A bearing vibration signal denoising method based on multi-scale mean variational modal decomposition

Abstract

The present invention discloses a bearing vibration signal denoising method based on multi-scale mean variational modal decomposition. First, a mechanical vibration simulation test bench is built to collect rolling bearing fault vibration signals, and vibration signals of rolling bearing inner and outer ring faults are obtained. Second, variational modal decomposition is performed on the original signal to obtain K IMF components. After that, a scale factor S is established. v , reconstruct the components using multi-scale mean values; then, calculate the multi-scale permutation entropy of each reconstructed sequence for screening and reconstruction; finally, set the signal-to-noise ratio index, discriminate the reconstructed signal, and output the denoised signal to complete the denoising. The multi-scale mean variational modal decomposition denoising method proposed in this invention effectively solves the problem of feature splitting caused by parameter selection or weak features through multi-scale mean reconstruction. At the same time, the introduction of the autocorrelation coefficient that is sensitive to signal stationarity and periodicity solves the problem of inaccurate feature positioning. It can achieve good denoising effect on rolling bearing fault signals for non-stationary nonlinear signals.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent fault diagnosis of vibration signals of mechanical rotating parts, and particularly relates to a bearing vibration signal denoising method based on multi-scale mean variational modal decomposition. Background Art

[0002] With the development of social productivity, mechanical equipment is increasingly being used in daily life and production. As a crucial component of mechanical equipment, rolling bearings are often exposed to harsh operating conditions such as high speeds and high loads, making them prone to damage and even failure, resulting in economic losses. Therefore, the use of advanced technologies to process vibration signals and perform fault diagnosis has significant practical significance for reducing maintenance costs and preventing safety accidents.

[0003] In actual operating conditions, the signal acquisition process is inevitably mixed with engineering noise and environmental noise, which greatly increases the non-stationary and nonlinear characteristics of the signal. Direct feature extraction of such signals can easily lead to redundant information interference, resulting in inaccurate feature extraction. Furthermore, using traditional signal processing methods for stationary linear signals for noise reduction can easily filter out some important fault characteristics in the signal. Among the noise reduction methods for non-stationary, nonlinear signals in actual operating conditions, variational mode decomposition (VMD) has demonstrated good performance. However, the quality of VMD results is affected by parameter selection, and information aliasing is still prone to occur in the decomposed components, resulting in feature loss.

[0004] Multi-scale mean variational modal decomposition is based on considerations such as the difficulty of denoising, feature loss and the particularity of nonlinear and non-stationary signals. The non-stationary nonlinear signal is first decomposed by variational modal decomposition, and then the components are reconstructed by multi-scale averaging by setting the scale factor. The sensitivity of autocovariance to signal stationarity is used to construct the autocorrelation coefficient, and the reconstructed components are preliminarily screened to ensure the multi-quantity integrity of the features. Then, with the help of MPE, the high-frequency noise components in the reconstructed components of the two fault signals are eliminated and reconstructed. At the same time, the signal-to-noise ratio evaluation index is set, which makes a good improvement to the variational modal decomposition denoising method and can effectively reduce the noise of the non-stationary nonlinear signals of rolling bearing faults. Summary of the Invention

[0005] Purpose of the invention: The present invention provides a bearing vibration signal denoising method based on multi-scale mean variational modal decomposition, which can achieve good denoising effect on rolling bearing fault signals for non-stationary nonlinear signals.

