An EEMD-ISVD-based rolling bearing vibration signal denoising method and device, electronic equipment and medium

Abstract

The application discloses a rolling bearing vibration signal denoising method and device based on EEMD-ISVD, electronic equipment and medium, comprising EEMD decomposition of the collected rolling bearing original vibration signal, obtaining a plurality of intrinsic mode function IMF signals;According to the sensitive IMF function screening criterion, select the effective IMF component from the plurality of intrinsic mode function IMF signals, and determine the denoising number of each effective IMF component;Each IMF component is respectively denoised by the improved singular value decomposition denoising ISVD for the corresponding number of times;The denoised each IMF component is accumulated and reconstructed in order from low to high frequency, and the denoised rolling bearing vibration signal is obtained.The application can effectively suppress the vibration signal noise and improve the extraction accuracy of useful signal.

Description

Technical Field

[0001] This invention relates to the field of vibration signal processing technology, specifically to a method, device, electronic device, and medium for noise reduction of rolling bearing vibration signals based on EEMD-ISVD. Background Technology

[0002] As a crucial component of high-speed train gearboxes, rolling bearings play a vital role in the overall operation of the train. Continuous, prolonged operation can easily lead to fatigue in the equipment components, and the frequent start-stop cycles and speed changes can cause sudden force fluctuations in rotating parts, resulting in failures. Once a failure occurs, it often causes vibration in the rolling bearing. Therefore, rolling bearing vibration signals typically contain a significant amount of fault information. However, in practical applications, the operating conditions of the equipment are complex, and noise pollution is severe, making it difficult to directly observe effective fault information. Furthermore, due to external limitations or internal structural factors of the rolling bearing, vibration monitoring equipment cannot be directly installed in areas prone to failure. This results in energy loss and the inclusion of other structural vibration information components during the transmission of the collected vibration signals, further increasing the difficulty of signal analysis.

[0003] To accurately diagnose equipment faults, effective noise reduction analysis of rolling bearing vibration signals is necessary. Traditional noise reduction methods, such as filter noise reduction and wavelet WT noise reduction, are mostly used for constant rotational speeds. However, vibration signals sampled at equal time intervals under varying rotational speeds lose their periodicity. The intervals and energy intensities of impact components fluctuate non-periodicly with changes in rotational speed, resulting in frequency modulation, amplitude modulation, and phase modulation phenomena. Consequently, these methods are ineffective for noise reduction under varying rotational speeds. Traditional Empirical Mode Decomposition (EMD) methods suffer from end-effects and mode aliasing. While the further ensemble empirical mode decomposition (EEMD) method can effectively suppress mode aliasing, it still produces residual white noise during the noise reduction process. Furthermore, the selection of IMF components relies entirely on experience. When removing noise components that meet the criteria, the removed components may contain useful signals. The distinction between noise and useful components is largely subjective and relies on human judgment, leading to inaccurate fault signal extraction. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, device, electronic device and medium for noise reduction of rolling bearing vibration signals based on EEMD-ISVD, which can effectively suppress vibration signal noise while improving the extraction accuracy of useful signals.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] In a first aspect, the present invention provides a method for noise reduction of rolling bearing vibration signals based on EEMD-ISVD, the method comprising:

[0007] The original vibration signal of the rolling bearing was decomposed by EEMD to obtain multiple intrinsic mode function (IMF) signals.

[0008] Based on the sensitive IMF function screening criteria, effective IMF components are selected from the multiple intrinsic mode function IMF signals, and the number of noise reduction steps for each effective IMF component is determined.

[0009] Each of the IMF components is denoised using an improved singular value decomposition denoising (ISVD) method, with each component undergoing a corresponding number of denoising operations.

[0010] The noise-reduced IMF components are accumulated and reconstructed in order of frequency from low to high to obtain the noise-reduced rolling bearing vibration signal.

[0011] In conjunction with the first aspect, preferably, the step of selecting effective IMF components from the plurality of intrinsic mode function (IMF) signals according to the sensitive IMF function screening criteria, and determining the number of noise reduction operations for each effective IMF component, includes:

[0012] Calculate the cross-correlation coefficients between each intrinsic mode function (IMF) signal and the original vibration signal;

[0013] The intrinsic mode function (IMF) signals with cross-correlation coefficients greater than a preset threshold are selected as valid IMF components.

[0014] The product WK of waveform kurtosis and waveform coefficient of each IMF component is calculated to characterize the noise distribution of each IMF component.

[0015] Based on the WK value and cross-correlation coefficient of each IMF component, the IMF component with the most noise is identified.

[0016] The noise reduction steps for the IMF component with the most noise are set to no less than two, while the noise reduction steps for the remaining IMF components are set to one or two.

[0017] In conjunction with the first aspect, the preferred formula for calculating the cross-correlation coefficients between the intrinsic mode function (IMF) signals and the original vibration signals is as follows:

[0018]

[0019] In the formula, R(x,imf) j ) represents the cross-correlation coefficient of the j-th intrinsic mode function (IMF) signal; x(k) represents the original vibration signal, imf j (k) represents the j-th intrinsic mode function (IMF) signal; j = 1, 2, ..., J, where J represents the number of intrinsic mode function (IMF) signals and N represents the number of data points for each IMF signal.

