Novel time-frequency analysis method, device and equipment for uninterrupted overlapping spectrum and medium

Abstract

The invention discloses a novel time-frequency analysis method, device and equipment for an uninterrupted overlapping spectrum, and a medium, relates to the technical field of signal processing, and is used for solving the technical problems of low time-frequency resolution, weak suppression cross term interference resistance and the like in the prior art. The method comprises the steps that if it is determined that a current iteration period reaches the maximum number of iterations, a Hilbert transformation algorithm is adopted to carry out processing and linear superposition on a plurality of first intrinsic mode components IMF, and a target time-frequency graph is obtained; if it is determined that the current iteration period does not reach the maximum number of iterations, a preset VMD parameter optimization method is adopted to carry out adaptive optimization on the VMD parameters, and optimized VMD parameters are obtained; wherein the preset VMD parameter optimization method is determined based on an FA algorithm and a multi-modal feature weighting index MMFWI; the VMD parameters include a modal number and a penalty factor. Therefore, the method can effectively suppress cross term interference while maintaining high time-frequency resolution through a divide-conquer-overlap strategy and VMD parameter optimization.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of signal processing, and provides a new time-frequency analysis method, device, equipment and medium of non-interrupted overlapping spectrum. BACKGROUND

[0002] It is well known that time-frequency analysis is a core technology for processing non-stationary signals, which aims to reveal the law of frequency components of signals changing over time. Existing time-frequency analysis techniques mainly include Short-Time Fourier Transform (STFT), Wavelet Transform (WT), Wigner-Ville Distribution (WVD), etc. However, these existing techniques have the following inherent limitations: (1) For STFT, the time resolution and frequency resolution are restricted by the Heisenberg Uncertainty Principle, and the integral of the time-frequency product has an inherent upper limit. Once the window function is selected, the resolution on the entire time-frequency plane is fixed and cannot be changed, which cannot meet the needs of high time resolution for high-frequency signals and high frequency resolution for low-frequency signals.

[0003] (2) For WT, although it solves the problem of fixed resolution of STFT to some extent by adaptive windowing, the selection of its basis function has a great influence on the analysis results, and there is a problem of energy leakage, that is, the energy of high-frequency signals may leak into adjacent frequency bands, resulting in non-concentrated energy distribution of the spectrum, and problems such as amplitude variation and phase distortion.

[0004] (3) For WVD, although it has high time-frequency focusing, it will produce serious Cross-term for multi-component signals. These Cross-terms are false time-frequency energy distributions and have no physical meaning, but are mathematical products of the WVD calculation method, which will seriously interfere with the judgment of real signal components and make the time-frequency spectrum become chaotic.

[0005] Therefore, how to provide a new time-frequency analysis method that can effectively suppress Cross-term interference while maintaining high time-frequency resolution and adapt to local characteristics of signals has become a problem to be solved. SUMMARY

[0006] The present application provides a new time-frequency analysis method, device, equipment and medium of non-interrupted overlapping spectrum, which is used to solve the technical problems of low time-frequency resolution and weak anti-interference of Cross-term in the prior art.

[0007] In one aspect, a new time-frequency analysis method of non-interrupted overlapping spectrum is provided, which comprises: determining whether a current iteration cycle of a firefly algorithm (FA) reaches a maximum iteration number; if it is determined that the current iteration cycle reaches the maximum iteration number, using a Hilbert transform algorithm to process and linearly superimpose a plurality of first intrinsic modal components (IMFs) to obtain a target time-frequency graph, wherein the first intrinsic modal components (IMFs) are obtained based on a variational modal decomposition (VMD) algorithm; if it is determined that the current iteration cycle does not reach the maximum iteration number, using a preset VMD parameter optimization method to adaptively optimize VMD parameters to obtain optimized VMD parameters, wherein the preset VMD parameter optimization method is determined based on the FA algorithm and a multi-modal feature weighted index (MMFWI); and the VMD parameters include a modal number and a penalty factor; if it is determined that a next iteration cycle of the current iteration cycle reaches the maximum iteration number, using the Hilbert transform algorithm to process and linearly superimpose a plurality of second IMFs to obtain the target time-frequency graph, wherein the second IMFs are obtained based on the optimized VMD parameters.

[0008] Optionally, before using the Hilbert transform algorithm to process and linearly superimpose the plurality of first intrinsic modal components (IMFs) to obtain the target time-frequency graph, the method further includes: initializing the VMD parameters using the FA algorithm to obtain initialized VMD parameters; performing non-discontinuous signal decomposition on the original signal using an alternating direction multiplier method (ADMM), the initialized VMD parameters, and a preset constraint variational equation to obtain a plurality of to-be-judged IMFs, wherein the preset constraint variational equation is used to minimize the sum of bandwidths of all to-be-judged IMFs, and the iterative solving is used to update each to-be-judged IMF in the frequency domain and update a center frequency corresponding to each to-be-judged IMF; determining whether the plurality of to-be-judged IMFs all satisfy a preset VMD convergence condition; if it is determined that the plurality of to-be-judged IMFs all satisfy the preset VMD convergence condition, determining the plurality of to-be-judged IMFs as the plurality of first intrinsic modal components (IMFs).

[0009] Optionally, the step of using the preset VMD parameter optimization method to adaptively optimize the VMD parameters to obtain the optimized VMD parameters includes: initializing FA algorithm parameters, a search space, and a firefly population, wherein a position coordinate of a firefly is represented by the VMD parameters; The brightness of each firefly is calculated by using a preset composite objective function; wherein the preset composite objective function is obtained based on a multi-modal feature weighting index MMFWI; The brightness of all fireflies is compared and moved two by two; The position of each firefly is updated; For any firefly, it is determined whether the new position of any firefly is within a preset range; If it is determined that the new position of any firefly is not within the preset range, the position of the firefly is updated to any boundary position of the preset range; The position of the firefly with the highest brightness in the current iteration is taken as the optimal VMD parameter.

[0010] Optionally, the step of taking the position of the firefly with the highest brightness in the current iteration as the optimal VMD parameter comprises: The brightness of each firefly after position update is calculated by using the preset composite objective function again; The position of the firefly with the highest brightness in the current iteration is taken as the optimal VMD parameter.