[0006] Technical solution: The present invention provides a bearing vibration signal denoising method based on multi-scale mean variational modal decomposition, which specifically includes the following steps:

[0007] (1) Obtain vibration signals of rolling bearings under different fault conditions in advance;

[0008] (2) Decompose the signal based on the variational mode decomposition method to obtain the IMF components under different states;

[0009] (3) Set the scale factor S for multi-scale averaging v , according to the scale factor S v , rearrange the components at different scales, average them, calculate the autocorrelation coefficients of the multi-scale mean reconstruction components at the same scale, and sort and eliminate them according to the order of the size of the autocorrelation sequence;

[0010] (4) Calculate the MPE entropy value of the remaining reconstructed components and screen the reconstructed signal;

[0011] (5) Set the signal-to-noise ratio evaluation index, calculate the signal-to-noise ratio of the reconstructed signal for comparison, and output the reconstructed signal to complete the noise reduction if it is less than the preset evaluation index. If it is greater than the preset evaluation index, repeat the above steps (2) to (4) iteratively until the noise reduction is completed.

[0012] Furthermore, the fault vibration signal in step (1) includes vibration signals of the inner ring fault and the outer ring fault of the rolling bearing.

[0013] Furthermore, the implementation process of step (2) is as follows:

[0014] Set the decomposition layer number K and penalty parameter α in VMD, intercept and decompose signal data under different states, and obtain the IMF components of different fault signals; decompose the original signal collected on the simulation test bench:

[0015]

[0016] Where u k (t) Satisfaction A k (t) is the instantaneous amplitude, f(t) is the original signal, is the instantaneous phase, instantaneous frequency and Ak(t)≥0;

[0017] The penalty factor α and the Lagrange multiplier λ are set to construct the augmented Lagrange function, thereby transforming the problem into an unconstrained variational problem. The Lagrange expression is as follows:

[0018]

[0019] Among them, u k (t) is the modal component obtained by decomposition, ω kis the frequency center of each component, λ is the Lagrange multiplier, α is the penalty factor, K is the number of decomposition layers, and δ(t) is the impulse function.

[0020] Furthermore, the implementation process of step (3) is as follows:

[0021] The decomposed modal component sequence {u k (t), k=1,2,3,…,K} perform multi-scale averaging to obtain a multi-scale averaging sequence

[0022]

[0023] Where, is the mean value sequence, s v is the scale factor of multi-scale mean variational mode decomposition;

[0024] When s v =1, the mean value sequence is the original decomposition mode sequence; when s v =2,3,..., the original sequence becomes (K+1-s v )’s mean-valued component sequence;

[0025] Get scales 1 to s respectively v The multi-scale mean reconstruction component sequence of ; calculate the autocorrelation coefficient of the multi-scale mean reconstruction component at the same scale:

[0026]

[0027] Where R is the autocorrelation coefficient, γ is the autocovariance of two adjacent reconstructed components of the same scale, and σ is the variance of the first component of the two reconstructed components;

[0028] Sort by the size of the autocorrelation sequence, retain the combinations with autocorrelation coefficients exceeding 0.8, and eliminate the rest.

[0029] Furthermore, the implementation process of step (4) is as follows:

[0030] Set the three parameters of the multi-scale permutation entropy, namely the delay time τ, the scale factor s of the multi-scale permutation entropy and the embedding dimension m;

[0031] For 1 to s v In the scale, the time series X of each level with length N is {x i , i=1,2,…,N} is processed to obtain a coarse-grained sequence

[0032]

[0033] in, is the coarse-grained sequence, s is the scale factor, s=1,2,···,[N / s] means rounding N / s; when s=1, the coarse-grained sequence is the original sequence; calculate each coarse-grained sequence The permutation entropy of each level is used to determine the multi-scale permutation entropy of each component; the high-frequency noise components in each level are eliminated according to the order of the MPE entropy values, and the remaining components are smoothed and reconstructed.

[0034] Furthermore, the implementation process of step (5) is as follows:

[0035] The signal-to-noise ratio is the ratio of the original signal energy to the noise energy:

[0036]

[0037] Where x(i) is the energy of the fault signal component in the reconstructed signal, is the energy of the noise component in the reconstructed signal, N is the length of the signal sequence;

[0038] Calculate the signal-to-noise ratio of the reconstructed signal and compare it with the evaluation index. If it is less than the evaluation index, output the reconstructed signal; if it is greater than the evaluation index, repeat steps (2) to (4) to perform iterative noise reduction until the requirements are met and the result is output.