[0020] In conjunction with the first aspect, the preferred formula for calculating the product WK of the waveform kurtosis and waveform coefficient of each IMF component is as follows:

[0021]

[0022]

[0023] WK j =K 1j ×K 2j (2)

[0024] In the formula, K 1j σ represents the waveform kurtosis of the j-th IMF component. j This represents the standard deviation of the j-th IMF component; K is the fourth-order central moment of the j-th IMF component; 2j Let represent the waveform coefficient of the j-th IMF component, where is the impulse factor of the j-th IMF component. Peak factor of the j-th IMF component WK j This represents the product of the waveform kurtosis and waveform coefficient of the j-th IMF component.

[0025] In conjunction with the first aspect, preferably, the step of performing noise reduction processing on each of the IMF components for a corresponding number of times through improved singular value decomposition (ISVD) includes:

[0026] The data points of each IMF component are flattened into a one-dimensional matrix using formula (3):

[0027] imf j ={a j,1 a j,2 , ..., a j,k , ..., a j,N ,k=1,2,3,…,N} (3)

[0028] In the formula: imf j Let a represent the j-th IMF component. j,k Let k be the k-th data point of the j-th IMF component, where k = 1, 2, ..., N, and N is the number of data points in the j-th IMF component.

[0029] Using the data points of the one-dimensional matrix as the first row of the phase space matrix, and following the rule that the data in the next row lags behind the data in the previous row by two data points, the phase space matrix of each IMF component is constructed, and its expression is:

[0030]

[0031] In the formula, D j Let m represent the m×N dimensional phase space matrix constructed for the j-th IMF component, where m is the dimension of the phase space matrix;

[0032] The phase space matrix is ​​decomposed by singular value transformation, and the effective rank order of the singular values ​​is determined. The noise reduction of each IMF component is then completed by combining the peak factor.

[0033] In conjunction with the first aspect, preferably, the step of performing singular value decomposition on the phase space matrix, determining the effective rank order of the singular values, and combining the peak factor to complete the noise reduction processing of each IMF component includes the following steps:

[0034] For phase space matrix D j Perform singular value transformation decomposition into D j =U j S j V j U j S j V j They are represented as follows:

[0035]

[0036] In the formula: U j and V j Let u be an m×m and an N×N orthogonal matrix obtained from singular value decomposition, respectively. mm Represents matrix U j The data in the m-th row and m-th column, v NN Represents matrix V j The data in the Nth row and Nth column; S j Let σ1, σ2, σ3, ..., σ be an m×N singular value matrix. m Form all singular values ​​and σ1≥σ2≥…≥σ m ;

[0037] Based on the singular value matrix S j The distribution of the singular values ​​is determined by formula (6), which determines the effective rank K of the singular values:

[0038]

[0039] In the formula: θ represents the error compensation coefficient, k cThe threshold representing the effective rank of the singular values, m is the dimension of the phase space matrix, and c1 is the singular value difference spectrum σ. p -σ p+1 The next singular value corresponding to the maximum peak, σ p and σ p+1 c1 and c2 represent the p-th and p+1-th singular values, respectively; c3 is the mean of all singular values; c4 is the sum of the first singular value σ1 and the last singular value σ2. m The difference, c4 is the singular value difference spectrum σ p -σ p+1 The mean;

[0040] The singular value matrix S j Set the singular values ​​of intermediate order greater than K to 0 to obtain the denoised S. j 'for:

[0041]

[0042] For matrix U j S j '、V j Performing inverse singular value transformation yields the denoised reconstruction matrix D. j '=U j S′ j V j That is, D′ j The expression is:

[0043]

[0044] In the formula, d mN Represents the reconstruction matrix D′ j The data in the m-th column and N-th row;

[0045] Based on the matrix U of each IMF component j The peak factor in the matrix will reconstruct the matrix D′ of each IMF component. j Each signal is then restored to a one-dimensional noise-reduced signal with the same dimension as the original vibration signal.

[0046] In conjunction with the first aspect, preferably, the matrix U based on each IMF component... j The peak factor in the matrix will reconstruct the matrix D′ of each IMF component. j The steps to recover the original vibration signal into a one-dimensional denoised signal with the same dimension as the original vibration signal include:

[0047] Calculate the matrix U of the j-th IMF component using formula (9). j Peak factor of each row vector in the data:

[0048]

[0049] In the formula, p a Represents matrix U j The peak factor of the a-th row vector in the vector, u ab The matrix U representing the j-th IMF component j The data in the a-th row and b-th column, where a = 1, 2, ..., m, b = 1, 2, ..., m;

[0050] The minimum peak factor is selected from the peak factors of each row vector, and the row number g of the minimum peak factor is determined.

[0051] Extract the reconstruction matrix D′ j The g-th row vector in the vector is used to obtain the one-dimensional denoised signal of the j-th IMF component.

[0052] Secondly, the present invention provides a noise reduction device for rolling bearing vibration signals based on EEMD-ISVD, the device comprising:

[0053] The EEMD decomposition module is used to perform EEMD decomposition on the acquired raw vibration signal of the rolling bearing to obtain multiple intrinsic mode function (IMF) signals.

[0054] The IMF component filtering module is used to select effective IMF components from the multiple intrinsic mode function IMF signals according to the sensitive IMF function filtering criteria, and to determine the number of noise reduction steps for each effective IMF component.

[0055] The ISVD noise reduction module is used to perform noise reduction processing on each of the IMF components for a corresponding number of times by means of improved singular value decomposition noise reduction (ISVD).

