Vibration source response signal-noise separation method and system based on multi-layer decomposition

Abstract

The present invention provides a method and system for separating the signal-noise of a vibration source response based on multi-layer decomposition, which belongs to the technical field of mechanical vibration signal processing. The mixed signal is decomposed, and the sub-components are selected and combined into a first real signal component by a common component selection method, and the remaining components are combined into a first noise signal component; the first real signal component and the first noise signal component are decomposed separately, and the second real signal component and the second noise signal component are obtained after combination; the noise with the same frequency as the impulse response in the second real signal component is removed to obtain a more complete and accurate third real signal component; the quality factor in the resonance sparse decomposition algorithm parameters is determined. The present invention purifies the impulse response containing various types of noise, has better robustness, meets the purification requirements for the collected signals under most working conditions, and has wide applicability; the improved vibration source response common component selection method is more comprehensive and accurate in determining the common components.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical vibration signal processing, and in particular to a vibration source response signal-noise separation method and system based on multi-layer decomposition. Background Art

[0002] The vibration signal analysis method based on signal processing is the main analysis method for mechanical fault diagnosis. However, the vibration signal measured by the vibration sensor installed on the mechanical system includes not only the vibration caused by the fault source, but also the vibration caused by other vibration sources and the noise in the environment. What is measured is a mixed signal. How to separate the noise signal from the mixed signal to locate and retain the vibration signal of the fault source has been a problem that has long plagued fault diagnosis researchers. The process of signal-to-noise separation is the process of removing noise from the mixed signal and leaving the real signal component of interest. In the field of mechanical equipment fault diagnosis based on signal processing, signal denoising is a very important and basic link. Only by obtaining the signal component that truly represents the fault state can various related fault diagnosis research continue to be carried out.

[0003] At present, the methods for signal-to-noise separation mainly include denoising methods in time domain, frequency domain, time-frequency domain and other domains. The time domain denoising method mainly denoises the signal from the perspective of the time domain waveform of the signal, and uses the periodicity of the rotating machinery vibration signal to remove the randomly distributed noise signal, such as the time domain averaging method. The frequency domain denoising method is mainly a spectrum analysis method that converts the vibration signal from the time domain to the frequency domain through Fourier transform. The time-frequency domain denoising method is the most commonly used signal denoising method in mechanical fault diagnosis based on signal processing, mainly including wavelet decomposition and empirical mode decomposition (EMD). Empirical mode decomposition EMD is a time-frequency analysis method proposed in 1998 that is suitable for processing nonlinear and non-stationary signals. EMD calculates the mean of the upper and lower envelopes of the signal and performs iterative operations to obtain multiple IMF components and residual components. Each IMF component is arranged from high frequency to low frequency, and the IMF component of the appropriate frequency band range is selected for reconstruction to remove noise.

[0004] The denoising methods in other domains that are widely used in fault diagnosis include singular spectrum analysis (SSA) and resonance sparse decomposition (RSSD).

[0005] Among the existing signal-to-noise separation methods, the time domain averaging method is very suitable for denoising periodic vibration signals, but the averaging method makes the vibration signal of each period lose its "individuality", and what is obtained is the modified signal component, not the real fault response component; although spectrum analysis is very effective in separating signals and noise in different frequency bands, it is completely powerless for other fault source signals and noise signals distributed in the same frequency band; although wavelet decomposition can use the multi-resolution characteristics and the threshold of wavelet coefficients to denoise the signal, the multi-resolution characteristics are related to the frequency band, and wavelet The threshold of the coefficient is related to the distribution of noise, and this information is difficult to obtain in the original mixed signal; although EMD and its derived decomposition methods can adaptively decompose the signal, they are prone to modal aliasing and false components; although SSA can convert the signal into phase space, greatly displaying the rich fault information contained in the signal, it is difficult to grasp the selection of phase space parameters and the selection of singular values ​​after decomposition; although sparse decomposition can sparsely represent a large amount of important information implicit in the signal, the constructed over-complete atomic library has a great impact on the results and the amount of calculation is much greater than other decomposition methods. Summary of the invention

[0006] The object of the present invention is to provide a method and system for separating source response signals from noise based on multi-layer decomposition, so as to solve at least one technical problem existing in the above-mentioned background technology.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] In one aspect, the present invention provides a method for separating source response signals from noise based on multi-layer decomposition, comprising:

[0009] Step 1: Decompose the mixed signal using singular spectrum analysis, and select subcomponents through the common principal component selection method and combine them into the first real signal component, and the remaining components are combined into the first noise signal component;

[0010] Step 2: Decompose the first real signal component and the first noise signal component respectively using a matching pursuit algorithm, and obtain a second real signal component and a second noise signal component after combining them;

[0011] Step 3: Use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component to obtain a more complete and accurate third real signal component; use the SOM clustering algorithm to determine the quality factor in the resonance sparse decomposition algorithm parameters.

[0012] Optionally, in step 1, the singular spectrum analysis includes matrix embedding operation, singular value decomposition and signal reconstruction: the original time series of a certain length is segmented according to the sliding window length, mapped into space, so as to construct a trajectory matrix in matrix form.

[0013] Optionally, the matching pursuit algorithm decomposes the original complex signal into several atoms, then ignores atoms with relatively small sparsity coefficients, retains atoms with large sparsity coefficients and combines them into a reconstructed signal, thereby retaining and highlighting the main features of the original signal and discarding the messy noise part.