[0011] Optionally, the preset composite objective function is represented by the following formula:

[0012] wherein K is the number of modes; is a penalty factor; are weight coefficients, satisfying ; is the average envelope entropy, is the inter-modal correlation coefficient, is the average instantaneous frequency standard deviation, is the average sparsity.

[0013] Optionally, the step of processing and linearly superimposing a plurality of first intrinsic modal components IMFs by using a Hilbert transform algorithm to obtain a target time-frequency map comprises: The plurality of first IMFs are processed by using a Hilbert transform algorithm to obtain a plurality of first Hilbert time-frequency maps; The plurality of first Hilbert time-frequency maps are linearly superimposed to obtain a target time-frequency map.

[0014] Optionally, the step of processing and linearly superimposing a plurality of first IMFs by using a Hilbert transform algorithm to obtain a plurality of first Hilbert time-frequency maps comprises: performing Hilbert transform on the any first IMF to obtain a corresponding analytic signal; obtaining, according to the analytic signal, an instantaneous amplitude, an instantaneous phase and an instantaneous frequency corresponding to the any first IMF; obtaining, according to the instantaneous amplitude, the instantaneous phase and the instantaneous frequency, a Hilbert time-frequency graph of the any first IMF.

[0015] In one aspect, a novel time-frequency analysis device of non-interrupted cross-spectrum is provided, and the device comprises: An iteration determination unit is configured to determine, for a current iteration cycle of a firefly algorithm (FA), whether the current iteration cycle reaches a maximum iteration number. A Hilbert transform unit is configured to, if it is determined that the current iteration cycle reaches the maximum iteration number, perform processing and linear superposition on a plurality of first intrinsic mode components (IMFs) respectively by using a Hilbert transform algorithm to obtain a target time-frequency graph, wherein the first IMFs are obtained based on a variational mode decomposition (VMD) algorithm. A VMD parameter optimization unit is configured to, if it is determined that the current iteration cycle does not reach the maximum iteration number, perform adaptive optimization on VMD parameters by using a preset VMD parameter optimization method to obtain optimized VMD parameters, wherein the preset VMD parameter optimization method is determined based on the FA algorithm and a multi-modal feature weighted index (MMFWI), and the VMD parameters include a mode number and a penalty factor. The Hilbert transform unit is further configured to, if it is determined that a next iteration cycle of the current iteration cycle reaches the maximum iteration number, perform processing and linear superposition on a plurality of second IMFs respectively by using the Hilbert transform algorithm to obtain the target time-frequency graph, wherein the second IMFs are obtained based on the optimized VMD parameters.

[0016] In one aspect, an electronic device is provided, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements any of the above methods when executing the computer program.

[0017] In one aspect, a storage medium is provided, which stores computer program instructions executable by a processor to implement any of the above methods.

[0018] Compared with the prior art, the present application has the following beneficial effects: In the present application, for any iteration cycle of the firefly algorithm FA, firstly, for the current iteration cycle of the firefly algorithm FA, it can be determined whether the current iteration cycle reaches the maximum iteration number; then, if it is determined that the current iteration cycle reaches the maximum iteration number, the Hilbert transform algorithm can be used to process and linearly superimpose a plurality of first intrinsic modal components IMF respectively to obtain a target time-frequency graph; wherein the first intrinsic modal component IMF is obtained based on the variational modal decomposition VMD algorithm; on the contrary, if it is determined that the current iteration cycle does not reach the maximum iteration number, a preset VMD parameter optimization method based on the FA algorithm and the multi-modal feature weighted index MMFWI can be used to adaptively optimize the VMD parameters to obtain optimized VMD parameters; wherein the preset VMD parameter optimization method is determined based on the FA algorithm and the multi-modal feature weighted index MMFWI; the VMD parameters include the modal number and the penalty factor; next, if it is determined that the next iteration cycle of the current iteration cycle reaches the maximum iteration number, the Hilbert transform algorithm can be used to process and linearly superimpose a plurality of second IMFs respectively to obtain a target time-frequency graph; wherein the second IMF is obtained based on the optimized VMD parameters.

[0019] Based on this, in the present application, since the Hilbert transform algorithm is used to process and linearly superimpose a plurality of first intrinsic modal components IMF decomposed by the VMD algorithm respectively, the present application can avoid the cross-term interference between multi-component signals from the root cause by the "divide and conquer-interlaced" strategy, so as to obtain a more pure and reliable time-frequency graph. And since the Hilbert transform is directly derived from the instantaneous phase of the analytic signal, the instantaneous frequency is obtained by taking the derivative of the instantaneous phase with respect to time, and the derivative is a local, point-to-point operation, therefore, the time resolution of the present application can theoretically reach infinitely high, which is not a bandwidth blurred peak on the frequency axis, but an accurate frequency value at a specific time, so the present application can coexist with high time resolution and high frequency resolution.

[0020] In addition, since the preset VMD parameter optimization method based on the FA algorithm and the multi-modal feature weighted index MMFWI is also used to adaptively optimize the VMD parameters, the present application can avoid the limitation of a single index through this comprehensive perspective, and thus greatly improve the accuracy of the VMD algorithm decomposition. BRIEF DESCRIPTION OF DRAWINGS

[0021] In order to more clearly illustrate the technical solutions in the embodiments or the related art, the drawings needed to be used in the embodiments or the related art description will be briefly introduced. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings based on the provided drawings without creating any creative labor.

