Time-varying structure instantaneous frequency identification method based on variational synchronous compression transformation

Abstract

The invention provides a time-varying structure instantaneous frequency identification method based on variational synchronous compression transformation. The method comprises the following steps: acquiring a vibration response signal of a time-varying engineering structure; performing signal continuation processing on the vibration response signal; performing time-frequency transformation on the continued vibration response signal to obtain a time-frequency spectrum and a time-frequency coefficient; locking a high-energy region corresponding to a time-varying structure characteristic frequency band from the time-frequency spectrum so as to eliminate interference points caused by test noise; based on the time-frequency coefficient in the high-energy region, estimating an instantaneous frequency through a variational optimization method of introducing a regularization smoothing item, the regularization smoothing item being used for suppressing false peak interference; performing synchronous compression transformation on a time-frequency coefficient based on the instantaneous frequency estimation value to obtain a refined frequency band; and extracting an instantaneous frequency curve of the time-varying engineering structure from the refined frequency band.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of modal parameter identification of time-varying engineering structures, and particularly relates to a time-varying structure instantaneous frequency identification method based on a variational synchronous compression transform. BACKGROUND

[0002] Time-varying modal analysis is a research hotspot and difficulty in the field of structural dynamics. For actual civil engineering structures, under the long-term action of working load, extreme load and environmental factors, the structure material deteriorates over time, resulting in changes in physical parameters (such as mass, stiffness and damping) over time. For example, fatigue accumulation and connection loosening of steel structures, cable force relaxation of long-span cable-stayed bridges or suspension bridge hangers, and cracks in the main load-bearing components of bridges due to overloading or fatigue, all of which will lead to a decrease in the overall or local stiffness of the structure, causing the modal parameters (frequency, mode shape and damping ratio, etc.) that characterize the dynamic characteristics of the structure to change over time. Therefore, most civil structures during service have time-varying characteristics. However, traditional modal identification methods are usually based on the time-invariant assumption, i.e. the structure's dynamic equation is a constant coefficient differential equation, which may confuse the time-varying effect of structure parameters with measurement noise, model error, etc. when extracting the modal parameters of time-varying structures, leading to distorted or decreased accuracy of the identified modal parameters, making it difficult to accurately determine the "current state" of the structure and find early signs of structural dynamic performance degradation, posing a hidden danger to the long-term safe operation of the structure. Therefore, developing a method that can accurately capture and track the time-varying law of structural modal parameters is of great significance for accurate evaluation of the service performance of actual civil structures, damage diagnosis and residual life prediction.

[0003] In recent years, time-frequency analysis methods based on structural vibration signals are one of the effective tools for extracting the instantaneous frequency of time-varying structures. Among them, the Synchrosqueezing Transform (SST) compresses and reorganizes the time-frequency graph with the estimated instantaneous frequency, with high time-frequency resolution. In addition, SST can also be used to reconstruct the vibration signal. However, SST is a global compression of the time-frequency graph, which inevitably compresses the false peak points in the time-frequency graph near the instantaneous frequency curve, resulting in the phenomenon of burr in the extracted instantaneous frequency, reducing the identification accuracy of the instantaneous frequency. Therefore, the high-order synchrosqueezing transform further introduces a high-order Taylor expansion to improve the estimation accuracy of the instantaneous frequency, but it is still a global compression of the time-frequency graph, and cannot completely get rid of the influence of false peaks.

[0004] To solve the above problems, the synchronous extraction transform uses the frequency position on the frequency axis and the instantaneous frequency estimation value to make a difference, and retains the instantaneous frequency estimation value with the smallest difference, so as to improve the identification accuracy of the instantaneous frequency. However, the synchronous extraction transform is insufficient in signal reconstruction accuracy. At the same time, the range of the time-frequency coefficients selected and retained by the synchronous extraction transform is mainly based on experience, and the selection range that is too small may lead to the folding of the extracted instantaneous frequency curve, thereby affecting the extraction accuracy of the instantaneous frequency. When the selection range is too large, the energy of the frequency band will be dispersed, and it is difficult to accurately track the instantaneous frequency. In view of the problems existing in the synchronous extraction transform, the multiple synchronous compression transform uses an instantaneous frequency iteration operator to improve the time-frequency concentration and estimation accuracy of the instantaneous frequency band. This method not only can accurately reconstruct the signal, but also does not need to select the retention range of the time-frequency coefficients. In addition, unlike the high-order synchronous compression transform, the multiple synchronous compression transform discards the high-order Taylor expansion of the instantaneous frequency estimation operator, and instead uses multiple iteration calculations, which greatly reduces the calculation complexity. It is worth mentioning that although the multiple synchronous transform improves some shortcomings of the existing method, it needs to be rounded when estimating the instantaneous frequency, and it is difficult to converge the time-frequency coefficients to a point at each time. At the same time, when there is a false peak value interference in the time-frequency diagram, the identification accuracy will also be reduced. SUMMARY

[0005] In view of the defects and deficiencies of the prior art, the present application provides a time-varying engineering structure instantaneous frequency identification method and system based on variational synchronous compression transform, aiming to solve the problems of insufficient identification accuracy caused by false peak value interference and end effect in time-varying structure instantaneous frequency identification.