[0056] The accumulation and reconstruction module is used to accumulate and reconstruct the noise-reduced IMF components in order of frequency from low to high to obtain the noise-reduced rolling bearing vibration signal.

[0057] Thirdly, the present invention provides an electronic device, including a processor and a storage medium;

[0058] The storage medium is used to store instructions;

[0059] The processor is configured to operate according to the instructions to perform the steps of the rolling bearing vibration signal noise reduction method based on EEMD-ISVD as described in any of the first aspects.

[0060] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the rolling bearing vibration signal noise reduction method based on EEMD-ISVD as described in any of the first aspects.

[0061] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0062] 1. This invention employs EEMD decomposition for signal pre-denoising, utilizing the statistical characteristics of Gaussian white noise to suppress mode aliasing and achieve good filtering results. Simultaneously, it utilizes improved singular value decomposition (ISVD) for secondary denoising, overcoming the incomplete denoising of random noise by ensemble empirical mode decomposition. This invention, through a combination of EEMD decomposition and improved ISVD, effectively enhances the impact characteristics of fault signals, highlights the weak characteristics of faults in strong noise environments, improves the signal-to-noise ratio, and facilitates early-stage fault diagnosis of rolling bearings, thus providing a certain level of assurance for the safe operation of high-speed trains.

[0063] 2. This invention improves the phase space matrix reconstruction method in the Singular Value Decomposition (ISVD) denoising process, making the signal components in the reconstructed matrix more complete and preserving more of the original signal impulse characteristics.

[0064] 3. This invention determines the effective rank order in the singular value decomposition noise reduction process. By using the error compensation coefficient and combining it with the influence of noise on the singular values, the effective rank order of the singular values ​​is determined, which further improves the noise removal effect of vibration signals.

[0065] 4. The present invention restores the reconstructed signal after singular value decomposition and denoising to a one-dimensional denoised signal. It combines peak factor to optimize the signal, thereby selecting a relatively smooth signal with high waveform restoration. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the noise reduction method for rolling bearing vibration signals based on EEMD-ISVD provided in an embodiment of the present invention;

[0067] Figure 2 A schematic diagram illustrating the specific process of the rolling bearing vibration signal noise reduction method based on EEMD-ISVD provided in an embodiment of the present invention;

[0068] Figure 3 This is a time-domain diagram of the original vibration signal of a rolling bearing provided in an embodiment of the present invention;

[0069] Figure 4 The original vibration signal frequency domain diagram of the rolling bearing provided in the embodiment of the present invention;

[0070] Figure 5 This is a schematic diagram of the correlation coefficients of each IMF component provided in an embodiment of the present invention;

[0071] Figure 6 (a) and (b) are the time-frequency diagram and frequency domain diagram of the IMF1 to IMF8 components provided in the embodiments of the present invention, respectively;

[0072] Figure 7 A schematic diagram of the WK values ​​of each IMF component provided in the embodiments of the present invention;

[0073] Figure 8 This is a time-domain diagram of the denoised signal provided in an embodiment of the present invention;

[0074] Figure 9 This is a frequency domain diagram of the noise-reduced signal provided in an embodiment of the present invention;

[0075] Figure 10 The structural principle block diagram of the rolling bearing vibration signal noise reduction device based on EEMD-ISVD provided in the embodiment of the present invention is shown. Detailed Implementation

[0076] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0077] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0078] Example 1:

[0079] like Figure 1 As shown in the figure, this invention provides a method for noise reduction of rolling bearing vibration signals based on EEMD-ISVD, which specifically includes the following steps:

[0080] Step S1: Perform EEMD decomposition on the acquired original vibration signal of the rolling bearing to obtain multiple intrinsic mode function (IMF) signals;

[0081] Step S2: Select effective IMF components from the multiple intrinsic mode function (IMF) signals according to the sensitive IMF function screening criteria, and determine the number of noise reduction steps for each effective IMF component;

[0082] Step S3: Perform noise reduction processing on each of the IMF components for a corresponding number of times by improving singular value decomposition and denoising (ISVD).

[0083] Step S4: Accumulate and reconstruct the noise-reduced IMF components in order of frequency from low to high to obtain the noise-reduced rolling bearing vibration signal.

[0084] Specifically, see below. Figure 2 The above steps are explained in detail.

[0085] As an embodiment of the present invention, the EEMD decomposition method in step S1 includes: adding a white noise e with a standard normal distribution to the original vibration signal x(k). i (k) to generate a new signal:

[0086] x i (k)=x(k)+e i (k) (1)

[0087] In the formula, e i (k) represents the i-th addition of the white noise sequence, x i (k) represents the additional noise signal of the i-th trial, i = 1, 2, ..., M, k = 1, 2, ..., N, where N is the number of data points and M is the total average number of white noise decompositions; for each obtained signal x i (k) Perform EMD decomposition separately to obtain the IMF signal in the form of each signal:

[0088]

[0089] In the formula, imf i,j (k) represents the j-th IMF signal obtained by adding white noise for the i-th time, r i (k) is the residual component obtained by adding white noise for the i-th decomposition; j = 1, 2, ..., J, where J is the number of IMF signals;

[0090] After performing M EMD decompositions, the average value of the j-th IMF signal obtained from each is calculated to obtain the j-th intrinsic mode function (IMF) signal:

[0091]

[0092] In the formula, imf j It is the j-th intrinsic mode function (IMF) signal obtained from EEMD decomposition.