[0022] Figure 1 This is a schematic diagram of an application scenario provided by an embodiment of this application; Figure 2 A schematic diagram illustrating a novel time-frequency analysis method for non-discontinuous overlapping spectra provided in this application embodiment; Figure 3 A schematic diagram of variational mode decomposition provided in an embodiment of this application; Figure 4 A schematic diagram of the Hilbert transform provided in an embodiment of this application; Figure 5 A schematic diagram illustrating VMD parameter optimization provided in an embodiment of this application; Figure 6 A time-domain diagram of the original signal provided in the embodiments of this application; Figure 7 A spectrum diagram of the original signal provided in the embodiments of this application; Figure 8 An IMF component map using a conventional VMD algorithm is provided as an embodiment of this application; Figure 9 An IMF component map using the FA-MMFWI-VMD algorithm of this application is provided for embodiments of this application; Figure 10 A time-frequency diagram of a conventional STFT provided in an embodiment of this application; Figure 11 A time-frequency diagram of a conventional WT provided in an embodiment of this application; Figure 12 A time-frequency diagram of conventional WVD provided in the embodiments of this application; Figure 13 A time-frequency diagram of VMD+Hilbert provided in an embodiment of this application; Figure 14 A time-frequency diagram using the FA-MMFWI-VMD+Hilbert method of this application is provided for an embodiment of this application; Figure 15 This is a schematic diagram of a novel time-frequency analysis device for non-discontinuous overlapping spectra provided in an embodiment of this application.

[0023] The diagram is labeled as follows: 10 - Novel time-frequency analysis device for non-discontinuous overlapping spectra, 101 - Processor, 102 - Memory, 103 - I / O interface, 104 - Database, 150 - Novel time-frequency analysis device for non-discontinuous overlapping spectra, 1501 - Iterative determination unit, 1502 - Hilbert transform unit, 1503 - VMD parameter optimization unit, 1504 - VMD decomposition unit. Detailed Implementation

[0024] In order to make the purposes, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work belong to the scope of protection of the present application. The embodiments in the present application and the features in the embodiments can be combined with each other arbitrarily without conflict. Moreover, although a logical order is shown in the flowchart, in some cases, the steps shown or described can be performed in an order different from that here.

[0025] It is well known that time-frequency analysis is a core technology for processing non-stationary signals, which aims to reveal the law of frequency components of signals changing over time. Existing time-frequency analysis techniques mainly include Short-Time Fourier Transform (STFT), Wavelet Transform (WT), Wigner-Ville Distribution (WVD), etc. However, these existing techniques have the following inherent limitations: (1) For STFT, the time resolution and frequency resolution are restricted by the Heisenberg Uncertainty Principle, and the integral of the time-frequency product has an inherent upper limit. Once the window function is selected, the resolution on the entire time-frequency plane is fixed and cannot be changed, which cannot meet the needs of high time resolution for high-frequency signals and high frequency resolution for low-frequency signals.

[0026] (2) For WT, although the adaptive windowing solves the problem of fixed resolution of STFT to some extent, the selection of the base function has a great influence on the analysis results, and there is a problem of energy leakage. The energy of high-frequency signals may leak into adjacent frequency bands, resulting in non-concentrated spectral energy distribution, phase distortion, etc.

[0027] (3) For WVD, although it has high time-frequency focusing, it will produce serious Cross-term for multi-component signals. These Cross-terms are false time-frequency energy distributions and have no physical meaning, but are mathematical products of the WVD calculation method, which will seriously interfere with the judgment of the real signal components and make the time-frequency spectrum become chaotic.

[0028] Based on this, the embodiment of the present application provides a new time-frequency analysis method of non-continuous overlapping spectrum, in which, for the current iteration period of the firefly algorithm FA, it can be determined whether the current iteration period reaches the maximum iteration number; then, if it is determined that the current iteration period reaches the maximum iteration number, the Hilbert transform algorithm can be used to process and linearly superimpose a plurality of first intrinsic modal components IMFs respectively to obtain a target time-frequency diagram; wherein the first intrinsic modal component IMF is obtained based on the variational modal decomposition VMD algorithm; on the contrary, if it is determined that the current iteration period does not reach the maximum iteration number, a preset VMD parameter optimization method based on the FA algorithm and the multi-modal feature weighted index MMFWI can be used to adaptively optimize the VMD parameters to obtain optimized VMD parameters; wherein the preset VMD parameter optimization method is determined based on the FA algorithm and the multi-modal feature weighted index MMFWI; the VMD parameters include the modal number and the penalty factor; next, if it is determined that the next iteration period of the current iteration period reaches the maximum iteration number, the Hilbert transform algorithm can be used to process and linearly superimpose a plurality of second IMFs respectively to obtain a target time-frequency diagram; wherein the second IMF is obtained based on the optimized VMD parameters.

[0029] Based on this, in the present application, since the Hilbert transform algorithm is used to process and linearly superimpose a plurality of first intrinsic modal components IMFs decomposed by the VMD algorithm respectively, the present application can avoid the cross-term interference between multi-component signals from the root by the "divide and conquer-overlapping" strategy, so as to obtain a more pure and reliable time-frequency diagram. And since the Hilbert transform is directly derived from the instantaneous phase of the analytic signal, the instantaneous frequency is obtained by taking the derivative of the instantaneous phase with respect to time, and the derivative is a local and point-to-point operation, therefore, the time resolution of the present application can theoretically reach infinitely high, which is not a bandwidth blurred peak on the frequency axis, but an accurate frequency value at a specific time, so the present application can coexist with high time resolution and high frequency resolution. In addition, since the preset VMD parameter optimization method based on the FA algorithm and the multi-modal feature weighted index MMFWI is also used to adaptively optimize the VMD parameters, the present application can avoid the limitation of a single index through this comprehensive perspective, and thus greatly improve the accuracy of the VMD algorithm decomposition.

[0030] After introducing the design idea of the embodiment of the present application, the application scenarios to which the technical scheme of the embodiment of the present application can be applied will be briefly introduced, and it should be noted that the following application scenarios are only used to illustrate the embodiment of the present application, but not to limit. In the specific implementation process, the technical scheme provided by the present application can be flexibly applied according to actual needs.

[0031] As Figure 1As shown, an application scenario schematic diagram provided by the embodiment of the present application. The application scenario can include a new time-frequency analysis device 10 of non-interrupted overlapping spectrum.