[0006] The method first acquires the vibration response signal of the time-varying engineering structure, and performs extension processing on the signal through an autoregressive model to eliminate the end effect in subsequent time-frequency analysis; performs time-frequency transform on the extended signal to obtain a time-frequency spectrum and time-frequency coefficients; then, through normalization, Gaussian smoothing preprocessing, combined with Canny edge detection and morphological closing operation, the high-energy area corresponding to the structural characteristic frequency band is locked from the time-frequency spectrum, and isolated interference points caused by test noise are effectively excluded; based on the time-frequency coefficients in the high-energy area, a variational instantaneous frequency estimation operator is constructed, which realizes the suppression of false peaks and the smooth constraint of the instantaneous frequency trajectory by minimizing the objective function composed of the data fidelity term composed of the absolute value of the time-frequency coefficients and the regularization term composed of the regularization parameter and the square of the difference between the instantaneous frequency position and the estimation value; and then based on the instantaneous frequency estimation value, the time-frequency coefficients are subjected to synchronous compression transform to refine the frequency band, and finally the instantaneous frequency curve is extracted from the refined frequency band.

[0007] The corresponding identification system comprises a processor, a memory, a data acquisition device and functionally adapted signal acquisition, continuation, time-frequency transformation, high-energy region locking, variational optimization, synchronous compression and frequency extraction modules, and the above method is realized through hardware and software cooperation.

[0008] The technical scheme specifically adopted by the present application to solve the technical problems is:

[0009] A time-varying structure instantaneous frequency identification method based on variational synchronous compression transformation, comprising:

[0010] Obtaining the vibration response signal of the time-varying engineering structure;

[0011] Performing signal continuation processing on the vibration response signal;

[0012] Performing time-frequency transformation on the continued vibration response signal to obtain a time-frequency spectrum and time-frequency coefficients;

[0013] Locking the high-energy region of the characteristic frequency band of the corresponding time-varying structure from the time-frequency spectrum to exclude interference points caused by test noise;

[0014] Based on the time-frequency coefficients in the high-energy region, the instantaneous frequency is estimated by introducing a variational optimization method of a regularization smoothing term, and the regularization smoothing term is used to suppress false peak interference;

[0015] Based on the instantaneous frequency estimation value, the time-frequency coefficients are subjected to synchronous compression transformation to obtain a refined frequency band;

[0016] Extracting the instantaneous frequency curve of the time-varying engineering structure from the refined frequency band.

[0017] Further, the signal continuation processing is realized by using an autoregressive model to eliminate the end effect in the time-frequency transformation process.

[0018] Further, the specific process of locking the high-energy region of the characteristic frequency band of the corresponding time-varying structure comprises:

[0019] The time-frequency coefficient matrix is subjected to normalization and Gaussian smoothing pretreatment to preliminarily eliminate part of the test noise;

[0020] The Canny edge detection algorithm is used to locate the boundaries of energy mutation in the time-frequency spectrum;

[0021] The broken parts in the boundaries are connected through morphological closing operation to form a closed contour;

[0022] Fill the area formed by the closed contour, and remove isolated time-frequency interference areas with an area less than a preset value to obtain the high-energy area.

[0023] Further, the variational optimization method estimates the instantaneous frequency by minimizing an objective function composed of two terms: a first term is a negative value of the absolute value of the time-frequency coefficient; and a second term is a product of a regularization parameter and a square of a difference between an instantaneous frequency position and an instantaneous frequency estimate value.

[0024] Further, the regularization smoothing term achieves smooth constraint of the instantaneous frequency trajectory by penalizing high-energy time-frequency points deviating too far from the instantaneous frequency estimate value, thereby avoiding abnormal jumps of the instantaneous frequency curve.

[0025] Further, the time-frequency transform is a short-time Fourier transform.

[0026] Further, the maximum value method is used to extract the instantaneous frequency curve of the time-varying engineering structure from the refined frequency band.

[0027] Further, the method only needs to collect the vibration response output signal of the time-varying engineering structure, without collecting the excitation input signal of the structure, and is suitable for operational modal analysis of the time-varying engineering structure.

[0028] Further, the time-varying engineering structure is a civil engineering structure.

[0029] And a time-varying structure instantaneous frequency identification system based on variational synchronous compression transform, comprising a processor, a memory and a data acquisition device, the processor executes a computer program stored in the memory, cooperates with the data acquisition device to realize the instantaneous frequency identification method of the time-varying engineering structure as described above, and the system further comprises:

[0030] A signal acquisition module is configured to acquire the vibration response signal of the time-varying engineering structure through the data acquisition device;

[0031] A signal extension module is configured to perform signal extension processing on the vibration response signal;

[0032] A time-frequency transform module is configured to perform time-frequency transform on the extended vibration response signal to obtain a time-frequency spectrum and time-frequency coefficients;

[0033] A high-energy area locking module is configured to lock the high-energy area corresponding to the characteristic frequency band of the time-varying structure from the time-frequency spectrum, and exclude interference points caused by test noise;

[0034] A variational optimization module is configured to estimate the instantaneous frequency based on the time-frequency coefficients in the high-energy area by introducing a regularization smoothing term in the variational optimization method, and the regularization smoothing term is used to suppress false peak interference;

[0035] a synchronous compression module, configured to perform a synchronous compression transform on the time-frequency coefficients based on the instantaneous frequency estimation value, to obtain a refined frequency band;

[0036] a frequency extraction module, configured to extract an instantaneous frequency curve of the time-varying engineering structure from the refined frequency band.