[0014] Optionally, the matching pursuit algorithm includes: constructing an overcomplete atom library, that is, the atoms in the atom library can span the entire Hilbert space and there are linearly related atoms; representing the original signal with a linear combination of the atoms in the overcomplete atom library and a residual signal.

[0015] Optionally, inner product operations are performed on the original signal and the atoms in the overcomplete atom library one by one, and the atom with the largest inner product is the best matching atom, and the inner product is the sparse coefficient corresponding to the atom; the product of the inner product and the best matching atom is subtracted from the original signal to obtain a residual signal.

[0016] Optionally, the remaining signal is treated as the original signal and the above process is repeated until a threshold requirement is met or a specified number of iterations is reached, and the remaining signal is the residual signal.

[0017] In a second aspect, the present invention provides a source response signal-noise separation system based on multi-layer decomposition, comprising:

[0018] A first decomposition module is used to decompose the mixed signal by using singular spectrum analysis, and select subcomponents by using a common component selection method and combine them into a first real signal component, and the remaining components are combined into a first noise signal component;

[0019] A second decomposition module is used to decompose the first real signal component and the first noise signal component respectively by using a matching pursuit algorithm, and obtain a second real signal component and a second noise signal component after combining them;

[0020] The third decomposition module is used to use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component to obtain a more complete and accurate third real signal component; and use the SOM clustering algorithm to determine the quality factor in the resonance sparse decomposition algorithm parameters.

[0021] In a third aspect, the present invention provides a computer device comprising a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the vibration source response signal-noise separation method based on multi-layer decomposition as described above.

[0022] In a fourth aspect, the present invention provides an electronic device comprising a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the vibration source response signal-noise separation method based on multi-layer decomposition as described above.

[0023] In a fifth aspect, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the vibration source response signal-noise separation method based on multi-layer decomposition as described above.

[0024] The beneficial effects of the present invention are as follows: the SSA+MP+RSSD three-layer decomposition method is used to purify the impulse response containing various types of noise, the purification of the impulse response in various types of noise has better robustness, can meet the purification requirements of the collected signals under most working conditions, and has wide applicability; after the SSA decomposition, the improved vibration source response common component selection method is more comprehensive and accurate in determining the common components.

[0025] Additional aspects and advantages of the present invention will be given in part in the following description, which will become obvious from the following description, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of 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.

[0027] Figure 1 This is a flow chart of the method for separating source response signals from noise based on multi-layer decomposition according to an embodiment of the present invention.

[0028] Figure 2 It is a schematic diagram of the principle of sub-component similarity distance measurement of the improved method described in an embodiment of the present invention.

[0029] Figure 3 Schematic diagram of the selection process of similar components according to an embodiment of the present invention, wherein: Figure 3 (a) is the mutation point; Figure 3 (b) has the smallest permutation entropy.

[0030] Figure 4 Schematic diagram of time domain waveforms and frequency spectra corresponding to different quality factors according to an embodiment of the present invention.

[0031] Figure 5 It is a schematic diagram of the principle of decomposing and reconstructing a signal by using a dual-channel filter bank according to an embodiment of the present invention.

[0032] Figure 6 is a schematic diagram of a mixed signal x(t) according to an embodiment of the present invention, wherein: Figure 6 a) is a schematic diagram of the waveform before white noise is added. Figure 6 b) is a schematic diagram of a fragment in a) and its composition; Figure 6 c) is a schematic diagram of the waveform after adding white noise. Figure 6 d) is a schematic diagram of a fragment in c) and its composition.

[0033] Figure 7 Schematic diagram of the SSA decomposition result of the fourth segment after slicing the mixed signal x(t) according to an embodiment of the present invention, wherein: Figure 7 (a) SSA decomposition result of fragment 4, Figure 7 (b) is the decomposition result using the improved common component selection method.

[0034] Figure 8 This is a schematic diagram of the result of applying MP to decompose the components 1-1 and 1-2 after SSA decomposition according to an embodiment of the present invention, wherein: Figure 8 (a) is the second-level MP decomposition result, Figure 8 (b) is the RSSD decomposition result of the third layer. DETAILED DESCRIPTION

[0035] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below by the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0036] It should be understood by those skilled in the art that unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art to which this invention belongs.

[0037] It should also be understood that terms, such as those defined in commonly used dictionaries, should be understood to have a meaning consistent with that in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless as defined herein.

[0038] Those skilled in the art will appreciate that, unless otherwise stated, the singular forms "a", "an", "said" and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements and / or groups thereof.

[0039] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples, unless they are contradictory.

[0040] To facilitate understanding of the present invention, the present invention is further explained below with reference to specific embodiments in conjunction with the accompanying drawings, and the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0041] Those skilled in the art should understand that the drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily necessary for implementing the present invention.

[0042] Example 1

[0043] This embodiment 1 provides a source response signal-noise separation system based on multi-layer decomposition, including:

[0044] A first decomposition module is used to decompose the mixed signal by using singular spectrum analysis, and select subcomponents by a common component selection method and combine them into a first real signal component, and the remaining components are combined into a first noise signal component;

[0045] A second decomposition module is used to decompose the first real signal component and the first noise signal component respectively by using a matching pursuit algorithm, and obtain a second real signal component and a second noise signal component after combining them;

[0046] The third decomposition module is used to use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component to obtain a more complete and accurate third real signal component; and use the SOM clustering algorithm to determine the quality factor in the resonance sparse decomposition algorithm parameters.