[0032] The new time-frequency analysis device 10 of non-interrupted overlapping spectrum can perform new time-frequency analysis based on the non-interrupted overlapping spectrum technology, for example, can be a vehicle-mounted computer, a personal computer (PC), a server, a laptop, etc. The new time-frequency analysis device 10 of non-interrupted overlapping spectrum can include one or more processors 101, a memory 102, an I / O interface 103, and a database 104. Specifically, the processor 101 can be a central processing unit (CPU), or a digital processing unit, etc. The memory 102 can be a volatile memory, such as a random-access memory (RAM); the memory 102 can also be a non-volatile memory, such as a read-only memory, a flash memory, a hard disk drive (HDD) or a solid-state drive (SSD); or the memory 102 can be any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited to. The memory 102 can be a combination of the above memories. The memory 102 can store part of the program instructions of the new time-frequency analysis method of non-interrupted overlapping spectrum provided by the embodiment of the present application, and when the processor 101 executes these program instructions, the steps of the new time-frequency analysis method of non-interrupted overlapping spectrum provided by the embodiment of the present application can be implemented to solve the technical problems of low time-frequency resolution and weak anti-suppression cross-term interference in the prior art. The database 104 can be used to store the time-domain graph of the original signal, the frequency spectrum graph of the original signal, the plurality of initial IMF graphs, the plurality of optimized IMF graphs, the plurality of initial Hilbert time-frequency graphs and the target time-frequency graph, etc. data involved in the scheme provided by the embodiment of the present application.

[0033] In the embodiment of the present application, the new time-frequency analysis device 10 of non-interrupted overlapping spectrum can obtain the time-frequency analysis instruction through the I / O interface 103, and then the processor 101 of the new time-frequency analysis device 10 of non-interrupted overlapping spectrum solves the technical problems of low time-frequency resolution and weak anti-suppression cross-term interference existing in the prior art according to the program instruction of the new time-frequency analysis method of non-interrupted overlapping spectrum provided in the memory 102. In addition, the time domain graph of the original signal, the frequency spectrum graph of the original signal, the plurality of initial IMF graphs, the plurality of optimized IMF graphs, the plurality of initial Hilbert time-frequency graphs and the target time-frequency graph and the like can be stored in the database 104.

[0034] Of course, the method provided in the embodiment of the present application is not limited to the application scenarios shown in the Figure 1 application scenarios shown in the Figure 1 application scenarios shown in the application scenarios shown in the

[0035] application scenarios shown in the Figure 2 application scenarios shown in the Figure 1 application scenarios shown in the

[0036] Step 201: using the VMD algorithm, the original signal is non-interruptedly decomposed to obtain a plurality of first intrinsic mode components IMF.

[0037] Specifically, as shown in the Figure 3 application scenarios shown in the application scenarios shown in the

[0038] application scenarios shown in the application scenarios shown in the

[0039] application scenarios shown in the application scenarios shown in the application scenarios shown in the application scenarios shown in the

[0040] application scenarios shown in the application scenarios shown in the

[0041] The preset constraint variational equation is used to minimize the sum of the bandwidths of all the intrinsic mode functions (IMFs) to be determined. The iterative solution is used to update each IMF to be determined in the frequency domain, as well as update the center frequency corresponding to each IMF to be determined.

[0042] That is, when performing uninterrupted signal decomposition, the IMF can be obtained by "constructing a constrained variational problem" and "solving the constrained variational problem". Specifically, in "constructing the constrained variational problem", it is assumed that the original signal... It is decomposed into K eigenmode components The objective of the problem is to minimize the sum of the bandwidths of all IMFs while ensuring that the sum of all IMFs accurately reconstructs the original signal. Based on this, the constrained variational problem can be expressed as follows:

[0043] in, For the k-th intrinsic mode component (IMF); The center frequency of the k-th IMF; It is an impulse response; For time-dependent partial derivative operators; It is the frequency shift factor.

[0044] Next, VMD can iteratively solve the above-mentioned "constrained variational problem" using the Alternating Directional Multiplier Method (ADMM). Each iteration includes two key steps: "updating each IMF to be decided in the frequency domain using Wiener filtering" and "updating the center frequency corresponding to each IMF to be decided".

[0045] In this application, the operation of "updating each IMF to be determined" essentially involves resizing the signal's spectrum around the currently estimated center frequency. The process involves "cropping" and "focusing" to retain only the energy within that frequency band. This update step can be represented by the following formula:

[0046] in, For frequency variables, Original signal The frequency domain form; It is the spectrum of the sum of the current estimates of all other IMFs except the current k IMFs; Divide the Fourier transform of the Lagrange multipliers by 2 to enforce the constraints. This ensures that the sum of all IMFs can accurately reconstruct the original signal, playing a role in correcting bias and accelerating convergence during the iteration process; penalty factor It is a core hyperparameter of VMD, which directly controls the bandwidth of IMF.

[0047] After updating each IMF to be judged, we can "update the center frequency corresponding to each IMF to be judged". Also in the frequency domain, the first moment of the power spectrum of the IMF to be judged is taken as its new center frequency. The first moment of the power spectrum of the kth IMF to be judged can be expressed by the following formula:

[0048] in, Let be the power spectral density of the k-th IMF to be determined, which represents the distribution of signal energy in the frequency domain.

[0049] Step 2013: Determine whether all the IMFs to be judged meet the preset VMD convergence conditions.

[0050] For example, the preset VMD convergence condition can be "the change in all IMFs to be determined is less than the set threshold" or "the change in all IMFs to be determined and the center frequency is less than the set threshold".

[0051] Step 2014: If it is determined that multiple IMFs to be determined all satisfy the preset VMD convergence conditions, then the multiple IMFs to be determined are determined as multiple first intrinsic mode component IMFs.

[0052] Step 2015: If it is determined that multiple IMFs to be determined do not uniformly meet the preset VMD convergence conditions, then update each IMF to be determined again in the frequency domain, and update the center frequency corresponding to each IMF to be determined.

[0053] That is, steps 2012-2015 need to be repeated until the preset VMD convergence condition is met, and finally K intrinsic mode components are output. and its corresponding center frequency .

[0054] Step 202: For the current iteration cycle of the Firefly Algorithm FA, determine whether the current iteration cycle has reached the maximum number of iterations.

[0055] Step 203: If it is determined that the current iteration period has reached the maximum number of iterations, the Hilbert transform algorithm is used to process and linearly superimpose multiple first intrinsic mode components (IMFs) to obtain the target time-frequency map.

