A new time-frequency analysis method, device, equipment and medium of non-continuous overlapping spectrum

Abstract

The application discloses a new time-frequency analysis method and device of non-continuous overlapping spectrum, equipment and medium, relates to the technical field of signal processing, and is used for solving the technical problems of low time-frequency resolution and weak anti-suppression cross-term interference existing in the prior art. The method comprises the following steps: if it is determined that the current iteration period reaches the maximum iteration number, a Hilbert transform algorithm is used to process and linearly superimpose a plurality of first intrinsic mode function (IMF) components respectively, and a target time-frequency diagram is obtained; if it is determined that the current iteration period does not reach the maximum iteration number, a preset VMD parameter optimization method is used to adaptively optimize VMD parameters, and the optimized VMD parameters are obtained; wherein the preset VMD parameter optimization method is determined based on a FA algorithm and a multi-modal feature weighted index (MMFWI); and the VMD parameters comprise a mode number and a penalty factor. Therefore, the application can effectively suppress the cross-term interference while maintaining high time-frequency resolution through the "divide and conquer-overlapping" strategy and VMD parameter optimization.

Description

Technical Field

[0001] This application relates to the field of signal processing technology, and provides a novel time-frequency analysis method, apparatus, device and medium for non-discontinuous overlapping spectrum. Background Technology

[0002] As is well known, time-frequency analysis is a core technology for processing non-stationary signals, aiming to reveal the patterns of frequency component changes over time. Existing time-frequency analysis techniques mainly include Short-Time Fourier Transform (STFT), Wavelet Transform (WT), and Wigner-Ville Distribution (WVD), etc. However, these existing techniques have the following inherent limitations: (1) For the Short Time Fourier Transform (STFT), its time resolution and frequency resolution are constrained 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 across the entire time-frequency plane is fixed and cannot simultaneously meet the requirements of high time resolution for high-frequency signals and high frequency resolution for low-frequency signals.

[0003] (2) For wavelet transform WT, although it solves the fixed resolution problem of STFT to a certain extent through adaptive variable window, the choice of its basis function has a great impact on the analysis results and there is an energy leakage problem. The energy of high frequency signals may leak to adjacent frequency bands, resulting in a non-concentrated distribution of spectral energy and problems such as amplitude distortion and phase distortion.

[0004] (3) Regarding the Wigner quasi-probability distribution (WVD), although it has a high time-frequency focusing property, it will produce serious cross-terms for multi-component signals. These cross-terms are false time-frequency energy distributions, have no physical meaning, and are purely mathematical products of the WVD calculation method. They will seriously interfere with the interpretation of the real signal components, making the time-frequency spectrum diagram chaotic.

[0005] Therefore, how to provide a novel time-frequency analysis method that can effectively suppress cross-term interference while maintaining high time-frequency resolution and adapt to local signal characteristics has become an urgent problem to be solved. Summary of the Invention

[0006] This application provides a novel time-frequency analysis method, apparatus, device, and medium for non-discontinuous overlapping spectra, which addresses the technical problems of low time-frequency resolution and weak resistance to suppression of cross-term interference in existing technologies.

[0007] On the one hand, a novel time-frequency analysis method for non-discontinuous overlapping spectra is provided, the method comprising: For the current iteration cycle of the Firefly Algorithm (FA), determine whether the current iteration cycle 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.

[0008] Optionally, 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.

[0009] Optionally, 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.

[0010] Optionally, 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.

[0011] Optionally, the preset composite objective function is expressed using the following formula:

[0012] 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 .

[0013] Optionally, 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.

[0014] Optionally, the step of using the Hilbert transform algorithm to calculate the overlapping spectrum time-frequency distribution of multiple first IMFs to 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.

[0015] On the one hand, a novel time-frequency analysis device for non-discontinuous overlapping spectra is provided, the device comprising: 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.

[0016] On one hand, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement any of the methods described above.

[0017] On the one hand, a storage medium is provided that stores computer program instructions thereon, which, when executed by a processor, implement any of the methods described above.