[0093] It should be noted that EEMD decomposition is used to adaptively decompose noisy signals into multiple approximate narrowband IMF signals. Each IMF component reflects the composition of the signal at different levels of detail, thus taking into account the time domain information of the signal while maintaining the frequency characteristics of the signal components.

[0094] Furthermore, step S2 provided in this embodiment of the invention specifically includes:

[0095] Step A: Calculate the cross-correlation coefficients between each intrinsic mode function (IMF) signal and the original vibration signal;

[0096] The calculation formula is:

[0097]

[0098] In the formula, R(x,imf) j ) represents the cross-correlation coefficient of the j-th intrinsic mode function (IMF) signal; x(k) represents the original vibration signal, imf j (k) represents the j-th intrinsic mode function (IMF) signal; j = 1, 2, ..., J, where J represents the number of intrinsic mode function (IMF) signals and N represents the number of data points for each IMF signal.

[0099] Step B: Select the intrinsic mode function (IMF) signals with cross-correlation coefficients greater than a preset coefficient threshold as valid IMF components; wherein, the preset coefficient threshold provided in this embodiment of the invention is 0.01;

[0100] It should be noted that during signal decomposition, due to interpolation errors, boundary effects, and other reasons, some pseudo-components unrelated to the original signal will be decomposed. The frequencies of these components are easily confused with the frequencies of the effective information, affecting the signal denoising effect. Therefore, screening out pseudo-components is crucial. In order to distinguish pseudo-vectors, the magnitude of the cross-correlation coefficient between each component and the original signal is used to determine whether an IMF is a pseudo-component. The larger the cross-correlation coefficient, the higher the similarity to the signal. Generally speaking, when the cross-correlation coefficient is less than 0.01, the component is a pseudo-component. Therefore, in this embodiment of the invention, IMF components with a cross-correlation coefficient greater than 0.01 are selected for denoising.

[0101] Step C: Calculate the product WK of waveform kurtosis and waveform coefficient for each IMF component to characterize the noise distribution of each IMF component;

[0102] Specifically, the formula for calculating the product WK of the waveform kurtosis and waveform coefficient of each IMF component is as follows:

[0103]

[0104]

[0105] WK j =K 1j ×K 2j (5)

[0106] In the formula, K 1j σ represents the waveform kurtosis of the j-th IMF component. j This represents the standard deviation of the j-th IMF component; K is the fourth-order central moment of the j-th IMF component; 2jLet represent the waveform coefficient of the j-th IMF component, where is the impulse factor of the j-th IMF component. Peak factor of the j-th IMF component WK j This represents the product of the waveform kurtosis and waveform coefficient of the j-th IMF component;

[0107] To further clarify, waveform kurtosis is a dimensionless parameter primarily used to characterize the peak value of a waveform. Generally speaking, the vibration signal of a normal rolling bearing can be considered to follow a Gaussian distribution, with a waveform kurtosis value of approximately 3. If a rolling bearing has a fault, the kurtosis value of its vibration signal will increase significantly. Therefore, if the waveform kurtosis value of some IMF components is greater than 3, it indicates that there are impact components in these IMF components. That is, after the original vibration signal is decomposed, most of its fault characteristic information will be retained in these IMF components. Thus, the selection method based on the sensitive IMF function screening criterion can highlight the fault characteristic information hidden in the noise and eliminate other information unrelated to the fault characteristics.

[0108] Furthermore, the waveform coefficient is the ratio of the effective value to the absolute average value of the signal within one period. Its value reflects the energy intensity and stability of the signal. If the index becomes abnormally large, it indicates that there is a certain fault in the rolling bearing. As shown in formula (5), the waveform coefficient is equal to the ratio of the impulse factor to the peak factor. The impulse factor is used to detect whether there is an impact in the signal, and the peak factor represents the extreme degree of the peak in the waveform. Since the rolling bearing signal is in a strong noise background, its fault signal is submerged in the noise. The traditional method of using the cross-correlation coefficient to screen the IMF component alone cannot accurately determine which IMF component the noise is mainly distributed in.

[0109] Step D: Based on the WK value and cross-correlation coefficient of each IMF component, determine the IMF component with the most noise.

[0110] Step E: Determine that the noise reduction steps for the IMF component with the most noise should be no less than two, and the noise reduction steps for the remaining IMF components should be one or two.

[0111] This invention utilizes the product of kurtosis and waveform coefficient, WK, to characterize the noise distribution of IMF components; WK takes into account the degree of noise distribution from non-impact faults, where waveform kurtosis K... 1j It describes the characteristics of the useful signal distribution; the larger the value, the more useful signal is distributed; waveform coefficient K 2jThis describes the characteristics of noise distribution; the smaller the value, the more noise is distributed. For each IMF component, the smaller the corresponding WK, the greater the noise interference and the less useful signal. The IMF component with the most noise needs to be denoised at least twice to remove the excess noise. For other IMF components with larger WK values, since they contain more useful signals, denoising will inevitably damage the useful signals, so only one or two denoising operations are needed.

[0112] As an embodiment of the present invention, step S3, which involves performing noise reduction processing on each of the IMF components for a corresponding number of times using improved singular value decomposition (ISVD), includes:

[0113] Step 1: Plot the data points of each IMF component into a one-dimensional matrix using formula (6):

[0114] imf j ={a j,1 a j,2 , ..., a j,k , ..., a j,N ,k=1,2,3,…,N} (6)

[0115] In the formula: imf j Let a represent the j-th IMF component. j,k Let k be the k-th data point of the j-th IMF component, where k = 1, 2, ..., N, and N is the number of data points in the j-th IMF component.