[0047] In this embodiment 1, the above system is used to implement a method for separating source response signals from noise based on multi-layer decomposition, including:

[0048] Step 1: Decompose the mixed signal using singular spectrum analysis, select subcomponents through a common component selection method and combine them into a first real signal component, and combine the remaining components into a first noise signal component;

[0049] Step 2: Decompose the first real signal component and the first noise signal component respectively using a matching pursuit algorithm, and obtain a second real signal component and a second noise signal component after combining them;

[0050] Step 3: Use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component to obtain a more complete and accurate third real signal component; use the SOM clustering algorithm to determine the quality factor in the resonance sparse decomposition algorithm parameters.

[0051] In step 1, singular spectrum analysis includes matrix embedding operation, singular value decomposition and signal reconstruction: the original time series of a certain length is segmented according to the sliding window length, mapped into space, so as to construct a trajectory matrix in matrix form.

[0052] The purpose of the matching pursuit algorithm is to decompose the original complex signal into several atoms, then ignore the atoms with relatively small sparsity coefficients, retain the atoms with large sparsity coefficients to combine into a reconstructed signal, retain and highlight the main features of the original signal, and discard the messy noise part.

[0053] The matching pursuit algorithm includes: constructing an overcomplete atom library, that is, the atoms in the atom library can span the entire Hilbert space and there are linearly related atoms; representing the original signal with a linear combination of atoms in the overcomplete atom library and a residual signal.

[0054] Perform inner product operations on the original signal and the atoms in the overcomplete atom library one by one. The atom with the largest inner product is the best matching atom, and the inner product is the sparse coefficient corresponding to the atom; subtract the product of the inner product and the best matching atom from the original signal to obtain a residual signal.

[0055] The remaining signal is treated as the original signal and the above process is repeated until the threshold requirement is met or the specified number of iterations is reached. The remaining signal is then called the residual signal.

[0056] Example 2

[0057] For mixed signals containing different noises, a single decomposition method will more or less over-decompose the real signal, i.e., the impulse response, or there will be residual noise signals on the real signal sub-components. In order to solve the problem that a single decomposition method cannot completely and effectively separate the real signal, the purification performance of the mixed signal by a multi-layer decomposition method combining multiple decomposition methods is studied, that is, further removing the noise signal from the real signal component obtained by the single-layer decomposition method or further extracting the real signal from the noise signal component to obtain a more accurate real signal component. Experiments have found that the SSA+MP double-layer decomposition method has a very good purification effect when the real signal and noise do not overlap in the time and frequency domains. Therefore, in this embodiment 2, RSSD, which has a relatively ideal purification effect when the time domain and frequency domain overlap, is used to supplement it, and a three-layer signal decomposition method with wide applicability is obtained, which greatly improves the purification effect of the mixed signal. Experiments have proved that the three-layer denoising method proposed in this method can effectively improve the signal denoising effect and has wide applicability for a variety of noisy signals.

[0058] In this embodiment 2, the flowchart of the SSA+MP+RSSD three-layer decomposition method provided is as follows: Figure 1 shown.

[0059] First, SSA decomposition is applied to the mixed signal. This method proposes an improved common component selection method, which is used to select sub-components and combine them into the real signal component 1-1, and the remaining components are combined into the noise signal component 1-2. The best choice of the SSA step parameter M is the width of a single peak or its multiple, but in order to reduce the calculation amount of the improved common component selection method, 4≤M≤8 is generally selected.

[0060] Secondly, MP is used to decompose the real signal component 1-1 and the noise signal component 1-2 respectively, and then the real signal component 2-1 and the noise signal component 2-2 are obtained after combination. The parameters of MP mainly include displacement u, scale s and sparse coefficient p, where u is selected according to the position of the impulse response in the mixed signal; s is selected according to the frequency band range of the impulse response, and the frequency band range of atoms with s≥8 in the atomic library is 0~10kHz, which completely includes the frequency band of the impulse response; p is selected to remove noise with very small amplitude, and p≥10%~25% is generally selected.

[0061] Finally, RSSD is used to supplement the real signal component 2-1 to remove the noise with the same frequency as the impulse response and obtain a more complete and accurate real signal component 3-1. The SOM clustering algorithm is used to determine the most critical high and low quality factors Q1 and Q2 in the RSSD parameters.

[0062] The three-layer decomposition methods in this method will be introduced separately below.

[0063] 1. Singular Spectrum Analysis (SSA)

[0064] Singular spectrum analysis (SSA) is a nonlinear time series analysis method that can decompose the original signal into a series of meaningful components, such as slowly changing signal trend terms, vibration components, and unstructured noise.

[0065] The SSA algorithm consists of three steps: matrix embedding operation, singular value decomposition (SVD) and signal reconstruction, among which SVD is the core part of the algorithm. L ) is taken as the research object to explain the signal decomposition principle of SSA.

[0066] Matrix embedding operation. The original time series x of length L is segmented according to the sliding window length τ and mapped to the M×N space, thereby constructing a trajectory matrix A in matrix form, called the Hankel matrix, where N = L-M+1. Usually, the selection of the sliding window length τ refers to the experimental application conditions and the characteristics of the target component. In this method, τ is selected as an integer multiple of the period of the data to be analyzed.