[0056] The first intrinsic mode component (IMF) is obtained based on the variational mode decomposition (VMD) algorithm.

[0057] Specifically, such as Figure 4 The diagram shown is a schematic representation of the Hilbert transform provided in an embodiment of this application.

[0058] Step 2031: using Hilbert transform algorithm, the first IMF is overlapped spectrum time-frequency distribution calculation, obtain a plurality of first Hilbert time-frequency diagram.

[0059] Specifically, in the Hilbert transform algorithm, the first IMF is overlapped spectrum time-frequency distribution calculation, obtain a plurality of first Hilbert time-frequency diagram, for any first IMF, first, can be carried out on any first IMF Hilbert transform, the transformation process can be carried out using the following formula is expressed as:

[0060] Wherein, P is the Cauchy principal value; The Hilbert transform is obtained.

[0061] Based on this, we can get the following formula shown in the analytical signal :

[0062] Then, according to the analytical signal, we can get the first IMF corresponding to the instantaneous amplitude, instantaneous phase and instantaneous frequency.

[0063] Wherein, the instantaneous amplitude Can be expressed as follows:

[0064] Instantaneous phase Can be expressed as follows:

[0065] Instantaneous frequency Can be expressed as follows:

[0066] Next, according to the instantaneous amplitude, instantaneous phase and instantaneous frequency, we can get the first IMF Hilbert time-frequency diagram. Wherein, the first IMF Hilbert time-frequency diagram (time-frequency-energy three-dimensional distribution) can be expressed as follows:

[0067] Based on this, the final target time-frequency diagram Can be expressed as follows: ​

[0068] Step 2032: obtaining the target time-frequency graph by linear superposition on the plurality of first Hilbert time-frequency graphs.

[0069] Step 204: if it is determined that the current iteration period does not reach the maximum iteration number, adopting a preset VMD parameter optimization method to adaptively optimize the VMD parameters to obtain the optimized VMD parameters.

[0070] Wherein, the preset VMD parameter optimization method is determined based on the FA algorithm and a multi-modal feature weighting index (MMFWI); the VMD parameters include a mode number K and a penalty factor .

[0071] In actual application, for the mode number K, if K is too small, mode aliasing will be caused; and if K is too large, false and meaningless IMF will be generated. For the penalty factor , if is too large, IMF will be over-smoothed and details will be lost; and if is too small, IMF bandwidth will be too wide and may contain redundant information.

[0072] Therefore, in order to obtain the best VMD parameters, in the present application, the best (K, ) combination of VMD is selected based on the FA algorithm with the multi-modal feature weighting index MMFWI as the target.

[0073] As shown in FIG. 5, it is a schematic diagram of VMD parameter optimization provided by the embodiment of the present application. Figure 5

[0074] Step 2041: initializing the FA algorithm parameters, search space and firefly population.

[0075] Wherein, the position coordinates of the firefly are represented by the VMD parameters; that is, the two VMD parameters to be optimized, the mode number K and the penalty factor , can be taken as the position coordinates of a firefly. Therefore, the position of the firefly i is a two-dimensional vector .

[0076] Step 2042: calculating the brightness of each firefly by adopting a preset composite objective function.

[0077] In the present application, the preset composite objective function is obtained based on the multi-modal feature weighting index MMFWI, and the preset composite objective function can be represented by the following formula:

[0078] ​Where K is the number of modes; As a penalty factor; All are weighting coefficients, satisfying ; The average envelope entropy, The intermodal correlation coefficient is... The standard deviation of the average instantaneous frequency. The average sparsity is denoted as .

[0079] In this application, the average envelope entropy Intermodal correlation coefficient Standard deviation of mean instantaneous frequency and average sparsity Specifically, it can be obtained in the following ways: (1) Average envelope entropy : The average envelope entropy reflects the sparsity of signal features. The smaller the entropy value, the more prominent the impact characteristics of the surface IMF and the less noise it contains. For the k-th IMF component... Its Hilbert envelope can be expressed by the following formula:

[0080] The probability distribution is obtained by normalizing the envelope signal:

[0081] Calculate the envelope entropy of the k-th IMF:

[0082] Finally, calculate the average of the envelope entropies of all K IMFs:

[0083] (2) Intermodal correlation coefficient : Calculate the Pearson correlation coefficient matrix between all pairs of IMF components. Take the average of the absolute values ​​of the upper or lower triangular portions (excluding the diagonal) of the matrix as... , The smaller the value, the lower the degree of overlap between the various IMFs on the surface and the stronger their independence. This can be expressed by the following formula:

[0084] (3) Standard deviation of mean instantaneous frequency : The smaller the value, the smaller the instantaneous frequency fluctuation of each IMF, that is, the better the frequency stability of that component. This can be expressed by the following formula:

[0085] (4) Average sparsity : Since the average sparsity value (the ratio of L1 / L2 norm) is larger, the energy of the surface IMF is more concentrated in a few points, and the signal characteristics are more obvious. Therefore, in order to optimize the feature prominence, in the present application, the larger the average sparsity is, the better, and in the objective function, (1- ) is used to make it a minimization problem. It can be expressed by the following formula:

[0086] It can be seen that all the IMF components of the present application simultaneously satisfy multiple excellent characteristics, rather than simply satisfying one characteristic, and by fusing multiple characteristics into a comprehensive score, the preset composite objective function is minimized to find the optimal parameter combination (K, ). Based on this, since the FA algorithm is to maximize the brightness, and the goal of the preset composite objective function is to minimize, therefore, a mapping is also needed, that is, the brightness .

[0087] Step 2043: Perform brightness pairwise comparison and movement on all fireflies.

[0088] For any two fireflies, since the one with lower brightness will be attracted and moved to the one with higher brightness, therefore, in the present application, the brightest firefly can be determined by repeatedly performing brightness pairwise comparison and movement on all fireflies. Among them, if the brightness of firefly j is greater than firefly i, then firefly i will move to j, and the distance between them The attraction force can be expressed by the following formula:

[0089] Among them, is the maximum attraction force, is the light absorption coefficient.

[0090] Step 2044: Update the position of each firefly.

