Signal noise reduction method based on symplectic geometry difference spectrum

Abstract

The invention belongs to the technical field of equipment state monitoring and diagnosis, and particularly relates to a signal noise reduction method based on a symplectic geometry difference spectrum. The method comprises the following steps: acquiring an original vibration signal to be diagnosed; decomposing the original vibration signal by using a symplectic geometric similarity transformation method; recombining the covariance matrix, applying a fast Fourier transform (FFT) to each singular value component of the matrix; selecting the frequency value with the maximum amplitude as an index characteristic in the differential spectrum method; performing first-order lag difference processing to obtain a symplectic geometric difference spectrum, setting a threshold value, selecting a required singular value, and performing recombination to obtain a final matrix; bringing the final matrix back to the previous step to obtain a de-noised signal; according to the signal noise reduction method provided by the invention, analysis is carried out through the envelope spectrum, the state characteristics can be identified according to the envelope spectrum, the characteristic frequency and the frequency multiplication thereof can be effectively obtained, and the diagnosis effect is good.

Description

Technical Field

[0001] The invention belongs to the technical field of equipment status monitoring and diagnosis, and in particular relates to a signal noise reduction method based on symplectic geometric difference spectrum. Background Art

[0002] Time-frequency analysis is a signal analysis technology that can simultaneously reflect the frequency domain and time domain information of a signal. It is often used in signal analysis in various fields. Common time-frequency analysis methods include wavelet transform (WT), empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), singular spectrum analysis (SSA), etc. The multi-scale characteristics of WT allow different signals to choose different wavelet basis functions and scales, but WT is a Fourier transform with an adjustable window, which is difficult to effectively solve problems such as modal aliasing. When processing non-stationary signals, EMD can adaptively transform a multi-component complex signal into the sum of multiple modal functions, but it has defects such as modal aliasing, under-envelope and poor noise robustness in envelope interpolation problems. EEMD plays a certain role in suppressing the modal aliasing problem of EMD, but it cannot completely neutralize the added white noise. SSA has strong noise robustness, but it relies on prior experience to select the window function size, which cannot guarantee its decomposition effect, especially in a strong background noise environment. Although the above methods have good decomposition effects in fault diagnosis, they still have certain limitations when analyzing multi-modal coupled signals, such as difficulty in protecting signal structure information and unsatisfactory decomposition under strong noise.

[0003] In recent years, based on symplectic geometry theory, relevant scholars have proposed a variety of symplectic geometry modal analysis methods, which can achieve noise removal while protecting the structured information of the signal. However, both symplectic geometry spectral analysis (SGSA for short) and symplectic geometry mode decomposition (SGMD for short) have defects. SGSA applies it to time series analysis, but this method relies on empirical selection of the embedding dimension and does not give a termination criterion; SGMD uses the power spectral density (PSD for short) to obtain parameter information. Although it can adaptively determine the embedding dimension, the selection of the number of eigenvalues in the SGMD method is subjective. Generally, the first k (k < r) significant eigenvalues contain important attributes of the true signal, while the noise signal is contained in the remaining (r - k) eigenvalues. Selecting too high an SVD order will result in the filtered signal containing noise information, thus hindering the desired denoising effect. On the contrary, when the selected singular order is too low, it may inadvertently filter out valuable components as noise.

[0004] Aiming at the deficiencies of existing time-frequency analysis methods, the inventor hopes to provide a signal denoising method based on symplectic geometry difference spectrum. Summary of the Invention

[0005] The purpose of the present invention is to overcome the above problems existing in the traditional technology and provide a signal denoising method based on symplectic geometry difference spectrum. The method provided by the present invention can effectively select the number of eigenvalues. And, through the application of FFT and first-order lag difference processing, the symplectic geometry difference spectrum is obtained. Finally, a predetermined threshold range (determined by experience) is established for the difference. In the symplectic geometry difference spectrum, the singular values before the first difference exceeding the threshold are retained, while the remaining singular values are invalidated. After obtaining the required singular values, the matrix is solved inversely by SVD, and then the covariance matrix is replaced for denoising decomposition, and then diagnosis is performed from the envelope spectrum diagram. The method provided by the present invention can effectively extract the components containing rich fault information and has a good diagnosis effect.

