specifically:

[0044] S31. Calculate the wavelet ridge: The analytical form of the real wavelet ψ(t) is Then the analytical wavelet transform of the asymptotic signal s(t) is as follows:

[0045]

[0046] in,

[0047] The integral value of the above formula depends on the stationary point t s , and satisfy Φ′ a,b (t) = 0 and Φ′ a ' ,b (t s )≠0, these continuous stationary points form the wavelet ridge R={(a,b)∈Ω,t s (a,b)=b};

[0048] S32. Wavelet curve fitting: The wavelet curve is a curve passing through the point (a r (b0),b0), and satisfies t s The set of all points (a, b) where (a, b) = b0, that is, C = {(a, b)∈R 2 ; a>0,t s The (a,b)=b0} wavelet curve is completely composed of the phase function of the analytical wavelet Sure;

[0049] S33. Wavelet ridge extraction: By multiplying the real symmetric window function g(t) by the complex sine wave Construct an approximate analytical wavelet Where ω0 is the center frequency (angular frequency) of ψ(t), and Let the wavelet coefficient of the signal s(t) with respect to the wavelet ψ(t) be W s (a,b), then we have

[0050]

[0051] Among all the wavelet coefficients at time b, the ridge point of the wavelet (a r (b), the wavelet coefficient mode at b) is the largest when the instantaneous frequency f of the signal s(t) at time t s (t) and instantaneous amplitude A s(t) For example:

[0052]

[0053] Calculated as Figure 2 The wavelet ridges shown in the figure show that there are 4 obvious wavelet ridges, and then the VMD modal decomposition number K is determined to be 4. In this embodiment, the sound signal is processed in the same way;

[0054] S4. In this embodiment, according to the modal decomposition number K=4, the vibration signal is subjected to variational modal decomposition, and then the bearing fault characteristics are extracted using the extracted modal function. Specifically:

[0055] S41. Define the variational problem, which is a functional problem of minimizing the sum of the bandwidths of each mode, as follows:

[0056]

[0057] Among them, [(δ(t)+j / (πt))*u k (t)] is to find the analytical signal of the original signal, Indicates that the spectrum is shifted to the baseband, {u k (t)} represents the K IMF components obtained by VMD decomposition, {ω k (t)} represents the center frequency of each IMF component, represents partial derivative, and j represents the imaginary unit.

[0058] S42. Solve the Lagrangian function: Use the augmented Lagrangian method to transform the above constrained variational problem into an unconstrained variational problem, and then use the alternating multiplier method to solve u k,n+1 ,ω k , After that, it looks like this:

[0059]

[0060] Among them, k represents the serial number of the mode, n represents the number of iterations, and ∧ represents Fourier transform; in the process of iterative solution of the variational model, the frequency center and bandwidth of each IMF component are continuously updated until the iteration stop condition is met as shown below:

[0061]

[0062] The frequency centers of the IMF components are calculated to be [326Hz, 1629Hz, 2931Hz, 3505Hz]. Using the traditional envelope analysis function and calculating its Fourier transform, the results are as follows: Figure 3 As shown;

[0063] S5. In this embodiment, vibration and sound are fused at the feature level to form an acoustic-vibration feature vector set, which is input into the support vector machine for fault diagnosis model training. Vibration features or acoustic features are respectively input into the support vector machine to perform bearing fault diagnosis. The diagnosis based solely on vibration features shows that the bearing fault diagnosis rate is 87.5%, the three faults cannot be completely distinguished, and the fault information collected by the acceleration sensor is incomplete. The diagnosis results based solely on acoustic signal features show that the overall diagnosis rate is 85.5%. Figure 4 As shown, after integrating vibration and sound features, the overall diagnosis rate reached up to 95%.