[0116] Step 2: Using the data points of the one-dimensional matrix as the first row of the phase space matrix, and following the rule that the data in the next row lags behind the data in the previous row by two data points, construct the phase space matrix of each IMF component. Its expression is:

[0117]

[0118] In the formula, D j Let m represent the m×N dimensional phase space matrix constructed for the j-th IMF component, where m is the dimension of the phase space matrix, and 5≤m≤20;

[0119] To further explain, matrix D j The first row of data in the matrix is ​​a raw bearing vibration signal. The next row lags the previous row by two data points. Each row of vectors in the matrix is ​​transformed from a complete one-dimensional signal, which has high row signal integrity and complete periodic impact vibration components. Furthermore, by transforming the one-dimensional bearing signal, m-1 additional sub-component signals can be obtained. These sub-component signals have good correlation, which is more conducive to the extraction and recovery of subsequent signals.

[0120] Step 3: Perform singular value transformation decomposition on the phase space matrix, determine the effective rank order of the singular values, and combine the peak factor to complete the noise reduction processing of each IMF component.

[0121] As an embodiment of the present invention, step 3 specifically includes:

[0122] a: Phase space matrix D j Perform singular value transformation decomposition into D j =U j S j V j U j S j V j They are represented as follows:

[0123]

[0124] In the formula: U j and V j Let u be an m×m and an N×N orthogonal matrix obtained from singular value decomposition, respectively. mm Represents matrix U j The data in the m-th row and m-th column, v NN Represents matrix V j The data in the Nth row and Nth column; S j Let σ1, σ2, σ3, ..., σ be an m×N singular value matrix. m Form all singular values ​​and σ1≥σ2≥…≥σ m ;

[0125] b: Based on the singular value matrix S j The distribution of the singular values ​​is determined by formula (9), which determines the effective rank K of the singular values:

[0126]

[0127] In the formula: θ represents the error compensation coefficient, k c The threshold representing the effective rank of the singular values, m is the dimension of the phase space matrix, and c1 is the singular value difference spectrum σ. p -σ p+1 The next singular value corresponding to the maximum peak, σ p and σ p+1 c1 and c2 represent the p-th and p+1-th singular values, respectively; c3 is the mean of all singular values; c4 is the sum of the first singular value σ1 and the last singular value σ2. m The difference, c4 is the singular value difference spectrum σ p -σ p+1 The mean;

[0128] Furthermore, in this embodiment of the invention, the error compensation coefficient θ is 0.8. During the operation of the bearing, there will be some high-frequency noise around it. The singular values ​​obtained from these high-frequency noises are often small and their magnitude is generally below the mean. At the same time, combined with the abrupt change of the noise and the actual signal in the singular values, the effective rank order is determined by K.

[0129] c: The singular value matrix S j Set the singular values ​​of intermediate order greater than K to 0 to obtain the denoised S. j 'for:

[0130]

[0131] It should be noted that singular values ​​represent the purity of a signal. The larger the singular value, the higher the purity. Therefore, it is necessary to determine the effective rank of the singular values, set the singular values ​​with low signal purity to zero, and finally restore the signal through inverse transform to complete the noise reduction process.

[0132] d: For matrix U j S j '、V j Performing inverse singular value transformation yields the denoised reconstruction matrix D. j '=U j S′ j V j That is, D′ j The expression is:

[0133]

[0134] In the formula, d mN Represents the reconstruction matrix D′ j The data in the m-th column and N-th row;

[0135] e: Based on the matrix U of each IMF component j The peak factor in the matrix will reconstruct the matrix D′ of each IMF component. j Each signal is then reconstructed into a one-dimensional noise-reduced signal with the same dimension as the original vibration signal.

[0136] Specifically, the signal of the j-th IMF component is... j ={a j,1 ,a j,2 ,…,a j,k ,…,a j,N ,k=1,2,3,…,N} is a 1×N matrix, and the reconstructed signal D after noise reduction is... j 'Given an m×N matrix, the reconstructed matrix D needs to be...' j'Restore the signal to a one-dimensional denoised signal with the same dimension as the original vibration signal; the larger the peak factor, the more severely the signal is affected by noise, by finding U...' j The row vector containing the minimum peak factor in each row vector of the matrix represents the signal least affected by noise. The specific steps are as follows:

[0137] Calculate the matrix U of the j-th IMF component using formula (12). j Peak factor of each row vector in the data:

[0138]

[0139] In the formula, p a Represents matrix U j The peak factor of the a-th row vector in the vector, u ab The matrix U representing the j-th IMF component j The data in the a-th row and b-th column, where a = 1, 2, ..., m, b = 1, 2, ..., m;

[0140] The minimum peak factor is selected from the peak factors of each row vector, and the row number g of the minimum peak factor is determined.

[0141] Extract the reconstruction matrix D′ j The g-th row vector in the vector is used to obtain the one-dimensional denoised signal of the j-th IMF component.

[0142] As an embodiment of the present invention, this embodiment uses a NU1007 cylindrical roller bearing with an outer ring crack to simulate the method of the present invention under a strong noise background. The sampling frequency of the original vibration signal is 20kHz, and the motor drives the test shaft to rotate at a frequency of 0-50Hz. The time domain and frequency domain diagrams of the experimental original vibration signal are shown in the figure. Figure 3 , Figure 4 As shown; some smaller-amplitude impact characteristics have been submerged by Gaussian white noise, making it impossible to observe their changing trends; from Figure 4 As can be seen, the high-frequency signal contains a lot of noise, which needs to be eliminated to reduce the impact of strong background noise on subsequent diagnosis. The original vibration signal of the experiment was decomposed by EEMD to obtain 16 IMF components.