[0006] To achieve the above technical objectives and reach the above technical effects, the present invention is realized through the following technical solutions:

[0007] The present invention provides a signal denoising method based on symplectic geometry difference spectrum, including the following steps:

[0008] S1. Collect the original vibration signal to be diagnosed;

[0009] S2. Decompose the original vibration signal by using the symplectic geometry similarity transformation method;

[0010] S3, reorganizing the covariance matrix and applying a fast Fourier transform (FFT) to each singular value component of the matrix;

[0011] S4, selecting the frequency value of the maximum amplitude as the indicator feature in the differential spectrum method;

[0012] S5. Obtain the symplectic geometric difference spectrum through first-order lag difference processing, set the threshold, select the required singular values, and reorganize to obtain the final matrix;

[0013] S6, bringing the final matrix back to step S2 to obtain a denoised signal;

[0014] S7, performing envelope spectrum analysis on the denoised signal;

[0015] S8. Identify state characteristics according to the envelope spectrum.

[0016] Furthermore, in step S3, the reorganized covariance matrix is ​​subjected to an FFT operation on each singular value component thereof:

[0017] After obtaining the covariance matrix A through the symplectic geometric similarity transformation in step S2, perform SVD decomposition on the matrix A to obtain a series of singular values ​​arranged in descending order:

[0018] A=U∑V T (1)

[0019] Among them, the orthogonal matrices U and V are the left and right singular matrices of the A matrix respectively, and ∑ is a singular value matrix of the following form:

[0020]

[0021] Among them, Δ=diag(λ1,λ2,…,λ r ), λ1≥λ2≥…≥λ r ≥0,λ r are the singular values ​​of matrix A, r is the rank of the matrix, and 0 is the zero matrix;.

[0022] Furthermore, in each iteration Δ, there is only one λ i are retained, while the remaining singular values ​​are set to zero.

[0023] Furthermore, the iterative process generates a singular value vector Δ' i =diag(0,…,λ i ,…,0), as well as the singular value matrix and the reorganized A matrix, are expressed in the following form:

[0024]

[0025] A′ i =UΣ' i VT (4)

[0026] Δ' i Each singular value λ in i Convert it to a matrix with singular values, and then use singular value decomposition to invert the matrix to get the transformation matrix A′ i .

[0027] Furthermore, A′ i The matrix is ​​diagonally averaged to obtain the component signal X corresponding to the original signal x. i , apply the FFT to each X i component signal.

[0028] Furthermore, in step S5, the steps of constructing the final matrix of symplectic geometric difference spectrum selection are as follows:

[0029] 1) Identify the frequency value of each component signal FFT, select the frequency value with the maximum amplitude of each component, and arrange these frequency values ​​in descending order according to the singular values ​​of the original signal;

[0030] 2) Through the application of first-order lag difference processing, the symplectic geometric difference spectrum is obtained;

[0031] 3) Establish a predetermined threshold for the difference to suit the specific situation.

[0032] Further, in the symplectic geometry difference spectrum, the singular values ​​before the first difference value exceeding the threshold are retained, while the remaining singular values ​​are invalidated.

[0033] Furthermore, after obtaining the required singular values, the matrix A is reconstructed by the inverse solution of SVD".

[0034] The beneficial effects of the present invention are:

[0035] The signal denoising technology based on symplectic geometric difference spectrum (SGDS) abandons the denoising method of SGMD and directly adopts singular value decomposition to select eigenvalues. The present invention designs an optimization method for selecting the effective order of singular value denoising, which includes reconstructing each singular value of the vibration signal into a one-dimensional signal, analyzing it in the frequency domain, and characterizing each singular value component with the frequency value with the highest amplitude as an index. The present invention maximizes the effectiveness of the denoising algorithm by selecting the singular value order corresponding to the first significantly changed frequency value as the effective order of the algorithm, realizes the effective extraction of state characteristics, can effectively obtain the characteristic frequency and its multiples, and accurately diagnose the vibration signal.

[0036] Of course, any product implementing the present invention does not necessarily need to achieve all of the above advantages at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0038] Figure 1 It is a flow chart of the signal denoising method based on symplectic geometric difference spectrum of the present invention;

[0039] Figure 2 Schematic diagram of the planetary gearbox test bench for collecting gear data;

[0040] Figure 3 It is the time domain waveform diagram of the gear fault vibration signal;

[0041] Figure 4 is the symplectic geometric difference spectrum of the vibration signal;

[0042] Figure 5 The comparative time domain waveform diagram of the results obtained by decomposing the vibration signal using two methods;

[0043] Among them, (a) is a signal denoising method based on symplectic geometry difference spectrum, and (b) is a singular value difference spectrum method;

[0044] Figure 6 Comparative envelope spectra for diagnosis of the components obtained by the two methods;

[0045] Among them, (a) is a signal denoising method based on symplectic geometry difference spectrum, and (b) is a singular value difference spectrum method. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0047] The specific embodiments of the present invention are as follows:

[0048] Embodiment 1

[0049] See also Figure 1 The signal denoising method based on symplectic geometric difference spectrum in this embodiment includes the following steps:

[0050] S1, collecting the original gear fault vibration signal to be diagnosed;

[0051] S2, using symplectic geometric similarity transformation method to decompose the original gear fault vibration signal;

[0052] S3, reorganizing the covariance matrix and applying a fast Fourier transform (FFT) to each singular value component of the matrix;

[0053] S4, selecting the frequency value of the maximum amplitude as the indicator feature in the differential spectrum method;

[0054] S5. Obtain the symplectic geometric difference spectrum through first-order lag difference processing, set the threshold, select the required singular values, and reorganize to obtain the final matrix;

[0055] S6, bringing the final matrix back to step S2 to obtain a denoised signal;

[0056] S7, performing envelope spectrum analysis on the denoised signal;

[0057] S8. Identify fault features based on the envelope spectrum.