[0067]

[0068] The trajectory matrix A is decomposed by SVD. To facilitate the understanding of SVD, the matrix A is regarded as M data sets with N-dimensional eigenvectors. The purpose of SVD can be regarded as the rank reduction of the matrix, that is, data compression. SVD finally decomposes A into the sum of orthogonal matrices with rank 1:

[0069]

[0070] To solve equation (2), first solve the covariance matrix S = A T The N eigenvalues ​​λ of A i , ∑ is the eigenvalue λ i The diagonal matrix is ​​arranged in descending order, U is the left singular vector of the trajectory matrix A, V is the right singular vector, V = [v1, ..., v N ] is the covariance matrix S = A T The eigenvector of A, an N-order orthogonal matrix, is derived from matrix-related theory to be the right singular vector corresponding to equation (2), and U is composed of u1,…u M The M-order orthogonal matrix is ​​constructed. Equations (4) and (5) are the corresponding relationships between singular values ​​and eigenvalues.

[0071] λ1≥λ2≥...λ N ≥0 (3)

[0072]

[0073]

[0074] Signal reconstruction: According to the actual requirements and the characteristics of the target signal, the signal is divided into several discontinuous subsets. According to actual needs, select several target principal component sequences p (p < d) subsets, I = {i1,..., ip}, then the matrix A' corresponding to the reconstructed signal is:

[0075]

[0076] In this Embodiment 2, when applying SSA to decompose the signal, successively select i1 to i d Reconstruct each eigencomponent, that is, decompose the matrix A into M one-dimensional vectors of length N, that is

[0077] 2. Method for selecting common components of vibration source response

[0078] After the signal decomposition method decomposes the collected mixed signal into multiple sub-components, in order to obtain more accurate and complete common components, an improved method for selecting common components of vibration source response is proposed.

[0079] Assume that the noisy mixed signal x(t) is sliced into n segments by period, that is, x 1 (t), x 2 (t),..., x n (t), the i-th (i = 1, 2,..., n) segment is decomposed into m i sub-components

[0080] (1) Combine freely the m sub-components obtained by decomposing the i-th segment, with a total of M cases. i kinds of situations.

[0081]

[0082] (2) Use DTW to measure the similarity distance between the sub-components obtained from the i-th segment and the j-th segment. Among them, for each combination case of the sub-components of the j-th segment, DTW similarity distance measurement is performed with all combination cases of the sub-components of the i-th segment, and a total of DTW i×j similarity distance values are obtained, and a distance matrix Dist(M i rows and M j columns) is constructed, as i ×M j ), as Figure 2 shown.

[0083] (3) If the original common component selection method is used to perform DTW similarity measurement on all n segments, a considerable number of distance values ​​will be obtained in total. When such a large data sample is clustered into two categories using k-means, the error will be very large. Therefore, this method selects the first segment as the basis and only uses the first segment and the other n-1 segments for DTW similarity measurement to obtain (n-1)·DTW i×j Similarity distance values, and the permutation entropy (PE) HP E Indicators determine common components.

[0084] Permutation entropy is a method to detect the stability of a system, which can give the stability performance index H of the system in a shorter time series. PE (0≤H PE ≤1), H PE The closer it is to 1, the more random and complex the system is. On the contrary, PE The closer it is to 0, the more stable and regular the system is. PE The change of reflects and amplifies the local changes of the system. The time series required by the permutation entropy algorithm is short, which is very suitable for detecting the regularity of the response of the fragmented vibration source. PE The smaller the value, the smoother and more regular the response fragment is. When the similarity distance value is not much different, H PE The smaller the component combination, the more likely it is to be a common component. The calculation process is as follows: i ((N-(dim-1)tau))

[0085] 1) Let the time series segment x i (t) has a length of N, that is, {x i (t), t = 1, 2, .., N}, and reconstruct its phase space to obtain the reconstructed phase space shown in formula (8).

[0086]

[0087] Where tau is the time delay, which is determined by the mutual information method; dim is the embedding dimension, which is determined by the pseudo nearest neighbor method.

[0088] 2) X i (k)∈R 1×dim The data is arranged from small to large, that is

[0089] X i (k) = {x i (k+(j1-1)tau)≤x i (k+(j2-1)tau)≤...≤x i (k+(j dim -1)tau)] (9)

[0090] In the formula, j1, j2, ..j dim is a symbol from 1 to dim. i (k+(j i1 -1)tau)=x i (k+(j i2 -1)tau), according to j i1 and j i2 Therefore, any X i (k) can get a set of symbol sequences:

[0091] Sym(n)={j1,j2,...,j dim} (10)

[0092] Where n = 1, 2, ..., g gg ≤ dim! , dim different symbols have dim! different permutations, and the probability P of each Sym(n) occurring is calculated. n (n=1,2,...,g),∑P n =1, then the permutation entropy H pE (dim) is:

[0093]

[0094] 3) When P n =1 / (dim!), H PE (dim) = ln(dim!) is the maximum value, that is, the symbol sequences of Sym(n) are all different, and there are dim! types in total, that is, the time series segment x i (t) is completely random and disordered, such as white noise. PE (dim) normalized to H PE ∈[0, 1], that is

[0095] H PE =H PE (dim) / ln(dim!) (12)

[0096] (4) Using permutation entropy to determine common components

[0097] 1) For the first segment x 1 (t) and the second segment x 2 The subcomponents of (t) are subjected to DTW similarity measurement to obtain a distance matrix Dist(M1×M1) with M1 rows and M2 columns.