[0143] Furthermore, the correlation coefficients between the above 16 IMF components and the noisy signal are calculated using formula (4) as follows: Figure 5 As shown; it can be seen that IMF1 has the highest similarity to the original signal, and the cross-correlation coefficient from IMF8 onwards is less than 0.01, which is almost negligible. Therefore, in this embodiment, the first 8 IMF components are taken as effective components and noise reduction processing is performed. (Refer to...) Figure 6The graphs are the time-domain and frequency-domain plots of the effective components IMF1 to IMF8. The noise distribution is mainly concentrated in the high-frequency IMF components, and their noise characteristics are similar, making them easily grouped into the same IMF component. Figure 6 It can be seen that different IMF component signals all contain some noise, and the first three IMF components contain more noise.

[0144] In this embodiment of the invention, WK analysis is performed on the first 8 IMF components using formula (5), and the WK value of each IMF component is determined by... Figure 7 It can be seen that among the first 8 IMF components, IMF2 has the largest WK value. According to the sensitive IMF function screening criteria, IMF2 contains the richest fault information; while IMF1 has a smaller WK value, and its WK value is relatively small. Figure 5 The component with the highest similarity coefficient to the original signal indicates that IMF1 contains a large amount of noise. Therefore, in this embodiment of the invention, IMF1 undergoes three rounds of improved singular value decomposition (ISVD) denoising, while the remaining components undergo two rounds of improved ISVD denoising. The eight denoised IMF signals are then progressively accumulated from the lowest frequency to reconstruct a new signal, which is the denoised signal. Figure 8 , Figure 9 The figures shown are the time-domain and frequency-domain plots of the denoised signal, respectively, and... Figure 3 and Figure 4 A comparison of the time-domain and frequency-domain plots of the original vibration signal shows that the noise reduction method provided in this embodiment can effectively suppress vibration signal noise while maintaining high waveform fidelity.

[0145] To better verify the denoising effect of the EEMD-ISVD-based rolling bearing vibration signal denoising method provided in this embodiment on actual signals, it was experimentally compared with four other commonly used denoising methods: wavelet (WT) denoising, traditional singular value decomposition (SVD) denoising, traditional empirical mode decomposition (EMD), and ensemble empirical mode decomposition (EEMD). The denoising results of each method are shown in Table 1 below.

[0146] Table 1 Analysis of Experimental Signal Noise Reduction Results

[0147]

[0148] As shown in Table 1, the traditional wavelet (WT) denoising method based on window functions performs poorly for non-stationary signals, failing to achieve ideal denoising results for both simulated and real signals. Other data-driven denoising algorithms (SVD, EMD, EEMD) outperform the wavelet WT denoising method in both signal-to-noise ratio (SNR) and root mean square error (RMSE). Among these, the EEMD-ISVD denoising method provided in this invention has the highest SNR (8.46) and the lowest RMSE (0.34) among all denoising algorithms. Therefore, the EEMD-ISVD-based denoising method for rolling bearing vibration signals provided in this embodiment of the invention exhibits the best denoising effect, effectively suppressing vibration signal noise while improving the extraction accuracy of useful signals.

[0149] In summary, the denoising method for rolling bearing vibration signals based on EEMD-ISVD provided in this invention combines EEMD decomposition based on noise-assisted data analysis with improved singular value decomposition denoising (ISVD) driven by a data matrix. It also incorporates correlation coefficients and peak factor to construct a sensitive IMF function screening criterion, thus completing the denoising process for rolling bearing vibration signals. Specifically, EEMD decomposition divides the signal into vibration mode components of different frequency bands, preserving the signal's time-domain characteristics. Since IMF components often exhibit signal and noise aliasing, the improved singular value decomposition denoising (ISVD) further separates the signal and noise. For rolling bearing vibration signals, whether stationary at constant speed or non-stationary at varying speeds, this invention demonstrates excellent denoising performance and high waveform restoration accuracy.

[0150] Example 2:

[0151] like Figure 10 As shown, this embodiment of the invention provides a rolling bearing vibration signal noise reduction device based on EEMD-ISVD, which can be used to implement the method described in Embodiment 1. The device includes:

[0152] The EEMD decomposition module is used to perform EEMD decomposition on the acquired raw vibration signal of the rolling bearing to obtain multiple intrinsic mode function (IMF) signals.

[0153] The IMF component filtering module is used to select effective IMF components from the multiple intrinsic mode function IMF signals according to the sensitive IMF function filtering criteria, and to determine the number of noise reduction steps for each effective IMF component.

[0154] The ISVD noise reduction module is used to perform noise reduction processing on each of the IMF components for a corresponding number of times by means of improved singular value decomposition noise reduction (ISVD).

[0155] The accumulation and reconstruction module is used to accumulate and reconstruct the noise-reduced IMF components in order of frequency from low to high to obtain the noise-reduced rolling bearing vibration signal.

[0156] The rolling bearing vibration signal noise reduction device based on EEMD-ISVD provided in this embodiment of the invention is based on the same technical concept as the rolling bearing vibration signal noise reduction method based on EEMD-ISVD provided in Embodiment 1, and can produce the beneficial effects described in Embodiment 1. For the contents not described in detail in this embodiment, please refer to Embodiment 1.