[0058] This embodiment proposes a signal denoising method based on symplectic geometric difference spectrum, and the obtained denoised component has a good recognition effect in identifying fault feature information in the envelope spectrum.

[0059] In step S2, the specific steps of performing a signal denoising method based on symplectic geometric difference spectrum on the original gear fault vibration signal are as follows:

[0060] For the original gear signal time series x={x1,x2,…,x N}, N is the length of its time series, construct the trajectory matrix X:

[0061]

[0062] The symplectic orthogonal matrix G can be constructed from the matrix X as follows:

[0063]

[0064] Where: B is an upper triangular matrix, and W is a Hamilton matrix constructed from the covariance matrix A of the matrix X.

[0065] According to the symplectic geometry theorem, the eigenvector matrix Q can be obtained from the matrix A through singular value decomposition, so the reconstruction matrix Z i It can be expressed as:

[0066]

[0067] For the initial single-component matrix Z i (i=1,2,…,d0) defines its structure as Z m×k =(z ij ) m×k, and its diagonal average transformation formula is:

[0068]

[0069] From the above formula, we can determine p1, p2, ..., p one by one N , so we get the reconstruction matrix Z i The corresponding set of one-dimensional sequences P with length N i . Follow the above steps to restructure d0 matrices Z i By diagonal averaging, we can obtain the sequence P of d0 group with length N. i , and its sum is the original time series.

[0070] In step S3, the reorganized covariance matrix is ​​subjected to an FFT operation on each singular value component:

[0071] After obtaining the covariance matrix A through the symplectic geometric similarity transformation in step S2, the matrix A is decomposed by SVD to obtain a series of singular values ​​arranged in descending order:

[0072] A=UΣV T (1)

[0073] Among them, the orthogonal matrices U and V are the left and right singular matrices of the A matrix, respectively, and are singular value matrices of the following form:

[0074]

[0075] Among them, Δ=diag(λ1,λ2,…,λ r ), λ1≥λ2≥…≥λ r ≥0,λ r are the singular values ​​of the A matrix, r is the rank of the matrix, and 0 is the zero matrix.

[0076] In each iteration Δ, there is only one λ r is retained, while the remaining singular values ​​are set to zero. This process generates a singular value vector Δ' i =diag(0,…,λ i ,…,0), as well as the singular value matrix and the reorganized A matrix, can be expressed in the following form:

[0077]

[0078] A′ i =UΣ' i V T (4)

[0079] Δ' i Each singular value λ in iConvert it to a matrix with singular values, and then use singular value decomposition to invert the matrix to get the transformation matrix A′ i As shown in the formulas (3) and (4) provided above. Then, A i 'The matrix is ​​averaged diagonally to obtain the component signal X corresponding to the original signal x i , apply the FFT to each X i component signal.

[0080] In step S5, the steps of constructing the final matrix of symplectic geometric difference spectrum selection are as follows:

[0081] 1) Identify the frequency value of each component signal FFT, select the frequency value with the maximum amplitude of each component, and arrange these frequency values ​​in descending order according to the singular values ​​of the original signal;

[0082] 2) Through the application of first-order lag difference processing, the symplectic geometric difference spectrum is obtained;

[0083] 3) To accommodate specific situations, we establish a predetermined threshold of 15 for the differences. In the symplectic geometry difference spectrum, the singular values ​​before the first difference exceeding the threshold are retained, while the remaining singular values ​​are invalidated. After obtaining the required singular values, the matrix A is reconstructed by the inverse solution of SVD.

[0084] The reconstructed matrix A" is used to replace the matrix A in step 2 to complete the remaining calculations, and the reconstructed signal is obtained and the envelope spectrum analysis is performed on it to obtain the envelope spectrum diagram containing the fault feature information.

[0085] Embodiment 2

[0086] In order to verify the effectiveness of Example 1 in planetary gearbox gear fault diagnosis, this example uses a signal denoising method based on symplectic geometric difference spectrum to effectively denoise the signal, and analyzes it with the singular value difference spectrum method (SVDS) to illustrate the effectiveness of the method.

