CN-121996910-A - Variation modal decomposition method and device based on orthogonal criterion and computing equipment

CN121996910ACN 121996910 ACN121996910 ACN 121996910ACN-121996910-A

Abstract

The application relates to the technical field of signal processing, and provides a variation modal decomposition method, a variation modal decomposition device and a calculation device based on an orthogonal criterion. The method comprises performing background equalization on input signal, and extracting empirical spectrum trend; the method comprises the steps of determining an initial parameter by using an empirical spectrum trend, constructing an orthogonal constraint variation model based on orthogonality of components of an input signal in a signal space, wherein the orthogonality is embodied between each mode and a residual corresponding to the modes, and iteratively updating the modes, the center frequency and the bandwidth based on the orthogonal constraint variation model until algorithm convergence conditions are met to obtain a signal decomposition result.

Inventors

HAO CHENGPENG
XUE MENG
YAN CHENG

Assignees

中国科学院声学研究所

Dates

Publication Date: 20260508
Application Date: 20251226

Claims (10)

1. A variation modal decomposition method based on an orthogonal criterion, applied to multi-component non-stationary signal processing in a complex noise environment, the method comprising: Performing background equalization on an input signal, and extracting an empirical spectrum trend, wherein the empirical spectrum trend indicates the overall fluctuation of the spectral energy of a target signal; Determining initial parameters based on the empirical spectrum trend, wherein the initial parameters comprise a decomposition mode number, initial center frequency of each mode and initial bandwidth; Constructing an orthogonal constraint variation model based on orthogonality of the input signals in a signal space, wherein the orthogonality is embodied between each mode and a residual corresponding to each mode; And iteratively updating each mode, the center frequency and the bandwidth of each mode based on the orthogonal constraint variation model to obtain a signal decomposition result.
2. The method of claim 1, wherein the orthogonal constraint variation model comprises: Wherein, the For the mode shape to be estimated, The mode center frequency to be estimated; The method is a modal bandwidth constraint parameter and is used for balancing the bandwidth of a modal and the fidelity of signal reconstruction; For inputting signals In the slave mode Orthographic projection on a specific base in the stretched signal space; Is a residual term; Is the first Residual errors corresponding to the individual modes; Is the first The modes correspond to the residual filters.
3. The method according to claim 1 or 2, further comprising solving an optimization problem of the orthogonal constraint variation model by using a Lagrange multiplier method to obtain an augmented Lagrange equation of the orthogonal constraint variation model, wherein the augmented Lagrange equation is: Wherein, the Represents the lagrangian multiplier; Representing an inner product operation.
4. The method according to claim 1 or 2, wherein the iterative updating of the modes, the center frequencies of the modes and the bandwidths based on the orthogonal constraint variation model comprises decomposing an optimization problem of the orthogonal constraint variation model into a series of sub-optimization problems by using an alternate direction multiplier method, and performing iterative solution in a frequency domain; In the first place In the iterative solution, the first The individual modes and their center frequencies are updated in the frequency domain as: Wherein, the 、、 Respectively represent 、 And Is a fourier transform of (a).
5. The method according to claim 1 or 2, wherein iteratively updating the modes, center frequencies and bandwidths of the modes based on the orthogonal constraint variation model comprises, according to a first aspect Initial Bandwidth determination of subbands Initial bandwidth constraint parameters of each mode, the bandwidth constraint parameters are updated by adopting a coarse-to-fine self-adaptive mechanism, and the method is characterized in that In the second iteration, the first The bandwidth constraint parameters corresponding to the modes are as follows: Wherein, the 、 Respectively is 、 Fourier transform of (a); the representation takes the real part of the complex number.
6. The method of claim 3, wherein iteratively updating the modes, center frequencies and bandwidths of the modes based on the orthogonal constraint variation model comprises, at a first node In the iterative updating, the Lagrangian multiplier is updated as follows: Wherein, the Is that Fourier transform of (a); And step parameters of the Lagrangian multiplier.
7. The method of claim 2,3,4 or 6, wherein the first Filter with residual errors corresponding to each mode The frequency response of (2) is: Wherein, the Is a smooth transition function, the first Effective bandwidth of individual modalities The method comprises the following steps: 。
8. the method according to any one of claims 4-6, wherein iteratively updating the modes, center frequencies and bandwidths of the modes based on the orthogonal constraint variation model comprises: calculating the sum of the corresponding variances of all modes of two adjacent iterations as an algorithm convergence evaluation index, and when the convergence evaluation index is smaller than a preset convergence parameter The condition of algorithm convergence is satisfied: Terminating the algorithm in case the algorithm convergence condition is satisfied Iterative updating of the spectrum, center frequency and bandwidth of each modality.
9. A variation modal decomposition device based on an orthogonality criterion, said device comprising: The system comprises an empirical spectrum trend extraction module, an empirical spectrum trend extraction module and a signal processing module, wherein the empirical spectrum trend extraction module is used for carrying out background equalization on an input signal and extracting an empirical spectrum trend, and the empirical spectrum trend indicates the integral fluctuation of the spectral energy of a target signal; The initial parameter setting module is used for determining initial parameters based on the empirical spectrum trend, wherein the initial parameters comprise the number of decomposition modes, the initial center frequency of each mode and the initial bandwidth; The orthogonal optimization module is used for constructing an orthogonal constraint variation model based on the orthogonality of the input signals in a signal space, wherein the orthogonality is embodied between each mode and the corresponding residual error; And the parameter updating module is used for carrying out iterative updating on each mode and the center frequency and bandwidth of each mode based on the orthogonal constraint variation model until the algorithm convergence condition is met, so as to obtain a signal decomposition result.
10. A computing device comprising at least one memory for storing a program, and at least one processor for executing the program stored in the memory, the processor for performing the method of any of claims 1-8 when the program stored in the memory is executed.