[0091] Since the firefly with lower brightness has moved to the position of the firefly with higher brightness, therefore, the position of the firefly with lower brightness needs to be updated, and the update process can be expressed by the following formula:

[0092] Among them, t represents the number of iterations; Let i be the position of the i-th firefly in the (t+1)-th iteration; Let i be the position of the i-th firefly at the t-th iteration; Let J be the position of the j-th firefly in the t-th iteration; This is the step size factor, used to control the magnitude of the random step size; This is a random perturbation term used to increase diversity and avoid premature convergence.

[0093] Step 2045: For any given firefly, determine whether the new location of the firefly is within the preset range.

[0094] Step 2046: If it is determined that the new position of any firefly is not within the preset range, then update the position of any firefly to any boundary position within the preset range.

[0095] That is, it is necessary to check whether the new position of each firefly exceeds the preset range. If it does, it is pulled back to the boundary.

[0096] Step 2047: Use the position of the firefly with the highest brightness in the current iteration as the optimal VMD parameter.

[0097] Specifically, after all fireflies have moved, the brightness of the entire population is recalculated. That is, the VMD algorithm and the preset composite objective function are used again to calculate the brightness of each firefly after its position is updated, and the brightness in the current iteration is determined. The highest fitness value for a firefly The smallest firefly is selected, and the position of the firefly with the highest brightness in the current iteration is used as the optimal VMD parameter.

[0098] Step 2048: If the new location of any firefly is determined to be within the preset range, then no action is taken on any firefly.

[0099] Step 204: If it is determined that the next iteration cycle of the current iteration cycle has reached the maximum number of iterations, the Hilbert transform algorithm is used to process and linearly superimpose multiple second IMFs to obtain the target time-frequency map.

[0100] The second IMF is obtained based on the optimized VMD parameters.

[0101] That is, if the iteration cycle of algorithm FA has not reached the maximum number of iterations, it needs to continue iterating and optimizing until the maximum number of iterations is reached, at which point the algorithm terminates. Output the globally optimal firefly position. and its corresponding optimal composite objective function value Furthermore, based on the optimal composite objective function value... This allows for the decomposition of the optimal second IMF. Based on this, the Hilbert transform algorithm is used to process and linearly superimpose multiple second IMFs to obtain the target time-frequency map.

[0102] Specific experimental example 1: like Figure 6 The image shown is a time-domain diagram of the original signal provided in an embodiment of this application. The original signal is a composite signal, comprising a linear frequency modulated signal (frequency range 5-20Hz), a sinusoidal signal (amplitude 0.5, frequency 150Hz), and Gaussian white noise (amplitude coefficient 0.1, standard normally distributed random number). Figure 7 The image shown is a spectrum diagram of the original signal provided in an embodiment of this application.

[0103] Furthermore, such as Figure 8 As shown, this is an IMF component map using the traditional VMD algorithm provided in an embodiment of this application. Figure 9 As shown, this is an IMF component map using the FA-MMFWI-VMD algorithm of this application, provided in an embodiment of this application. It can be seen that, based on... Figure 5-6 The original signal shown in the paper, when subjected to IMF decomposition using the traditional VMD algorithm and the FA-MMFWI-VMD algorithm of this application, clearly shows that the FA-MMFWI-VMD algorithm of this application has less modal aliasing than the traditional VMD algorithm, and its decomposition effect is better.

[0104] like Figure 10 As shown, this is a time-frequency diagram of a conventional STFT provided in an embodiment of this application, such as... Figure 11 As shown, this is a time-frequency diagram of a conventional WT provided in an embodiment of this application, such as... Figure 12 As shown, this is a time-frequency diagram of a conventional WVD provided in an embodiment of this application, such as... Figure 13 As shown, this is a time-frequency diagram of VMD+Hilbert provided in an embodiment of this application, as follows: Figure 14 As shown, this is a time-frequency diagram using the FA-MMFWI-VMD+Hilbert method provided in this application embodiment. It can be seen that the frequency resolution of the traditional STFT time-frequency diagram is very low, and it looks rather blurry; the 150Hz component of the traditional WT time-frequency diagram is relatively dispersed and almost invisible; the traditional WVD time-frequency diagram has relatively serious cross terms, and the time-frequency diagram looks chaotic; the frequency components of the VMD+Hilbert time-frequency diagram are relatively concentrated, and the linear frequency modulation signal only shows dispersion around 1 second; while the FA-MMFWI-VMD+Hilbert time-frequency diagram of this application has concentrated frequency components, little noise residue, and clearly shows the linear frequency modulation signal and the sine signal.

[0105] In summary, this application has the following advantages: (1) Completely eliminate cross terms: By using the "divide and conquer-overlap" strategy and the decomposition idea of ​​the FA-MMFWI-VMD algorithm, the complex multi-component signal problem is decomposed into several easy-to-solve single-component signal problems; then, after performing Hilbert transform on each single component, the results are synthesized into the final panoramic time spectrum by linear superposition (overlap). Therefore, this application can avoid cross interference between multi-component signals from the source, and the obtained time-frequency map is purer and more reliable.

[0106] (2) High time resolution and high frequency resolution coexist: Since the FA-MMFWI-VMD decomposition does not require any preset basis functions and is driven entirely by the data itself, this application fundamentally solves the problem of "basis function mismatch" and lays the foundation for high-precision analysis. Moreover, the Hilbert transform directly derives the instantaneous phase from the analytic signal, and the instantaneous frequency is obtained by differentiating the instantaneous phase with respect to time. The derivative is a local, point-to-point operation, which means that its time resolution can theoretically reach infinitely high (depending on the sampling rate of the data); it is not a bandwidth-ambiguous peak on the frequency axis, but a precise frequency value at a specific moment, so the frequency resolution is also extremely high.

[0107] (3) Multi-dimensional integration: Since the optimized FA-MMFWI-VMD decomposition algorithm is not a simple application of a single index, but a comprehensive evaluation of the decomposition quality from four key dimensions: noise robustness, modal independence, component stability and feature sparsity, this application can avoid the limitations of a single index through a comprehensive perspective.

[0108] (4) Clear physical meaning: Since each component after decomposition often corresponds to the real physical process in the signal, this application can make the time-frequency analysis results easier to interpret and understand.