[0039] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are: the multi-scale mean variational modal decomposition denoising method proposed in the present invention effectively solves the problem of feature splitting caused by parameter selection or weak features through multi-scale mean reconstruction, and at the same time introduces the autocorrelation coefficient that is sensitive to signal stationarity and periodicity to solve the problem of inaccurate feature positioning, and combines the multi-scale permutation entropy method to remove noise sequences, which can achieve good noise reduction effect on rolling bearing fault signals for non-stationary nonlinear signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flow chart of the present invention;

[0041] Figure 2 It is the mechanical vibration simulation test bench described in the example of the present invention;

[0042] Figure 3 This is a diagram of the internal structure of the gearbox and various sensors described in the examples of the present invention;

[0043] Figure 4 is a diagram of the sensor arrangement positions described in an example of the present invention;

[0044] Figure 5 It is a principle diagram of multi-scale averaging reconstruction components described in an example of the present invention;

[0045] Figure 6 : This is a comparison of the noise reduction results of the bearing inner ring fault using the present invention and other noise reduction methods; among them, (a) is the original signal diagram; (b) is the wavelet hard threshold noise reduction result diagram; (c) is the wavelet soft threshold noise reduction result diagram; (d) is the VMD method noise reduction result diagram; (e) is the noise reduction result diagram using the present invention;

[0046] Figure 7 : This is a comparison of the noise reduction results of the bearing outer ring fault using the present invention and other noise reduction methods; among them, (a) is the original signal diagram; (b) is the wavelet hard threshold noise reduction result diagram; (c) is the wavelet soft threshold noise reduction result diagram; (d) is the VMD method noise reduction result diagram; (e) is the noise reduction result diagram using the present invention;

[0047] Figure 8 This is a comparison chart of the SNR results of bearing fault noise reduction using different methods. DETAILED DESCRIPTION

[0048] The present invention will be further described in detail below with reference to the accompanying drawings.

[0049] The present invention proposes a bearing vibration signal denoising method based on multiscale mean variational modal decomposition (MMVMD), such as Figure 1 As shown, the specific steps include:

[0050] Step 1: pre-acquire vibration signals of rolling bearings under different faults, including vibration signals of rolling bearing inner ring faults and outer ring faults.

[0051] A mechanical vibration simulation test bench was built, and signals were collected using the LMS vibration and noise test system. A contact three-axis acceleration sensor was installed at the faulty part to collect vibration signals, and a non-contact acoustic sensor was set up nearby to collect acoustic signals.

[0052] The non-stationary nonlinear characteristics in mechanical vibration signals come from the nonlinear contact and nonlinear load distribution between internal components such as shafts and gears, and from the complex noise in the external working environment on the one hand. Therefore, when building a mechanical vibration simulation test bench, in order to obtain the most realistic non-stationary nonlinear signal, a gearbox is set up on the test bench, which contains shafts, gears, bearings and other components. In its external settings, in addition to using contact-type three-axis acceleration sensors 1A312E, 1A313E and 356A15 for vibration signal acquisition, a non-contact acoustic sensor AWA14604 is also used to collect working environment noise. Mechanical vibration simulation test bench such as Figure 2 As shown, the internal structure of the gearbox and the components of the signal acquisition system are as follows Figure 3 As shown, the sensor layout is as follows Figure 4 In addition, this test bench also includes driving equipment, water cooling equipment, loading equipment, and other disassembly and assembly tools.

[0053] The test speed was set at 1300 rpm, the sampling frequency was set at 25.6 kHz, and the sampling time was 30 seconds. A data set contained 768,000 points. The data from the contact-type triaxial accelerometer was selected in the z-direction because vibration in this direction is more pronounced than in the other two directions.