[0157] Example 3:

[0158] This invention provides an electronic device, including a processor and a storage medium;

[0159] The storage medium is used to store instructions;

[0160] The processor is configured to operate according to instructions to perform steps according to any of the methods in Embodiment 1.

[0161] Example 4:

[0162] This invention provides a computer-readable storage medium storing a computer program thereon, characterized in that, when the computer program is executed by a processor, it implements the steps of any of the methods in Embodiment 1.

[0163] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0164] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations 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, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0165] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0166] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0167] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An EEMD-ISVD-based rolling bearing vibration signal denoising method, characterized in that, The method comprises: EEMD decomposition is performed on the collected original vibration signal of the rolling bearing to obtain a plurality of intrinsic mode function (IMF) signals; effective IMF components are selected from the plurality of intrinsic mode function (IMF) signals according to a sensitive IMF function screening criterion, and the number of denoising of each effective IMF component is determined; each of the IMF components is subjected to denoising processing of a corresponding number of times by improved singular value decomposition denoising (ISVD); each of the denoised IMF components is accumulated and reconstructed in order from low to high frequency to obtain a denoised rolling bearing vibration signal; The step of performing denoising processing of a corresponding number of times on each of the IMF components by improved singular value decomposition denoising (ISVD) comprises: The data points of each of the IMF components are tiled into a one-dimensional matrix by formula (3): imf j = {a j,1 , a j,2 , …, a j,k , …, a j,N , k = 1, 2, 3, …, N} (3) where: imf j represents the jth IMF component, a j,k is the kth data point of the jth IMF component, k = 1, 2,..., N, N is the number of data points of the jth IMF component; The data points of the one-dimensional matrix are taken as the first row data of a phase space matrix, and the phase space matrix of each of the IMF components is constructed according to the rule that the next row data lags two data points behind the previous row data, and the expression is: In the formula, D j denotes the m x N-dimensional phase space matrix constructed for the jth IMF component, m is the dimension of the phase space matrix; singular value decomposition is performed on the phase space matrix, and the effective rank order of the singular value is determined, and the denoising processing of each IMF component is completed in combination with the peak factor; The step of performing singular value decomposition on the phase space matrix and determining the effective rank order of the singular value to complete the denoising processing of each IMF component comprises the following steps: The singular value decomposition of the phase space matrix D j is performed as D j = U j S j V j where U j , S j , V j are given by where: U j and V j are m x m and N x N orthogonal matrices, respectively, after singular value decomposition, u mm denotes the data in the mth row and mth column of matrix U j , v NN denotes the data in the Nth row and Nth column of matrix V j ; S j is an m x N singular value matrix, σ1, σ2, σ3, …, σ m consist of all singular values and σ1≥ σ2≥ …≥ σ m ; Based on the distribution of the singular value matrix S j , the effective rank order K of the singular value is determined by formula (6): where θ represents the error compensation coefficient, k c is a threshold value representing the effective rank order of singular values, m is the dimension of the phase space matrix, c1 is the singular value difference spectrum σ p -σ p+1 is the next singular value corresponding to the maximum peak, σ p and σ p+1 represent the pth and p+1th singular values, respectively; c2 is the mean of all singular values, c3 is the difference between the first singular value σ1 and the last singular value σ m , c4 is the mean of the singular value difference spectrum σ p -σ p+1 . The singular value matrix S is obtained by j The singular values of the middle order greater than K are set to 0 to obtain the denoised S j ′ is: On the matrix U j , S j , V j , the inverse singular value transformation is performed to obtain the denoised reconstruction matrix D j ' = U j S' j V j , that is, the expression of D' j . where d mN denotes the reconstructed matrix D' j the data in the mth column and Nth row of the matrix Based on the matrix U of each IMF component j The peak factor in the matrix will reconstruct the matrix D′ of each IMF component. j Each signal is then restored to a one-dimensional noise-reduced signal with the same dimension as the original vibration signal.

2. The EEMD-ISVD-based rolling bearing vibration signal denoising method according to claim 1, characterized in that, The step of selecting effective IMF components from the plurality of intrinsic mode function (IMF) signals according to a sensitive IMF function screening criterion and determining the number of denoising of each effective IMF component comprises: The cross-correlation coefficients between each intrinsic mode function (IMF) signal and the original vibration signal are calculated respectively; The intrinsic mode function (IMF) signals with cross-correlation coefficients greater than a preset coefficient threshold are screened out as effective IMF components; The product WK of the waveform kurtosis and the waveform skewness of each IMF component is calculated to represent the noise distribution of each IMF component; The IMF component with the most noise is determined according to the WK value and the cross-correlation coefficient of each IMF component; The number of denoising of the IMF component with the most noise is determined to be no less than two, and the number of denoising of the remaining IMF components is determined to be one or two.

3. The EEMD-ISVD-based rolling bearing vibration signal denoising method according to claim 2, characterized in that, The calculation formula of the cross-correlation coefficient between each intrinsic mode function (IMF) signal and the original vibration signal is: wherein R(x, imf j ) represents the cross-correlation coefficient of the jth intrinsic modal function IMF signal; x(k) represents the original vibration signal, imf j (k) represents the jth intrinsic modal function IMF signal; J represents the number of intrinsic modal function IMF signals, and N represents the number of data points of each intrinsic modal function IMF signal.