[0098]

[0099] Where, dtw 11Represents the first fragment x 1 (t) Case 1 and the second fragment x 2 (t) Case 1 DTW distance value.

[0100] 2) Change the sequence Arrange from small to large, and we get

[0101] Find the point where the slope changes suddenly Get the first k m -1 dtw value in the second segment x 2 The corresponding sub-component combination in (t) is calculated respectively. m -1 permutation entropy H of the combination PE (K) K = 1, 2, ..., k m -1, minimum permutation entropy The corresponding combination is regarded as the first fragment x 1 (t) Case 1 Similar components in the second segment Similarly, we get the first fragment x 1 The similar components of each case of (t) in the second segment by Take the example of similar components. Figure 3 shown.

[0102] Assuming that both fragments 1 and 2 are decomposed into 6 subcomponents, the eighth combination of fragment 1 is Calculate the DTW similarity distance between it and all combinations of fragment 2 to get {dtw 81 ,dtw 82 , ..., dtw 863}, sorted in ascending order as follows Figure 3 a), the slope mutation point is k m =33, indicating

[0103] There are 32 combinations of fragment 2, all of which are very similar to the 8th combination of fragment 1. Then use the permutation entropy to determine which situation is the most regular, which is the final similar component, such as Figure 3 As shown in b), the minimum permutation entropy corresponds to K = 14, and K = 14 corresponds to the 11th combination of fragment 2, that is, similar components

[0104]

[0105] 3) Repeat steps 1) and 2) to calculate the similarity components between the first segment and the remaining n-2 segments, and obtain the matrix:

[0106]

[0107] The corresponding DTW distance matrix is:

[0108]

[0109] Find the average value of each row of the DIST matrix Arrange them from smallest to largest

[0110] Find the point where the slope changes suddenly Get the front g k -1 The corresponding sub-component combination of the value in the first fragment is calculated separately

[0111] g k -1 permutation entropy H of the combination PE (G) G = 1, 2, ..., g k -1, minimum permutation entropy

[0112] The corresponding combination g min (1≤g min ≤M1) and its similar components in other n-1 fragments as a common component.

[0113] 3. Matching Pursuit (MP)

[0114] The MP algorithm is mainly divided into two parts. The first part is to build an overcomplete atom library, that is, the atoms in the atom library.

[0115] The second part is to use the original signal to

[0116] It is represented by a linear combination of atoms in the complete atom library and a residual signal.

[0117] The main process of MP algorithm implementation is as follows:

[0118] (1) Construct an overcomplete atom library G. The more the constructed atoms g∈G conform to the characteristics of the original signal x(t), the more the MP algorithm can use a small number of atoms to sparsely represent the main characteristics of x(t). Common overcomplete atom libraries include wavelet-based atom libraries, Gabor atom libraries, Chirplet atom libraries, etc. The atoms in the atom library are usually normalized, that is, the energy of each atom is made unit energy.

[0119] (2) Sparse representation of the original signal x(t).

[0120] 1) Perform inner product operations on the original signal x(t) and the atoms in the overcomplete atom library G one by one. The atom with the largest inner product is the best matching atom, and the inner product is the sparse coefficient corresponding to the atom.

[0121] λ1=<x(t),g1> (16)

[0122] 2) Subtract the product of the inner product and the best matching atom from the original signal x(t) to obtain a residual signal x 1 (t).

[0123] x 1 (t) = x(t) - λ1·g1 (17)

[0124] 3) The remaining signal x 1 (t) is treated as the original signal and steps 1 and 2 are repeated k times until the threshold ε is met or the specified number of iterations n is reached. The remaining signal is the residual signal r(t)

[0125] r(t)=x k (t) = x k-1 (t)-λ k ·g k , st∑r 2 ≤ε or k=n (18)

[0126] 4) The original signal x(t) is sparsely represented as the sum of the linear combination of atoms and the residual signal.

[0127] x(t)=∑ n λ i ·g i +r(t) (19)

[0128] The purpose of the MP algorithm is to decompose the original complex signal into several atoms, then ignore the atoms with relatively small sparse coefficients, retain the atoms with larger sparse coefficients and combine them into reconstructed signals, retaining and highlighting the main features of the original signal and discarding the messy noise part.

[0129] 4. Resonance Sparse Decomposition (RSSD)

[0130] Resonance sparse decomposition is a signal decomposition method based on resonance properties (Resonance), which is insensitive to frequency. Its decomposition process is mainly divided into two parts: Tunable-Q Wavelet Transform (TQWT) and Morphological Component Analysis (MCA).

[0131] (1) Resonance properties

[0132] The resonance property of a vibration signal expresses the oscillation characteristics of the signal, which has little to do with the frequency. It is generally quantified by the quality factor (Q). The calculation formula of the quality factor is as shown in formula (20), where f c and B W Represent the center frequency and bandwidth of the signal respectively. The bandwidth in this article refers to the frequency range defined when the amplitude drops from the highest point to 1 / 2. h and f l Respectively represent the upper and lower frequency limits of the bandwidth, such as Figure 4 The larger the quality factor, the more oscillations the vibration signal has, and vice versa.