[0054] Step 2: VMD decomposition to obtain IMF components: Set the two parameters required by the VMD method, the decomposition layer number K and the penalty parameter α, and then perform VMD decomposition on the two fault signals to obtain IMF components.

[0055] Variational mode decomposition (VMD) shares similarities with empirical mode decomposition (EMD) in their signal processing methods. For example, both methods can decompose the original signal in order of frequency to obtain several intrinsic mode components. However, EMD suffers from limitations such as modal mixing and endpoint effects. VMD offers superior performance, effectively overcoming these issues. Furthermore, it has a more comprehensive theoretical foundation, can stabilize non-stationary signals, and significantly offsets the redundant information of complex nonlinear signals.

[0056] First, set the necessary parameters in the VMD method, the number of decomposition layers K and the penalty parameter α. K is set to 4 and α is set to 3000.

[0057] Secondly, the original signal collected on the simulation test bench is decomposed into 8 IMF components. The formula of VMD decomposition is as follows:

[0058]

[0059] Where u k (t) Satisfaction A k (t) is the instantaneous amplitude, f(t) is the original signal, is the instantaneous phase, instantaneous frequency and Ak(t)≥0.

[0060] In order to achieve the optimal variational effect, the penalty factor α and the Lagrange multiplier λ are set to construct the augmented Lagrange function, thereby transforming the problem into an unconstrained variational problem. The Lagrange expression is as follows:

[0061]

[0062] Where u k (t) is the modal component obtained by decomposition, ω kis the frequency center of each component, λ is the Lagrange multiplier to ensure the strictness of the model, α is the penalty factor to ensure the reconstruction accuracy, K is the number of decomposition layers, and δ(t) is the impulse function.

[0063] Step 3: Multi-scale mean reconstruction component: Set the scale factor S v , according to the scale factor, the components are rearranged at different scales and averaged, the autocorrelation coefficients of the multi-scale mean reconstruction components at the same scale are calculated, and the autocorrelation sequences are sorted in order of size. The combinations with autocorrelation coefficients exceeding 0.8 are retained, and the rest are eliminated.

[0064] The multi-scale mean reconstruction component can effectively deal with the problem of feature omission caused by parameter selection and adaptive decomposition during VMD decomposition. Its expression is:

[0065]

[0066] Where, is the mean value sequence, s v is the scale factor of the multi-scale mean variational mode decomposition.

[0067] The multi-scale mean component construction method is as follows Figure 5 As shown. v = 3 as an example, the number of K first-generation modal components u k (t) After averaging, the reconstructed modal components with a length of (K-2) are obtained. The averaging sequences with scale factors of 1, 2 and 3 are obtained respectively to obtain the multi-scale mean reconstructed component sequence.

[0068] The autocorrelation coefficient is very sensitive to the periodic impact characteristics in the signal. It can be used to quickly locate the components with sufficient fault characteristics in the reconstructed components and eliminate the components with fewer characteristics. Calculate the autocorrelation coefficient of the multi-scale mean reconstructed components at the same scale:

[0069]

[0070] Where R is the autocorrelation coefficient, and γ is the autocovariance of two adjacent reconstructed components at the same scale, for example, and and And so on; σ is the variance of the first component of the two reconstructed components, such as and in

[0071] Sort by the size of the autocorrelation sequence, retain the combinations with autocorrelation coefficients exceeding 0.8, and eliminate the rest.

[0072] Step 4: Reconstruct the signal: Set the parameters required by the MPE method, embedding dimension m, delay time τ, and scale factor s, then calculate the MPE entropy value of each component at each scale, remove the high-frequency noisy components, and reconstruct the remaining components.

[0073] Multi-scale permutation entropy can cope with the complexity and randomness of complex signals at multiple scales.

[0074] First, the necessary parameters in the MPE method are set: the embedding dimension m is set to 6, the scale factor s is set to 9, and the delay time τ is set to 2.