[0018] Compared with the prior art, the beneficial effects of this application are as follows: In this 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 has reached the maximum number of iterations. Then, if it is determined that the current iteration cycle has reached the maximum number of iterations, the Hilbert transform algorithm can be used to process and linearly superimpose multiple first intrinsic mode components (IMFs) to obtain the target time-frequency map. The first IMFs are obtained based on the variational mode decomposition (VMD) algorithm. Conversely, if it is determined that the current iteration cycle has not reached the maximum number of iterations, a preset VMD parameter optimization method can be used to adaptively optimize the VMD parameters to obtain optimized VMD parameters. The preset VMD parameter optimization method is determined based on the FA algorithm and the multimodal feature weighting index (MMFWI). The VMD parameters include the number of modes and a penalty factor. Next, 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 can be used to process and linearly superimpose multiple second IMFs to obtain the target time-frequency map. The second IMFs are obtained based on the optimized VMD parameters.

[0019] Based on this, in this application, by employing the Hilbert transform algorithm to process and linearly superimpose the multiple first intrinsic mode components (IMFs) obtained from the VMD algorithm decomposition, this application can fundamentally avoid cross-term interference between multiple component signals through a "divide and conquer-overlap" strategy, thereby obtaining a purer and more reliable time-frequency diagram. Furthermore, since 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. Therefore, the time resolution of this application can theoretically reach infinitely high. It is not a bandwidth-ambiguous peak on the frequency axis, but a precise frequency value at a specific moment. Thus, this application can achieve both high time resolution and high frequency resolution simultaneously.

[0020] Furthermore, since a VMD parameter optimization method based on the FA algorithm and the multimodal feature weighted index MMFWI is also adopted to adaptively optimize the VMD parameters, this application can avoid the limitations of a single index through this comprehensive perspective, thereby greatly improving the accuracy of VMD algorithm decomposition. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[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] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. Unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than that shown here.

[0025] As is well known, time-frequency analysis is a core technology for processing non-stationary signals, aiming to reveal the patterns of frequency component changes over time. Existing time-frequency analysis techniques mainly include Short-Time Fourier Transform (STFT), Wavelet Transform (WT), and Wigner-Ville Distribution (WVD), etc. However, these existing techniques have the following inherent limitations: (1) For the Short Time Fourier Transform (STFT), its time resolution and frequency resolution are constrained 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 across the entire time-frequency plane is fixed and cannot simultaneously meet the requirements of high time resolution for high-frequency signals and high frequency resolution for low-frequency signals.

[0026] (2) For wavelet transform WT, although it solves the fixed resolution problem of STFT to a certain extent through adaptive variable window, the choice of its basis function has a great impact on the analysis results and there is an energy leakage problem. The energy of high frequency signals may leak to adjacent frequency bands, resulting in a non-concentrated distribution of spectral energy and problems such as amplitude distortion and phase distortion.

[0027] (3) Regarding the Wigner quasi-probability distribution (WVD), although it has a high time-frequency focusing property, it will produce serious cross-terms for multi-component signals. These cross-terms are false time-frequency energy distributions, have no physical meaning, and are purely mathematical products of the WVD calculation method. They will seriously interfere with the interpretation of the real signal components, making the time-frequency spectrum diagram chaotic.

[0028] Based on this, this application provides a novel time-frequency analysis method for non-discontinuous overlapping spectra. In this method, for the current iteration cycle of the Firefly Algorithm (FA), it can be determined whether the current iteration cycle has reached the maximum number of iterations. Then, if it is determined that the current iteration cycle has reached the maximum number of iterations, the Hilbert transform algorithm can be used to process and linearly superimpose multiple first intrinsic mode components (IMFs) to obtain the target time-frequency map. Here, the first intrinsic mode components (IMFs) are obtained based on the variational mode decomposition (VMD) algorithm. Conversely, if it is determined that the current iteration cycle has not reached the maximum number of iterations, a preset VMD parameter optimization method can be used to adaptively optimize the VMD parameters to obtain optimized VMD parameters. Here, the preset VMD parameter optimization method is determined based on the FA algorithm and the multimodal feature weighting index (MMFWI). The VMD parameters include the number of modes and a penalty factor. Next, 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 can be used to process and linearly superimpose multiple second IMFs to obtain the target time-frequency map. Here, the second IMFs are obtained based on the optimized VMD parameters.