[0133] Q=f c / B w =(f h +f l ) / 2(f h -f l ) (20)

[0134] Depend on Figure 4 It can be seen that although the center frequencies of (a) and (b) are the same, their quality factors are different because their oscillation times in the time domain are different; although the center frequencies of (a) and (c) are different, their quality factors are the same because their oscillation times in the time domain are similar.

[0135] (2) Tunable Quality Factor Wavelet Transform (TQWT)

[0136] The signal is decomposed and reconstructed using a dual-channel filter bank. The principle is as follows: Figure 5 shown.

[0137] Figure 5 H0(w) and H1(w) are low-pass and high-pass filters respectively, x(n) is the original signal, y(n) is the reconstructed signal, V0(n) is the low-pass component, and V1(n) is the high-pass component. α and β are related to the quality factor Q and the redundancy r.

[0138] β=2 / (Q+1) (21)

[0139] α=1-β / r (22)

[0140] Where β and α must satisfy α>0, β≤1, α+β>1. At the same time, the number of wavelet decomposition layers L is related to the center frequency and sub-bandwidth of the wavelet basis function, that is, the frequency resolution of the wavelet decomposition. Therefore, L should satisfy equation (23), where N is the length of the signal x(n).

[0141]

[0142] (3) Morphological component analysis (MCA)

[0143] Assume that the original signal x(n) is composed of the linear superposition of x1(n) with high quality factor Q1 and x2(n) with low quality factor Q2, that is,

[0144] x(n)=x1(n)+x2(n) (24)

[0145] Among them, x1(n) and x2(n) can be sparsely represented by basis function libraries S1 and S2 respectively. S1 and S2 are constructed through TQWT and are composed of 1+L1 and 1+L2 wavelet basis functions respectively. L1 and L2 are the wavelet decomposition layers of high and low resonance components respectively.

[0146] To use MCA to separate the signals x1(n) and x2(n) with different quality factors from the original signal x(n), it is necessary to find a set of the sparsest W1 and W2 so that the objective function J(W1, W2) can reach the minimum value.

[0147]

[0148] Among them, W1 and W2 represent the wavelet coefficients of the signal under the basis function library S1 and S2, respectively, λ1 and λ2 are the weight coefficient matrices of the high and low resonance components, || ||2 and || ||1 represent the 2-norm and 1-norm of the vector, respectively. It is difficult to solve equation (25) directly, so the split augmented Lagrangian shrinkage algorithm is used for iterative optimization calculation. When the objective function reaches the minimum value, the corresponding high and low quality factor wavelet transform coefficients are and The approximate values ​​of the high and low resonance components are and

[0149] 5. Verification of simulation results

[0150] In order to illustrate the wide applicability of the SSA+MP+RSSD three-layer decomposition method, the bearing impact response signal s(t) and the local same-frequency noise n are simulated. impulse , local high-frequency noise n h , low frequency noise n l , Gaussian white noise n w The mixed signal x(t) is

[0151] x(t)=s(t)+n immulse +n h +n l +n w (26)

[0152]

[0153] Where s(t) is the combination of multiple response fragments generated by the same fault, which is simulated by formula (3-24). m is the amplitude of the mth fault response, β is the attenuation frequency, ω r is the resonant frequency, u(t) is the unit step function, T p is the response time interval.

[0154] First, the step size of SSA is set to obtain subcomponents, and the improved common component selection method is used to freely select components for combination to obtain subcomponent 1-1 representing the real signal component, such as Figure 7 shown.

[0155] Figure 7 This is the SSA decomposition result of the 4th segment after the mixed signal x(t) is sliced. Using the improved method, components 1, 2, and 6 are combined into a component 1-1 as the common component. It can be seen that most of the high-frequency noise n h , low frequency noise n l and white noise n w has been removed, and the remaining is mainly the same frequency noise n impulse , and coincides with the impulse response in the time domain.

[0156] Next, set the parameters of MP to u, s, and p. Apply MP to decompose the components 1-1 and 1-2 after SSA decomposition, and obtain Figure 8 a) shows the decomposition result. Figure 8 a) It can be seen that the MP of the second layer has removed the noise in component 1-1 that does not overlap with the impulse response in the time domain, but the noise that overlaps in the time domain cannot be removed.

[0157] Finally, RSSD is applied to decompose component 2-1 and parameter Q1 is set.

[0158] Q2, r1, r2, J1, J2. The decomposition results are as follows Figure 8 As shown in b), it can be seen from the figure that component 3-1 has removed most of the same-frequency noise that overlaps in the time domain. In order to better evaluate the purification effect, the signal-to-noise ratio of each layer of decomposition results is calculated, as shown in Table 1.

[0159] It can be seen from the signal-to-noise ratio in Table 1 that the purification effect of the SSA+MP+RSSD three-layer decomposition method is significantly improved with the increase of the number of decomposition layers.

[0160] Table 1 Signal-to-noise ratio of SSA+MP+RSSD three-layer decomposition

[0161]

[0162] From the purification effect of the SSA+MP+RSSD three-layer decomposition method on the complex mixed signal x(t), it can be seen that SSA+MP+RSSD has better adaptability to the purification of impulse response in various types of noise, and can meet the purification requirements of the collected signals under most working conditions.