[0075] Then, for a time series X={x i , i=1,2,…,N} is processed to obtain a coarse-grained sequence Its expression is:

[0076]

[0077] Where s is the scale factor, s=1,2,···,[N / s] means rounding N / s. When s=1, the coarse-grained sequence is the original sequence. Calculate each coarse-grained sequence The permutation entropy of is used to determine its multi-scale permutation entropy.

[0078] Finally, the high-frequency noisy components are removed in order of the size of the MPE entropy values, and the remaining components are smoothed and reconstructed.

[0079] Step 5: Determine the reconstructed signal: Set the signal-to-noise ratio evaluation index, calculate the signal-to-noise ratio of the reconstructed signal and compare it with the evaluation index. If it meets the standard, output the reconstructed signal. Otherwise, repeat the above steps until it meets the standard. Finally, output the signal that meets the standard to complete the noise reduction.

[0080] The signal-to-noise ratio (SNR) is the ratio of the original signal energy to the noise energy and can be expressed as:

[0081]

[0082] Where x(i) is the energy of the fault signal component in the reconstructed signal, is the energy of the noise component in the reconstructed signal, where N is the length of the signal sequence.

[0083] Set the signal-to-noise ratio evaluation index SNR = 5. Calculate the signal-to-noise ratio of the reconstructed signal using formula (6) and compare it with the evaluation index. If the evaluation index is less than 5, output the reconstructed signal. If the evaluation index is greater than 5, repeat the above steps for iterative denoising until the requirements are met and output the result.

[0084] The results of the bearing inner ring MMVMD noise reduction method and the noise reduction results of the comparative method are shown as follows, where: Figure 6 (a) is the original signal diagram; Figure 6 Middle (b) is the result of wavelet hard threshold denoising; Figure 6 (c) is the result of wavelet soft threshold denoising; Figure 6 Middle (d) is the denoising result of VMD method; Figure 6 (e) is the noise reduction result of the present invention. The noise reduction results of the bearing outer ring MMVMD method and the noise reduction results of the comparative method are shown in Figure 2. Figure 7 As shown in, where Figure 7 (a) is the original signal diagram; Figure 7 Middle (b) is the result of wavelet hard threshold denoising; Figure 7 (c) is the result of wavelet soft threshold denoising; Figure 7 Middle (d) is the denoising result of VMD method; Figure 7 Figure (e) shows the noise reduction results using the present invention. The figure shows that, overall, the VMD-based method performs better than the non-VMD-based method, demonstrating the VMD method's superiority in processing nonstationary, nonlinear signals. Locally, the VMD-based method loses some periodic impulse characteristics compared to the other methods, while the MMMMD method not only achieves excellent noise reduction but also preserves the fault characteristics of the original signal.

[0085] The output SNR value comparison chart is as follows Figure 8 As shown in the figure, it can be seen from the analysis that, overall, the noise reduction effects of wavelet hard threshold noise reduction, wavelet soft threshold noise reduction, VMD noise reduction and MMVMD noise reduction methods show a linear upward trend; local analysis shows that the MMVMD method not only has the best noise reduction effect, but also meets the signal-to-noise ratio evaluation index.

Claims

1. A bearing vibration signal denoising method based on multi-scale mean variational modal decomposition, characterized in that: The following steps are involved: (1) Obtain vibration signals of rolling bearings under different fault conditions in advance; (2) Decompose the signal based on the variational mode decomposition method to obtain the IMF components under different states; (3) Set the scale factor S for multi-scale averaging v , according to the scale factor S v , rearrange the components at different scales, average them, calculate the autocorrelation coefficients of the multi-scale mean reconstruction components at the same scale, and sort and eliminate them according to the order of the size of the autocorrelation sequence; (4) Calculate the MPE entropy value of the remaining reconstructed components and filter the reconstructed signal; (5) Set the signal-to-noise ratio evaluation index, calculate the signal-to-noise ratio of the reconstructed signal for comparison, and output the reconstructed signal to complete the noise reduction if it is less than the preset evaluation index. If it is greater than the preset evaluation index, repeat the above steps (2) to (4) iteratively until the noise reduction is completed.