4. The EEMD-ISVD-based rolling bearing vibration signal denoising method according to claim 2, characterized in that, The calculation formula of the product WK of the waveform kurtosis and the waveform skewness of each IMF component is as follows: where K 1j denotes the kurtosis of the jth IMF component, σ j denotes the standard deviation of the jth IMF component; is the fourth-order central moment of the jth IMF component; K 2j denotes the waveform coefficient of the jth IMF component, where the pulse factor of the jth IMF component the peak factor of the jth IMF component WK j denotes the product of the kurtosis and the waveform coefficient of the jth IMF component.

5. The EEMD-ISVD-based rolling bearing vibration signal denoising method according to claim 2, characterized in that, The matrix U based on each IMF component j The peak factor in the matrix will reconstruct the matrix D′ of each IMF component. j The steps to recover the original vibration signal into a one-dimensional denoised signal with the same dimension as the original vibration signal include: The peak factor of each row vector in matrix U of the jth IMF component is calculated using equation (9) j The peak factor of each row vector in matrix U of the jth IMF component is calculated using equation (9) where p a denotes the peak factor of the athrow vector in matrix U j denotes the peak factor of the athrow vector in matrix U ab denotes the data in the athrow and bthcolumn of matrix U j denotes the data in the athrow and bthcolumn of matrix U The smallest peak factor is selected from the peak factors of each row vector, and the number of rows g where the smallest peak factor is located is determined. extracting the gth column vector of the reconstructed matrix D' j obtaining a one-dimensional denoised signal of the jth IMF component.

6. An EEMD-ISVD-based rolling bearing vibration signal denoising device, characterized in that, The device comprises: An EEMD decomposition module is configured to perform EEMD decomposition on the collected original vibration signal of the rolling bearing to obtain a plurality of intrinsic mode function (IMF) signals; An IMF component screening module is configured to select effective IMF components from the plurality of intrinsic mode function (IMF) signals according to a sensitive IMF function screening criterion, and determine the number of denoising of each effective IMF component; An ISVD denoising module is configured to perform denoising processing of a corresponding number of times on each of the IMF components by improved singular value decomposition denoising (ISVD). An accumulation reconstruction module is configured to accumulate and reconstruct each IMF component after noise reduction in order from low to high frequency to obtain a rolling bearing vibration signal after noise reduction. The step of performing noise reduction on each IMF component by improved singular value decomposition (ISVD) includes: The data points of each IMF component are tiled into a one-dimensional matrix by formula (3): imf j = {a j,1 , a j,2 , …, a j,k , …, a j,N , k = 1, 2, 3, …, N} (3) where: imf j represents the jth IMF component, a j,k is the kth data point of the jth IMF component, k = 1, 2,..., N, N is the number of data points of the jth IMF component; The data points of the one-dimensional matrix are taken as the first row data of the phase space matrix, and the phase space matrix of each IMF component is constructed according to the rule that the next row data lags two data points behind the previous row data, and the expression is: where D j denotes the m x N-dimensional phase space matrix constructed from the jth IMF component, m being the dimension of the phase space matrix; The singular value decomposition of the phase space matrix is performed, and the effective rank order of the singular value is determined, and the noise reduction of each IMF component is completed in combination with the peak factor; The singular value decomposition of the phase space matrix is performed, and the effective rank order of the singular value is determined, and the noise reduction of each IMF component is completed in combination with the peak factor, including the following steps: D j is singular value decomposed into D j = U j S j V j , where U j , S j , V j are given by where: U j and V j are m x m and N x N orthogonal matrices, respectively, after singular value decomposition, u mm denotes the data in the mth row and mth column of matrix U j , v NN denotes the data in the Nth row and Nth column of matrix V j ; S j is an m x N singular value matrix, σ1, σ2, σ3, …, σ m consist of all singular values and σ1≥ σ2≥ …≥ σ m ; Based on the distribution of the singular value matrix S j , the effective rank order K of the singular value is determined by formula (6): where θ represents the error compensation coefficient, k c is a threshold value representing the effective rank order of singular values, m is the dimension of the phase space matrix, c1 is the singular value difference spectrum σ p -σ p+1 is the next singular value corresponding to the maximum peak, σ p and σ p+1 represent the pth and p+1th singular values, respectively; c2 is the mean of all singular values, c3 is the difference between the first singular value σ1 and the last singular value σ m , c4 is the mean of the singular value difference spectrum σ p -σ p+1 . The singular value matrix S is obtained by j The singular values of the middle order greater than K are set to 0, and the S after noise reduction is obtained j ′ is: On the matrix U j , S j , V j , the inverse singular value transformation is performed to obtain the denoised reconstruction matrix D j ' = U j S' j V j , that is, the expression of D' j . where d mN denotes the reconstructed matrix D' j the data in the mth column and Nth row of the matrix According to the peak factor in the matrix U of each IMF component j The reconstruction matrix D' of each IMF component j is respectively recovered into a one-dimensional denoised signal with the same dimension as the original vibration signal.

7. An electronic device, comprising: It includes a processor and a storage medium. The storage medium is used to store instructions. The processor is used to operate according to the instructions to perform the steps of the EEMD-ISVD-based rolling bearing vibration signal noise reduction method according to any one of claims 1 to 5.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the EEMD-ISVD-based rolling bearing vibration signal noise reduction method according to any one of claims 1 to 5.

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