[0029] Based on this, in this application, by employing the Hilbert transform algorithm to process and linearly superimpose the multiple first intrinsic mode components (IMFs) obtained from the VMD algorithm decomposition, this application can fundamentally avoid cross-term interference between multiple component signals through a "divide-and-conquer-overlap" strategy, thereby obtaining a purer and more reliable time-frequency diagram. Furthermore, since 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. Therefore, the time resolution of this application can theoretically reach infinitely high. It is not a bandwidth-ambiguous peak on the frequency axis, but a precise frequency value at a specific moment. Thus, this application can achieve both high time resolution and high frequency resolution. In addition, by employing a VMD parameter optimization method based on the FA algorithm and the multimodal feature weighted index MMFWI to adaptively optimize the VMD parameters, this application can avoid the limitations of a single index through this comprehensive perspective, thereby greatly improving the accuracy of the VMD algorithm decomposition.

[0030] After introducing the design concept of the embodiments of this application, the following is a brief introduction to the application scenarios to which the technical solutions of the embodiments of this application can be applied. It should be noted that the application scenarios described below are only for illustrating the embodiments of this application and are not intended to limit the scope. In specific implementation, the technical solutions provided by the embodiments of this application can be flexibly applied according to actual needs.

[0031] like Figure 1The diagram shown illustrates an application scenario provided by an embodiment of this application. This application scenario may include a novel time-frequency analysis device 10 for non-discontinuous overlapping spectra.

[0032] The novel time-frequency analysis device 10 for uninterrupted overlapping spectrum can perform novel time-frequency analysis based on uninterrupted overlapping spectrum technology. For example, it can be used in vehicles, personal computers (PCs), servers, and laptops. The novel time-frequency analysis device 10 for uninterrupted overlapping spectrum can include one or more processors 101, memory 102, I / O interfaces 103, and database 104. Specifically, the processor 101 can be a central processing unit (CPU) or a digital processing unit, etc. The memory 102 can be volatile memory, such as random-access memory (RAM); the memory 102 can also be non-volatile memory, such as read-only memory, flash memory, hard disk drive (HDD), or 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 that can be accessed by a computer, but is not limited thereto. The memory 102 can be a combination of the aforementioned memories. The memory 102 can store some program instructions of the novel time-frequency analysis method for non-discontinuous overlapping spectra provided in this application embodiment. When these program instructions are executed by the processor 101, they can be used to implement the steps of the novel time-frequency analysis method for non-discontinuous overlapping spectra provided in this application embodiment, thereby solving the technical problems of low time-frequency resolution and weak resistance to suppression of cross-term interference in the prior art. The database 104 can be used to store data such as the time-domain diagram of the original signal, the spectrum diagram of the original signal, multiple initial IMF diagrams, multiple optimized IMF diagrams, multiple initial Hilbert time-frequency diagrams, and the target time-frequency diagram involved in the scheme provided in this application embodiment.

[0033] In this embodiment, the novel time-frequency analysis device 10 for uninterrupted overlapping spectra can acquire time-frequency analysis instructions through the I / O interface 103. Then, the processor 101 of the novel time-frequency analysis device 10 for uninterrupted overlapping spectra will solve the technical problems of low time-frequency resolution and weak resistance to cross-term interference in the prior art according to the program instructions of the novel time-frequency analysis method for uninterrupted overlapping spectra provided in this embodiment of the application stored in the memory 102. In addition, the time domain diagram of the original signal, the spectrum diagram of the original signal, multiple initial IMF diagrams, multiple optimized IMF diagrams, multiple initial Hilbert time-frequency diagrams, and the target time-frequency diagram can be stored in the database 104.

[0034] Of course, the methods provided in the embodiments of this application are not limited to... Figure 1 The application scenarios shown can also be used in other possible scenarios, and this application embodiment does not impose any limitations. Figure 1 The functions that the various devices in the application scenarios shown can achieve will be described in subsequent method embodiments, and will not be elaborated on here. Below, the methods of the embodiments of this application will be described in conjunction with the accompanying drawings.

[0035] like Figure 2 The diagram shown is a flowchart illustrating a novel time-frequency analysis method for non-discontinuous overlapping spectra provided in this application. This method can... Figure 1 The novel time-frequency analysis device 10 for non-discontinuous overlapping spectrum is used to perform the analysis. The specific process of this method is described below.

[0036] Step 201: Use the Variational Mode Decomposition (VMD) algorithm to perform non-discontinuous signal decomposition on the original signal to obtain multiple First Eigenmode Components (IMFs).