[0163] Example 3

[0164] Embodiment 3 of the present invention provides an electronic device, including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute a method for separating source response signals from noise based on multi-layer decomposition, the method comprising the following process steps:

[0165] Step 1: Decompose the mixed signal using singular spectrum analysis, and select subcomponents through a common component selection method and combine them into a first real signal component, and the remaining components are combined into a first noise signal component;

[0166] Step 2: Decompose the first real signal component and the first noise signal component respectively using a matching pursuit algorithm, and obtain a second real signal component and a second noise signal component after combining them;

[0167] Step 3: Use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component to obtain a more complete and accurate third real signal component; use the SOM clustering algorithm to determine the quality factor in the resonance sparse decomposition algorithm parameters.

[0168] Example 4

[0169] Embodiment 4 of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, a method for separating source response signals from noise based on multi-layer decomposition is implemented. The method includes the following steps:

[0170] Step 1: Decompose the mixed signal using singular spectrum analysis, and select subcomponents through a common component selection method and combine them into a first real signal component, and the remaining components are combined into a first noise signal component;

[0171] Step 2: Decompose the first real signal component and the first noise signal component respectively using a matching pursuit algorithm, and obtain a second real signal component and a second noise signal component after combining them;

[0172] Step 3: Use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component to obtain a more complete and accurate third real signal component; use the SOM clustering algorithm to determine the quality factor in the resonance sparse decomposition algorithm parameters.

[0173] Example 5

[0174] Embodiment 5 of the present invention provides a computer device, including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute a method for separating source response signals from noise based on multi-layer decomposition, the method comprising the following steps:

[0175] Step 1: Decompose the mixed signal using singular spectrum analysis, and select subcomponents through a common component selection method and combine them into a first real signal component, and the remaining components are combined into a first noise signal component;

[0176] Step 2: Decompose the first real signal component and the first noise signal component respectively using a matching pursuit algorithm, and obtain a second real signal component and a second noise signal component after combining them;

[0177] Step 3: Use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component to obtain a more complete and accurate third real signal component; use the SOM clustering algorithm to determine the quality factor in the resonance sparse decomposition algorithm parameters.

[0178] In summary, the vibration source response signal-noise separation method and system based on multi-layer decomposition described in the embodiment of the present invention adopts the SSA+MP+RSSD three-layer decomposition method to purify the impulse response containing various types of noise, and proposes a three-layer decomposition method of SSA+MP+RSSD with wide applicability. In order to solve the problem that there is still co-frequency noise after SSA+MP purification, the three-layer decomposition method of SSA+MP+RSSD is proposed by utilizing the good purification performance of RSSD in the case of overlapping frequency bands of real signals and noise signals. This method has better robustness for the purification of impulse responses in various types of noise, can meet the purification requirements of collected signals under most working conditions, and has wide applicability. The improved vibration source response common component selection method is more comprehensive and accurate in determining the common components.

[0179] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0180] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0181] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0182] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0183] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative labor on the basis of the technical solution disclosed in the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for separating source response signal from noise based on multi-layer decomposition, characterized in that: include: Step 1: Decompose the mixed signal by singular spectrum analysis, select subcomponents by common component selection method and combine them into a first real signal component, and combine the remaining components into a first noise signal component; the singular spectrum analysis includes data segmentation of the original time series x with a length of L according to the sliding window length τ, and mapping it to a space of M=N, thereby constructing a trajectory matrix A in matrix form, where N=L-M+1; perform singular value decomposition on the trajectory matrix A, and regard the trajectory matrix A as M data sets with N-dimensional eigenvectors. The purpose of singular value decomposition is to reduce the rank of the trajectory matrix, decompose A into the sum of orthogonal matrices with a rank of l, and obtain the corresponding relationship between singular values ​​and eigenvalues; According to actual needs and target signal characteristics, the signal is divided into several discontinuous subsets; Assume that the noisy mixed signal x(t) is divided into n segments according to periodic slicing, and the i-th segment is decomposed into m segments by signal decomposition method. i subcomponents; freely combine the m subcomponents obtained by decomposing the i-th fragment, a total of M i The similarity distance of the subcomponents obtained from the i-th segment and the j-th segment is measured by DTW, where each subcomponent combination of the j-th segment is measured by DTW similarity distance with all subcomponent combinations of the i-th segment, and the DTW similarity distance is obtained. i×j Similarity distance values, construct an M i Line M j The distance matrix Dist(M i ×M j ); select the first segment as the basis, and only use the first segment and the other n-1 segments to do DTW similarity measurement, and obtain (n-1)·DTW i×j Similarity distance values, and introduce permutation entropy H PE Indicators judge common components; Step 2: Use the matching pursuit algorithm to decompose the first real signal component and the first noise signal component respectively, and obtain the second real signal component and the second noise signal component after combination; the purpose of the matching pursuit algorithm is to decompose the original complex signal into several atoms, and then ignore the atoms with relatively small sparse coefficients, retain the atoms with large sparse coefficients to combine into a reconstructed signal, retain and highlight the main features of the original signal, and discard the messy noise part, including: constructing an over-complete atom library, that is, the atoms in the atom library can span the entire Hilbert space, and there are linearly related atoms; the original signal is represented by a linear combination of atoms in the over-complete atom library and a residual signal; Step 3: Use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component to obtain a more complete and accurate third real signal component; use the SOM clustering algorithm to determine the quality factor in the resonance sparse decomposition algorithm parameters; the resonance sparse decomposition algorithm includes: adjustable quality factor wavelet transform and morphological component analysis, use a dual-channel filter group to decompose and reconstruct the signal, and determine the approximate values ​​of high and low resonance components through morphological component analysis.