Description

Variation modal decomposition method and device based on orthogonal criterion and computing equipment Technical Field The present application relates to the field of signal processing technologies, and in particular, to a method, an apparatus, and a computing device for decomposition of a variation mode based on an orthogonal criterion. Background With the increasing demand for weak signal detection and non-stationary signal analysis in complex environments, adaptive signal decomposition (adaptive mode decomposition, AMD) methods, represented by empirical mode decomposition (EMPIRICAL MODE DECOMPOSITION, EMD), empirical wavelet transform, and variational mode decomposition (variational mode decomposition, VMD), have become important research directions. The EMD realizes signal self-adaptive decomposition from the time domain by gradually extracting the eigen mode function of the signal, has better time-frequency self-adaptability, but lacks mathematical foundation, and has the problems of mode aliasing, end-point effect, sensitivity to sampling and noise, unstable decomposition result and the like. The EWT realizes the decomposition of signals by adaptively dividing frequency bands on the frequency spectrum and constructing a filter bank, has better theoretical interpretability than EMD, but the frequency spectrum division depends on the detection of local extremum, is sensitive to noise, and the filtering boundary selection has larger influence on the decomposition precision. The VMD estimates the center frequency of the signal component and reconstructs the signal component by solving the variation constraint optimization problem established based on the narrow-band condition of the signal component, and the method is established on the basis of explicit mathematical theory such as wiener filtering, hilbert transformation, frequency mixing and the like, so as to form a brand-new self-adaptive non-recursive signal decomposition theory framework. Compared with the EMD method, the VMD is more efficient and has better anti-modal aliasing capability and noise robustness, so the VMD is widely focused on the academic world and the industrial world at home and abroad, and has been successfully applied to a plurality of fields such as mechanical fault diagnosis, biomedical signal analysis, image signal analysis, radar/sonar signal processing and the like. However, the performance of the VMD is closely related to the selection of model parameters, including the number of resolved modes, bandwidth constraint parameters, and mode initial center frequency. Therefore, how to determine the optimal variational model parameters is critical to the signal decomposition effect of the VMD and its application in various fields. Disclosure of Invention The application provides a variation mode decomposition method based on an orthogonal criterion, which is applied to multi-component non-stationary signal processing in a complex noise environment and comprises the steps of carrying out background equalization on an input signal, extracting an empirical spectrum trend, wherein the empirical spectrum trend indicates integral fluctuation of spectral energy of a target signal, the target signal comprises a mechanical vibration signal, a biomedical signal, an electromagnetic wave signal, an acoustic wave signal or an artificial signal, determining initial parameters based on the empirical spectrum trend, wherein the initial parameters comprise a decomposition mode number, initial center frequency and initial bandwidth of each mode, constructing an orthogonal constraint variation model based on orthogonality of the input signal in a signal space, wherein the orthogonality is embodied between each mode and corresponding residual error, and carrying out iterative update on the center frequency and bandwidth of each mode based on the orthogonal constraint variation model to obtain a signal decomposition result. In some possible implementations, the orthogonal constraint variation model includes: Wherein, the For the mode shape to be estimated,The mode center frequency to be estimated; The method is a modal bandwidth constraint parameter and is used for balancing the bandwidth of a modal and the fidelity of signal reconstruction; For inputting signals In the slave modeOrthographic projection on a specific base in the stretched signal space; Is a residual term; Is the first Residual errors corresponding to the individual modes; Is the first The modes correspond to the residual filters. In some possible embodiments, the method further comprises solving an optimization problem of the orthogonal constraint variation model by using a Lagrange multiplier method to obtain an augmented Lagrange equation of the orthogonal constraint variation model as follows: Wherein, the Represents the lagrangian multiplier; Representing an inner product operation. In some possible embodiments, the iterative updating of the modes, center frequencies and band