[0064] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition, characterized in that: The following steps are involved: S1. Collect the vibration signal and sound signal of the bearing during operation through the acceleration sensor installed on the motor bearing and the microphone sensor near the motor; S2. Use filtering technology to pre-process the collected vibration signals and sound signals, remove noise and interference signals, and highlight the signal components within the fault characteristic frequency range; S3. Using wavelet ridge extraction technology to extract the wavelet ridges of the bearing vibration signal from the wavelet time-frequency signal, and determining the number of variational mode decompositions K according to the number of wavelet ridges; S4. The preprocessed signal is input into the improved variational mode decomposition algorithm. First, the number of components K in the original signal is determined according to the wavelet ridge extraction algorithm. Then K is input into the variational mode decomposition to decompose the complex vibration and sound signals into a set of intrinsic mode functions, thereby separating the signal components related to the bearing fault and suppressing the irrelevant interference components. S5. Input the extracted vibration and sound characteristic parameters into the support vector machine fault diagnosis model, identify different types of bearing faults, and output the diagnosis results.

2. The motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition according to claim 1 is characterized in that: In step S1, the vibration sensor is installed on the platform directly above the motor, and the microphone sensor is installed as close to the bearing as possible, 2 to 5 cm away from the bearing position.

3. The motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition according to claim 1 is characterized in that: In step S2, a bandpass filter is used to process the collected vibration and sound signals.

4. The motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition according to claim 1 is characterized in that: In step S3, the wavelet ridge extraction technique is mainly divided into three steps, including: S31. Calculate the wavelet ridge: The analytical form of the real wavelet ψ(t) is Then the analytical wavelet transform of the asymptotic signal s(t) is as follows: in, The integral value of the above formula depends on the stationary point t s , and satisfy Φ′ a,b (t) = 0 and Φ″ a,b (t s )≠0, these continuous stationary points form the wavelet ridge R={(a,b)∈Ω,t s (a,b)=b}; S32. Wavelet curve fitting: The wavelet curve is a curve passing through the point (a r (b0),b0), and satisfies t s The set of all points (a, b) where (a, b) = b0, that is, C = {(a, b)∈R 2 ; a>0,t s The (a,b)=b0} wavelet curve is completely composed of the phase function of the analytical wavelet Sure; S33. Wavelet ridge extraction: By multiplying the real symmetric window function g(t) by the complex sine wave Construct an approximate analytical wavelet Where ω0 is the center frequency (angular frequency) of ψ(t), and Let the wavelet coefficient of the signal s(t) with respect to the wavelet ψ(t) be W s (a,b), then we have Among all the wavelet coefficients at time b, the ridge point of the wavelet (a r (b), the wavelet coefficient mode at b) is the largest when the instantaneous frequency f of the signal s(t) at time t s (t) and instantaneous amplitude A s (t) For example:

5. The motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition according to claim 1 is characterized in that: In step S4, the vibration and sound signals are decomposed using the variational mode decomposition method. The specific steps are as follows: S41. Define the variational problem, which is a functional problem of minimizing the sum of the bandwidths of each mode, as follows: Among them, [(δ(t)+j / (πt))*u k (t)] is to find the analytical signal of the original signal, Indicates that the spectrum is shifted to the baseband, {u k (t)} represents the K IMF components obtained by VMD decomposition, {ω k (t)} represents the center frequency of each IMF component, represents partial derivative, j represents imaginary unit; S42. Solve the Lagrangian function: Use the augmented Lagrangian method to transform the above constrained variational problem into an unconstrained variational problem, and then use the alternating multiplier method to solve u k,n+1 ,ω k , After that, it looks like this: Among them, k represents the serial number of the mode, n represents the number of iterations, and ∧ represents Fourier transform; in the process of iterative solution of the variational model, the frequency center and bandwidth of each IMF component are continuously updated until the iteration stop condition is met as shown below:

6. The motor bearing fault diagnosis method based on wavelet ridge and variational mode decomposition according to claim 1 is characterized in that: In step S5, the extracted vibration features: bearing characteristic frequency, frequency octave features, vibration amplitude, high-frequency acceleration, average value and sound features: Mel-frequency cepstral coefficients, 1 / 3 frequency octave features, loudness, sharpness, effective value, average value features are fused and input into the support vector machine fault diagnosis model to identify different types of bearing faults and output the diagnosis results.

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