[0109] Based on the same inventive concept, embodiments of this application provide a novel time-frequency analysis device 150 for non-discontinuous overlapping spectra, such as... Figure 15 As shown, the novel time-frequency analysis device 150 for non-discontinuous overlapping spectra includes: The iteration determination unit 1501 is used to determine whether the current iteration period of the Firefly Algorithm FA has reached the maximum number of iterations for the current iteration period. Hilbert transform unit 1502 is used to process and linearly superimpose multiple first intrinsic mode components (IMFs) using the Hilbert transform algorithm if it is determined that the current iteration period has reached the maximum number of iterations, thereby obtaining a target time-frequency map; wherein the first intrinsic mode components (IMFs) are obtained based on the variational mode decomposition (VMD) algorithm. The VMD parameter optimization unit 1503 is configured to, if it is determined that the current iteration period does not reach the maximum number of iterations, perform adaptive optimization on the VMD parameters by using a preset VMD parameter optimization method to obtain optimized VMD parameters, wherein the preset VMD parameter optimization method is determined based on the FA algorithm and the multi-modal feature weighted index MMFWI, and the VMD parameters include the mode number and the penalty factor. The Hilbert transform unit 1502 is further configured to, if it is determined that the next iteration period of the current iteration period reaches the maximum number of iterations, perform processing and linear superposition on the plurality of second IMFs respectively by using a Hilbert transform algorithm to obtain a target time-frequency graph, wherein the second IMF is obtained based on the optimized VMD parameters.

[0110] Optionally, the new time-frequency analysis device 150 for non-continuous overlapping spectrum further includes a VMD decomposition unit 1504, configured to: initialize the VMD parameters by using the FA algorithm to obtain initialized VMD parameters; perform non-continuous signal decomposition on the original signal by using the alternating direction multiplier method ADMM, the initialized VMD parameters, and a preset constraint variational equation to obtain a plurality of to-be-judged IMFs, wherein the preset constraint variational equation is used to minimize the sum of bandwidths of all to-be-judged IMFs, and the iterative solving is used to update each to-be-judged IMF and the center frequency corresponding to each to-be-judged IMF in the frequency domain; determine whether the plurality of to-be-judged IMFs all satisfy a preset VMD convergence condition; if it is determined that the plurality of to-be-judged IMFs all satisfy the preset VMD convergence condition, the plurality of to-be-judged IMFs are determined as the plurality of first intrinsic modal components IMFs.

[0111] Optionally, the VMD parameter optimization unit 1503 is further configured to: initialize the FA algorithm parameters, the search space, and the glowworm population, wherein the position coordinates of the glowworms are represented by using the VMD parameters; calculate the brightness of each glowworm by using a preset composite objective function, wherein the preset composite objective function is obtained based on the multi-modal feature weighted index MMFWI; perform brightness pairwise comparison and movement on all glowworms; update the position of each glowworm; for any one glowworm, determine whether the new position of the any one glowworm is within a preset range; if it is determined that the new position of the any one glowworm is not within the preset range, update the position of the any one glowworm to any boundary position of the preset range; The position of the glowworm with the highest brightness in the current iteration is taken as the optimal VMD parameter.

[0112] Optionally, the VMD parameter optimization unit 1503 is further configured to: The brightness of each glowworm after position updating is calculated again by using the preset composite objective function. The position of the glowworm with the highest brightness in the current iteration is taken as the optimal VMD parameter.

[0113] Optionally, the Hilbert transformation unit 1502 is further configured to: The first Hilbert time-frequency diagram is obtained by performing cross-spectrum time-frequency distribution calculation on the plurality of first IMFs by using a Hilbert transformation algorithm. The target time-frequency diagram is obtained by performing linear superposition on the plurality of first Hilbert time-frequency diagrams.

[0114] Optionally, the Hilbert transformation unit 1502 is further configured to: The analytic signal corresponding to the first IMF is obtained by performing Hilbert transformation on the first IMF. The instantaneous amplitude, the instantaneous phase and the instantaneous frequency corresponding to the first IMF are obtained according to the analytic signal. The Hilbert time-frequency diagram of the first IMF is obtained according to the instantaneous amplitude, the instantaneous phase and the instantaneous frequency.

[0115] The non-stop cross-spectrum new time-frequency analysis device 150 can be used to execute the method performed by the non-stop cross-spectrum new time-frequency analysis device in the embodiment shown in Figure 2-4 The functions of the functional modules of the non-stop cross-spectrum new time-frequency analysis device 150 can be referred to the description of the embodiment shown in Figure 2-4 The functions of the functional modules of the non-stop cross-spectrum new time-frequency analysis device 150 can be referred to the description of the embodiment shown in

[0116] In some possible implementation manners, each aspect of the method provided in the present application can also be implemented in the form of a program product, which includes program code for causing a computer device to execute the steps in the method according to various exemplary embodiments of the present application described above in the specification when the program product is run on the computer device, for example, the computer device can execute the method performed by the non-stop cross-spectrum new time-frequency analysis device in the embodiment shown in Figure 2-4 The method performed by the non-stop cross-spectrum new time-frequency analysis device in the embodiment shown in

[0117] Those skilled in the art can understand that all or part of the steps of the foregoing method embodiments can be completed by program instruction related hardware, and the foregoing program can be stored in a computer readable storage medium, and the program performs the steps of the foregoing method embodiments when executed; and the foregoing storage medium includes: mobile storage equipment, read-only memory (ROM), random access memory (RAM), magnetic disc or optical disc, and various media that can store program codes. Alternatively, when the integrated units of the present application are realized in the form of software function modules and sold or used as independent products, they can also be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the embodiments of the present application can be embodied in the form of software products, and the computer software products are stored in a storage medium, including a plurality of instructions for causing a computer device (which can be a personal computer, a server or a network device, etc.) to execute all or part of the methods described in the embodiments of the present application. The foregoing storage medium includes: mobile storage equipment, ROM, RAM, magnetic disc or optical disc, and various media that can store program codes.

[0118] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications to the embodiments once they know the basic inventive concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0119] Obviously, those skilled in the art can make various modifications and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application also intends to include these modifications and variations.