[0087] The experimental equipment used for the experimental verification is the planetary gearbox fault test bench of Hunan University, such as Figure 2 As shown in the figure, it contains 4 planetary gears with 36 teeth. The corresponding sun gear and inner ring gear have 28 and 100 teeth respectively, and the calculated transmission ratio is 4.571. At the same time, the acceleration sensor is used to obtain the vibration signal, the sampling frequency is set to 8192Hz, the motor speed is 1200r / min, and the fault frequency is calculated to be f r =62.5Hz. Its time domain waveform is as follows Figure 3 shown.

[0088] First, the gear crack fault vibration signal is decomposed by SGDS and SVDS to obtain the following: Figure 4The symplectic geometric difference spectrum is shown in Figure 1. The predefined threshold is set to 15. Obviously, the first singular value exceeds the preset threshold by 4, so the first 4 singular values ​​are retained and the remaining singular values ​​are set to zero. The denoising result is shown in Figure 1. Figure 5 As shown. The envelope spectrum analysis of the decomposed denoised signal is performed as follows Figure 6 As shown. Figure 6 It can be seen that compared with SVDS, SGDS has a higher fault characteristic frequency f r There is an obvious peak at the position of the gearbox, and the frequency doubling is prominent. Therefore, it can be effectively diagnosed as a planetary gearbox gear crack fault.

[0089] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to specific implementation methods. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A signal denoising method based on symplectic geometric difference spectrum, characterized in that: The steps include: S1, collecting the original vibration signal to be diagnosed; S2, decomposing the original vibration signal using the symplectic geometric similarity transformation method; S3, reorganizing the covariance matrix and applying a fast Fourier transform to each singular value component of the matrix; S4, selecting the frequency value of the maximum amplitude as the indicator feature in the differential spectrum method; S5, obtain the symplectic geometric difference spectrum through first-order lag difference processing, set the threshold, select the required singular values, and reorganize to obtain the final matrix; S6, bringing the final matrix back to step S2 to obtain a denoised signal; S7, performing envelope spectrum analysis on the denoised signal; S8. Identify state characteristics according to the envelope spectrum.

2. The signal denoising method based on symplectic geometric difference spectrum according to claim 1, characterized in that: In step S3, the reorganized covariance matrix is ​​subjected to an FFT operation on each singular value component: After obtaining the covariance matrix A through the symplectic geometric similarity transformation in step S2, perform SVD decomposition on the matrix A to obtain a series of singular values ​​arranged in descending order: A=U∑V T (1) Among them, the orthogonal matrices U and V are the left and right singular matrices of the A matrix respectively, and ∑ is a singular value matrix of the following form: Among them, Δ=diag(λ1,λ2,…,λ r ), λ1≥λ2≥…≥λ r ≥0,λ r are the singular values ​​of matrix A, r is the rank of the matrix, and 0 is the zero matrix;.

3. The signal denoising method based on symplectic geometric difference spectrum according to claim 2, characterized in that: In each iteration Δ, there is only one λ i are retained, while the remaining singular values ​​are set to zero.

4. The signal denoising method based on symplectic geometric difference spectrum according to claim 3, characterized in that: The iterative process generates the singular value vector Δ' i =diag(0,…,λ i ,…,0), as well as the singular value matrix and the reorganized A matrix, are expressed in the following form: A' i =U∑' i In T (4) Δ' i Each singular value λ in i Convert it to a matrix with singular values, and then use singular value decomposition to invert the matrix to get the transformation matrix A' i .

5. The signal denoising method based on symplectic geometric difference spectrum according to claim 4, characterized in that: A' i The matrix is ​​diagonally averaged to obtain the component signal X corresponding to the original signal x. i , apply the FFT to each X i component signal.

6. The signal denoising method based on symplectic geometric difference spectrum according to claim 5, characterized in that: In step S5, the steps of constructing the final matrix of symplectic geometric difference spectrum selection are as follows: 1) Identify the frequency value of each component signal FFT, select the frequency value with the maximum amplitude of each component, and arrange these frequency values ​​in descending order according to the singular values ​​of the original signal; 2) Through the application of first-order lag difference processing, the symplectic geometric difference spectrum is obtained; 3) Establish a predetermined threshold for the difference to suit the specific situation.

7. The signal denoising method based on symplectic geometric difference spectrum according to claim 6, characterized in that: In the symplectic geometry difference spectrum, the singular values ​​before the first difference exceeding the threshold are retained, while the remaining singular values ​​are invalidated.

8. The signal denoising method based on symplectic geometric difference spectrum according to claim 7, characterized in that: After obtaining the required singular values, the matrix A is reconstructed by the inverse solution of SVD".

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