[0037] Specifically, such as Figure 3 The diagram shown is a schematic representation of variational mode decomposition provided in an embodiment of this application.

[0038] Step 2011: Initialize the VMD parameters using the FA algorithm to obtain the initialized VMD parameters.

[0039] That is, the modality number K and penalty factor in the VMD parameters can be adjusted by initializing the parameters of the FA algorithm, the search space, and the firefly population. Initialization is performed, where the firefly's position coordinates are determined using the VMD parameter (K, ) is used to represent.

[0040] Step 2012: Using the Alternating Direction Multiplier Method (ADMM), initialized VMD parameters, and preset constraint variational equations, the original signal is decomposed into a non-discontinuous signal to obtain multiple IMFs to be determined.

[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; This 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 the Hilbert transform algorithm, calculate the time-frequency distribution of the overlapping spectrum of multiple first IMFs to obtain multiple first Hilbert time-frequency maps.

[0059] Specifically, when 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, for any one first IMF, firstly, a Hilbert transform can be performed on any one first IMF. This transformation process can be specifically represented by the following formula:

[0060] Where P is the Cauchy principal value; To The value obtained by performing the Hilbert transform.

[0061] Based on this, the analytical signal shown in the following formula can be obtained. :

[0062] Then, based on the analyzed signal, the instantaneous amplitude, instantaneous phase, and instantaneous frequency corresponding to any first IMF can be obtained.

[0063] Among them, instantaneous amplitude It can be expressed using the following formula:

[0064] Instantaneous phase It can be expressed using the following formula:

[0065] instantaneous frequency It can be expressed using the following formula:

[0066] Next, based on the instantaneous amplitude, instantaneous phase, and instantaneous frequency, the Hilbert time-frequency plot of any first IMF can be obtained. The Hilbert time-frequency plot (time-frequency-energy three-dimensional distribution) of this first IMF can be represented by the following formula:

[0067] Based on this, the final target time-frequency map is formed by the direct linear superposition of all the above independent time-frequency distributions. It can be expressed using the following formula:

[0068] Step 2032: Obtain the target time-frequency map by linearly superimposing multiple first Hilbert time-frequency maps.

[0069] Step 204: If it is determined that the current iteration cycle has not reached the maximum number of iterations, then the preset VMD parameter optimization method is used to adaptively optimize the VMD parameters to obtain the optimized VMD parameters.

[0070] The preset VMD parameter optimization method is determined based on the FA algorithm and the MultiModal Feature Weighting Index (MMFWI); the VMD parameters include the number of modes K and the penalty factor. .

[0071] In practical applications, regarding the modality number K, if K is too small, it will lead to mode aliasing; while if K is too large, it will produce spurious and meaningless IMFs. Regarding the penalty factor... ,like If it's too large, it will cause the IMF to become too smooth, losing detail; if... If the bandwidth is too small, the IMF bandwidth will be too wide, potentially including redundant information.

[0072] Therefore, in order to obtain the optimal VMD parameters, this application employs a multimodal feature weighted index (MMFWI) based on the FA algorithm to select the optimal (K, )combination.

[0073] like Figure 5 The diagram shown is a schematic representation of VMD parameter optimization provided in an embodiment of this application.

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

[0075] The firefly's position coordinates are represented using VMD parameters; that is, the two parameters to be optimized in VMD, the mode number K and the penalty factor, can be used. Let i be the coordinates of a firefly's position. Therefore, the position of firefly i is a two-dimensional vector. .

[0076] Step 2042: Calculate the brightness of each firefly using a preset composite objective function.

[0077] In this application, the preset composite objective function is obtained based on the multimodal feature weighted index MMFWI, and the preset composite objective function can be expressed 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 a larger average sparsity value (based on the L1 / L2 norm ratio) results in a more concentrated energy of the surface IMF at a few points, the signal characteristics are more pronounced. Therefore, to optimize feature saliency, this application prefers a larger average sparsity. In the objective function, (1- This transforms the problem into a minimization problem. Specifically, it can be expressed using the following formula:

[0086] It is evident that all IMF components in this application simultaneously satisfy multiple desirable properties, rather than simply satisfying one property. They find the optimal parameter combination (K) by integrating multiple properties into a comprehensive score to minimize the pre-defined composite objective function. Therefore, since the FA algorithm aims to maximize brightness, while the preset composite objective function aims to minimize it, a mapping is also needed, namely, brightness... .