Claims

1. A novel time-frequency analysis method for non-discontinuous overlapping spectra, characterized in that, The method includes: For the current iteration period of the Firefly Algorithm (FA), determine whether the current iteration period has reached the maximum number of iterations; If it is determined that the current iteration period has reached the maximum number of iterations, the Hilbert transform algorithm is used to process and linearly superimpose multiple first intrinsic mode components (IMFs) to obtain the target time-frequency map; wherein, the first intrinsic mode components (IMFs) are obtained based on the variational mode decomposition (VMD) algorithm. If it is determined that the current iteration cycle has not reached the maximum number of iterations, a preset VMD parameter optimization method is used to adaptively optimize the VMD parameters to obtain the optimized VMD parameters; wherein, the preset VMD parameter optimization method is determined based on the FA algorithm and the multimodal feature weighted index MMFWI; the VMD parameters include the number of modes and the penalty factor; If it is determined that the next iteration cycle of the current iteration cycle reaches the maximum number of iterations, the Hilbert transform algorithm is used to process and linearly superimpose multiple second IMFs to obtain the target time-frequency map; wherein, the second IMF is obtained based on the optimized VMD parameters.

2. The method as described in claim 1, characterized in that, Before using the Hilbert transform algorithm to process and linearly superimpose multiple first intrinsic mode components (IMFs) to obtain the target time-frequency map, the method further includes: The FA algorithm is used to initialize the VMD parameters to obtain the initialized VMD parameters; The original signal is decomposed into multiple uninterrupted signals using the Alternating Directional Multiplier Method (ADMM), initialized VMD parameters, and a preset constraint variational equation to obtain multiple IMFs to be determined. The preset constraint variational equation is used to minimize the sum of the bandwidths of all IMFs to be determined, and the iterative solution is used to update each IMF to be determined in the frequency domain and update the center frequency corresponding to each IMF to be determined. Determine whether all of the multiple IMFs to be determined satisfy the preset VMD convergence condition; If it is determined that all of the plurality of IMFs to be determined satisfy the preset VMD convergence condition, then the plurality of IMFs to be determined are determined as the plurality of first intrinsic mode component IMFs.

3. The method as described in claim 1, characterized in that, The step of adaptively optimizing the VMD parameters using a preset VMD parameter optimization method to obtain the optimized VMD parameters includes: The FA algorithm parameters, search space, and firefly population are initialized; the firefly position coordinates are represented by VMD parameters. The brightness of each firefly is calculated using a preset composite objective function; wherein the preset composite objective function is obtained based on the multimodal feature weighted index MMFWI. Compare and move all fireflies pairwise by brightness; Update the location of each firefly; For any given firefly, determine whether its new location is within a preset range; If it is determined that the new location of any firefly is not within the preset range, then the location of the firefly is updated to any boundary location of the preset range. The position of the firefly with the highest brightness in the current iteration is taken as the optimal VMD parameter.

4. The method as described in claim 3, characterized in that, The step of using the position of the firefly with the highest brightness in the current iteration as the optimal VMD parameter includes: The preset composite objective function is used again to calculate the brightness of each firefly after the position is updated; The position of the firefly with the highest brightness in the current iteration is taken as the optimal VMD parameter.

5. The method as described in claim 3, characterized in that, The preset composite objective function is expressed by the following formula: Where K is the number of modes; As a penalty factor; All are weighting coefficients, satisfying ; The average envelope entropy, The intermodal correlation coefficient is... The standard deviation of the average instantaneous frequency. The average sparsity is denoted as .

6. The method as described in claim 1, characterized in that, The step of using the Hilbert transform algorithm to process and linearly superimpose multiple first intrinsic mode components (IMFs) to obtain the target time-frequency map includes: The Hilbert transform algorithm is used to calculate the time-frequency distribution of the overlapping spectrum of multiple first IMFs to obtain multiple first Hilbert time-frequency maps; The target time-frequency map is obtained by linearly superimposing the multiple first Hilbert time-frequency maps.

7. The method as described in claim 6, characterized in that, The step of using the Hilbert transform algorithm to calculate the overlapping spectrum time-frequency distribution of multiple first IMFs and obtain multiple first Hilbert time-frequency maps includes: For any first IMF, perform a Hilbert transform on the first IMF to obtain the corresponding analytical signal; Based on the analyzed signal, the instantaneous amplitude, instantaneous phase, and instantaneous frequency corresponding to any one of the first IMFs are obtained; Based on the instantaneous amplitude, instantaneous phase, and instantaneous frequency, the Hilbert time-frequency diagram of any one of the first IMFs is obtained.

8. A novel time-frequency analysis device for non-discontinuous overlapping spectra, characterized in that, The device includes: The iteration determination unit is used to determine whether the current iteration period of the Firefly Algorithm (FA) has reached the maximum number of iterations. The Hilbert transform unit is used to process and linearly superimpose multiple first intrinsic mode components (IMFs) using the Hilbert transform algorithm if it is determined that the current iteration period has reached the maximum number of iterations, thereby obtaining the target time-frequency map; wherein the first intrinsic mode components (IMFs) are obtained based on the variational mode decomposition (VMD) algorithm. The VMD parameter optimization unit is used to adaptively optimize the VMD parameters using a preset VMD parameter optimization method if it is determined that the current iteration cycle has not reached the maximum number of iterations, thereby obtaining the optimized VMD parameters. The preset VMD parameter optimization method is determined based on the FA algorithm and the multimodal feature weighted index MMFWI. The VMD parameters include the number of modes and a penalty factor. The Hilbert transform unit is also used to process and linearly superimpose multiple second IMFs respectively to obtain a target time-frequency map if it is determined that the next iteration period of the current iteration period reaches the maximum number of iterations; wherein the second IMF is obtained based on the optimized VMD parameters.

9. An electronic device, characterized in that, The device includes: Memory, used to store program instructions; A processor is configured to invoke program instructions stored in the memory and execute the method described in any one of claims 1-7 according to the obtained program instructions.

10. A storage medium, characterized in that, The storage medium stores computer-executable instructions for causing a computer to perform the method described in any one of claims 1-7.

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