2. The method for separating source response signal from noise based on multi-layer decomposition according to claim 1, characterized in that: In step 1, singular spectrum analysis includes matrix embedding operation, singular value decomposition and signal reconstruction: the original time series of a certain length is segmented according to the sliding window length, mapped into space, so as to construct a trajectory matrix in matrix form.

3. The method for separating source response signal from noise based on multi-layer decomposition according to claim 1, characterized in that: The matching pursuit algorithm decomposes the original complex signal into several atoms, then ignores the atoms with relatively small sparsity coefficients, retains the atoms with larger sparsity coefficients and combines them into a reconstructed signal, retaining and highlighting the main features of the original signal and discarding the messy noise part.

4. The method for separating source response signal from noise based on multi-layer decomposition according to claim 3 is characterized in that: The matching pursuit algorithm includes: constructing an overcomplete atom library, that is, the atoms in the atom library can span the entire Hilbert space and there are linearly related atoms; representing the original signal with a linear combination of atoms in the overcomplete atom library and a residual signal.

5. The method for separating source response signal from noise based on multi-layer decomposition according to claim 4 is characterized in that: Perform inner product operations on the original signal and the atoms in the overcomplete atom library one by one. The atom with the largest inner product is the best matching atom, and the inner product is the sparse coefficient corresponding to the atom; subtract the product of the inner product and the best matching atom from the original signal to obtain a residual signal.

6. The method for separating source response signal from noise based on multi-layer decomposition according to claim 5, characterized in that: The remaining signal is treated as the original signal and the above process is repeated until the threshold requirement is met or the specified number of iterations is reached. The remaining signal is then called the residual signal.

7. A source response signal-noise separation system based on multi-layer decomposition, characterized in that: include: The first decomposition module is used to selectively decompose the mixed signal by singular spectrum analysis, and combine the sub-components into a first real signal component by a common component selection method, and combine the remaining components into a first noise signal component; the singular spectrum analysis includes data segmentation of the original time series x with a length of L according to the sliding window length τ, and mapping it to an M×N space, so as to construct a trajectory matrix A in matrix form, where N=L-M+1; singular value decomposition is performed using the trajectory matrix A, and the trajectory matrix A is regarded as M data sets with N-dimensional eigenvectors. The purpose of the singular value decomposition is to reduce the rank of the trajectory matrix, decompose A into the sum of orthogonal matrices with a rank of l, and obtain the corresponding relationship between singular values ​​and eigenvalues; According to actual needs and target signal characteristics, the signal is divided into several discontinuous subsets; Assume that the noisy mixed signal x(t) is divided into n segments according to periodic slicing, and the i-th segment is decomposed into m segments by signal decomposition method. i subcomponents; freely combine the m subcomponents obtained by decomposing the i-th fragment, a total of M i The similarity distance of the subcomponents obtained from the i-th segment and the j-th segment is measured by DTW, where each subcomponent combination of the j-th segment is measured by DTW similarity distance with all subcomponent combinations of the i-th segment, and the DTW similarity distance is obtained. i×j Similarity distance values, construct an M i Line M j The distance matrix Dist(M i ×M j ); select the first segment as the basis, and only use the first segment and the other n-1 segments to do DTW similarity measurement, and obtain (n-1)·DTW i×j Similarity distance values, and introduce permutation entropy H PE Common components of indicator judgment The second decomposition module is used to decompose the first real signal component and the first noise signal component respectively by using the matching pursuit algorithm, and obtain the second real signal component and the second noise signal component after combination; the matching pursuit algorithm aims to decompose the original complex signal into a plurality of atoms, and then ignore the atoms with relatively small sparse coefficients, retain the atoms with large sparse coefficients and combine them into a reconstructed signal, retain and highlight the main features of the original signal, and discard the messy noise part, including: constructing an overcomplete atom library, that is, the atoms in the atom library can span the entire Hilbert space, and there are linearly related atoms; the original signal is represented by a linear combination of the atoms in the overcomplete atom library and a residual signal; The third decomposition module is used to use the resonance sparse decomposition algorithm to remove the noise with the same frequency as the impulse response in the second real signal component, so as to obtain a more complete and accurate third real signal component; the SOM clustering algorithm is used to determine the quality factor in the resonance sparse decomposition algorithm parameters; the resonance sparse decomposition algorithm includes: adjustable quality factor wavelet transform and morphological component analysis, using a dual-channel filter group to decompose and reconstruct the signal, and determining the approximate values ​​of high and low resonance components through morphological component analysis.

8. A computer device, comprising a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the source response signal-noise separation method based on multi-layer decomposition as described in any one of claims 1-6.

9. An electronic device, characterized in that: It includes a memory and a processor, the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the source response signal-noise separation method based on multi-layer decomposition as described in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that: It stores a computer program, which, when executed by a processor, implements the method for separating source response signals from noise based on multi-layer decomposition as described in any one of claims 1 to 6.

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