2. The bearing vibration signal denoising method based on multi-scale mean variational modal decomposition according to claim 1 is characterized in that: The vibration signal in step (1) includes vibration signals of inner ring fault and outer ring fault of the rolling bearing.

3. The bearing vibration signal denoising method based on multi-scale mean variational modal decomposition according to claim 1 is characterized in that: The implementation process of step (2) is as follows: Set the decomposition layer number K and penalty parameter α in VMD, intercept and decompose signal data under different states, and obtain the IMF components of different fault signals; decompose the original signal collected on the simulation test bench: Where u k (t) Satisfaction A k (t) is the instantaneous amplitude, f(t) is the original signal, is the instantaneous phase, instantaneous frequency and Ak(t)≥0; The penalty factor α and the Lagrange multiplier λ are set to construct the augmented Lagrange function, thereby transforming the problem into an unconstrained variational problem. The Lagrange expression is as follows: Among them, u k (t) is the modal component obtained by decomposition, ω k is the frequency center of each component, λ is the Lagrange multiplier, α is the penalty factor, K is the number of decomposition layers, and δ(t) is the impulse function.

4. The bearing vibration signal denoising method based on multi-scale mean variational modal decomposition according to claim 1 is characterized in that: The implementation process of step (3) is as follows: The decomposed modal component sequence {u k (t), k+1,2,3,…,K} are multi-scale averaged to obtain a multi-scale averaged sequence Where, is the mean value sequence, s v is the scale factor of multi-scale mean variational mode decomposition; When s v =1, the mean value sequence is the original decomposition mode sequence; when s v =2,3,..., the original sequence becomes (K+1-s v )’s mean-valued component sequence; Get scales 1 to s respectively v The multi-scale mean reconstruction component sequence of ; calculate the autocorrelation coefficient of the multi-scale mean reconstruction component at the same scale: Where R is the autocorrelation coefficient, γ is the autocovariance of two adjacent reconstructed components of the same scale, and σ is the variance of the first component of the two reconstructed components; Sort by the size of the autocorrelation sequence, retain the combinations with autocorrelation coefficients exceeding 0.8, and eliminate the rest.

5. The bearing vibration signal denoising method based on multi-scale mean variational modal decomposition according to claim 1 is characterized in that: The implementation process of step (4) is as follows: Set the three parameters of the multi-scale permutation entropy, namely the delay time τ, the scale factor s of the multi-scale permutation entropy and the embedding dimension m; For 1 to s v In the scale, the time series X of each level with length N is {x i , i=1,2,…,N} is processed to obtain a coarse-grained sequence in, is the coarse-grained sequence, s is the scale factor, s=1,2,···,[N / s] means rounding N / s; when s=1, the coarse-grained sequence is the original sequence; calculate each coarse-grained sequence The permutation entropy of each level is used to determine the multi-scale permutation entropy of each component; the high-frequency noise components in each level are eliminated according to the order of the MPE entropy values, and the remaining components are smoothed and reconstructed.

6. The bearing vibration signal denoising method based on multi-scale mean variational modal decomposition according to claim 1 is characterized in that: The implementation process of step (5) is as follows: The signal-to-noise ratio is the ratio of the original signal energy to the noise energy: Where x(i) is the energy of the fault signal component in the reconstructed signal, is the energy of the noise component in the reconstructed signal, N is the length of the signal sequence; Calculate the signal-to-noise ratio of the reconstructed signal and compare it with the evaluation index. If it is less than the evaluation index, output the reconstructed signal; if it is greater than the evaluation index, repeat steps (2) to (4) to perform iterative noise reduction until the requirements are met and the result is output.

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