[0087] Step 2043: Compare the brightness of all fireflies pairwise and move them.

[0088] For any two fireflies, since the one with lower brightness will be attracted to and move towards the one with higher brightness, in this application, the brightest firefly can be determined by repeatedly comparing and moving all fireflies pairwise. Specifically, if the brightness of firefly j is greater than that of firefly i, then firefly i will move towards j, and the distance between them... Using Euclidean distance, attraction It can be expressed using the following formula:

[0089] in, To maximize appeal, is the light absorption coefficient.

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

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

[0092] Where 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... Figures 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 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; 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 a 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, use the Hilbert transform algorithm to process and linearly superimpose multiple second IMFs to obtain a target time-frequency map; wherein the second IMF is obtained based on the optimized VMD parameters.

[0110] Optionally, the novel time-frequency analysis device 150 for non-discontinuous overlapping spectra also includes a VMD decomposition unit 1504, used for: 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.

[0111] Optionally, the VMD parameter optimization unit 1503 is also used for: 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.

[0112] Optionally, the VMD parameter optimization unit 1503 is also used for: 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.

[0113] Optionally, the Hilbert transform unit 1502 is also used for: 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.

[0114] Optionally, the Hilbert transform unit 1502 is also used for: 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.

[0115] The novel time-frequency analysis device 150 for non-discontinuous overlapping spectra can be used to perform... Figures 2-4 The method performed by the novel time-frequency analysis device for non-discontinuous overlapping spectra in the illustrated embodiment can be referenced here for the functions that each functional module of the novel time-frequency analysis device 150 for non-discontinuous overlapping spectra can achieve. Figures 2-4 The embodiments shown are described in detail below.

[0116] In some possible implementations, various aspects of the methods provided in this application can also be implemented as a program product comprising program code that, when run on a computer device, causes the computer device to perform the steps of the methods according to the various exemplary embodiments of this application described above. For example, the computer device may perform actions such as... Figures 2-4 The method performed by the novel time-frequency analysis device for non-discontinuous overlapping spectra in the illustrated embodiment.

[0117] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks. Alternatively, if the integrated units of this application are implemented as software functional 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 this application, or the parts that contribute to the prior art, can be embodied in the form of software products. These computer software products are stored in a storage medium and include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0118] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0119] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such 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 calculate the overlapping spectrum time-frequency distribution of multiple first intrinsic mode components (IMFs) to obtain multiple first Hilbert time-frequency maps; the multiple first Hilbert time-frequency maps are linearly superimposed to obtain a target time-frequency map; wherein, the first intrinsic mode components (IMFs) are obtained based on the variational mode decomposition (VMD) algorithm; the step of using the Hilbert transform algorithm to calculate the overlapping spectrum time-frequency distribution of multiple first intrinsic mode components (IMFs) to obtain multiple first Hilbert time-frequency maps includes: for any first IMF, performing a Hilbert transform on the any first IMF to obtain a corresponding analytical signal; based on the analytical signal, obtaining the instantaneous amplitude, instantaneous phase, and instantaneous frequency corresponding to the any first IMF; and based on the instantaneous amplitude, instantaneous phase, and instantaneous frequency, obtaining the Hilbert time-frequency map of the any first IMF; 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. 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 calculate the overlapping spectrum time-frequency distribution of 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 multiple first Hilbert time-frequency maps; and to linearly superimpose the multiple first Hilbert time-frequency maps to obtain a target time-frequency map; wherein the first IMFs are obtained based on the variational mode decomposition (VMD) algorithm; the step of calculating the overlapping spectrum time-frequency distribution of multiple first IMFs using the Hilbert transform algorithm to obtain multiple first Hilbert time-frequency maps includes: performing a Hilbert transform on any first IMF to obtain a corresponding analytical signal; obtaining the instantaneous amplitude, instantaneous phase, and instantaneous frequency corresponding to any first IMF based on the analytical signal; and obtaining the Hilbert time-frequency map of any first IMF based on the instantaneous amplitude, instantaneous phase, and instantaneous frequency. 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.

7. 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 1-5 according to the obtained program instructions.

8. 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 1-5.

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