[0037] and a non-transitory computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the method described above.

[0038] Compared with the prior art, the present application and the preferred solutions thereof at least have the following beneficial effects:

[0039] The end effect in time-frequency analysis is effectively alleviated, the adverse effects of signal distortion on the identification result are reduced, a reliable foundation is laid for subsequent time-frequency processing and feature extraction, the interference of false peaks in the time-frequency analysis process is effectively suppressed through the innovative construction of the variational instantaneous frequency estimation element, the accuracy and reliability of the instantaneous frequency identification are significantly improved, the interference caused by test noise is effectively excluded through the automatic locking of the high-energy region by combining edge detection and morphological operation, the identification result is more in line with the actual dynamic characteristics of the structure, the end effect in time-frequency transformation is eliminated through signal continuation processing, the accuracy of the instantaneous frequency identification at the signal boundary is ensured, the present application only needs to collect the vibration response output signal of the structure, without the need for input excitation information, is particularly suitable for the working modal analysis scene in which the input excitation is difficult to obtain in actual engineering, and provides a more practical technical means for the health monitoring of civil engineering structures, the overall scheme realizes the accurate capture of the dynamic characteristic evolution of the time-varying structure, helps to find early signs of structural performance degradation in a timely manner, and provides a scientific basis for the safety evaluation and maintenance decision of engineering structures.

[0040] The corresponding identification system hardware and software functionally cooperate and adapt to each other, can stably realize the core process of the method, and is convenient for engineering implementation. Overall, the present application can accurately capture the time-varying law of the modal parameters of the time-varying engineering structure, significantly improves the accuracy and reliability of the instantaneous frequency identification, and provides strong technical support for the health monitoring, damage diagnosis and residual life assessment of civil engineering structures. BRIEF DESCRIPTION OF DRAWINGS

[0041] The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0042] Figure 1 A flowchart of the instantaneous frequency identification of the time-varying structure based on the variational synchronous compression transform of the embodiments of the present application. DETAILED DESCRIPTION

[0043] In order to make the features and advantages of the present application more obvious and easy to understand, specific examples are given below, and the detailed description is as follows: In order to make the features and advantages of the present application more obvious and easy to understand, specific examples are given below, and the detailed description is as follows:

[0044] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0045] It is also important to note that the terms "example" and / or "exemplary" as used herein illustrate certain exemplary embodiments and should not be construed as applying to the free practice or application of such exemplary embodiments. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising", when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0046] In view of the deficiencies of the multiple synchronous compression transform, the application proposes a time-varying structure instantaneous frequency identification method based on variational synchronous compression transform: first, the signal extension method and edge detection are combined to narrow the range of synchronous compression, and then the time-frequency coefficients in the selected range are compressed and rearranged by constructing a variational instantaneous frequency estimator, so as to reduce the interference caused by false peaks in the time-frequency diagram. The specific technical route is shown in Figure 1 As shown in the figure, first, the response signal of the structure is extended by an autoregressive model, then the time-frequency spectrum and time-frequency coefficients of the signal are extracted by using short-time Fourier transform, then the high-energy area of the time-frequency spectrum is locked by combining Canny edge detection and morphological closing operation, then the instantaneous frequency estimator is constructed to calculate the estimated value of the instantaneous frequency, and then the high-energy area is subjected to synchronous compression transform by using the obtained instantaneous frequency estimate, so as to refine the frequency band of the response signal, finally the maximum value method is used to extract the instantaneous frequency curve of the refined frequency band. The design and implementation of the scheme specifically include the following steps:

[0047] Step 1: signal extension. Since there is an end effect phenomenon when using edge detection and time-frequency transform, the autoregressive model is used to extend the response signal of the structure.

[0048] Step 2: Extract the time-frequency spectrum. After the response signal is extended, the time-frequency spectrum and time-frequency coefficients of the extended signal are further obtained by using short-time Fourier transform.

[0049] Step 3: Locking high-energy area. Each bright and continuous high-energy area in the time-frequency spectrum is usually the area where each order characteristic frequency band of the structure appears, and the outside of the frequency band is the isolated point caused by test noise and other interference. In order to accurately locate the high-energy area in the time-frequency diagram, Canny edge detection and morphological closing operation are introduced to lock the area where each frequency band is located.

[0050] Specifically, firstly, the time-frequency coefficient matrix is normalized and preprocessed by Gaussian smoothing to preliminarily eliminate part of the noise; then, the Canny edge detection algorithm is used to locate the boundary of energy mutation, and a morphological closing operation is performed to connect the broken edges, so as to form a closed contour; then, the closed region is filled and the interference region with an area too small is removed, so as to obtain a high-energy region, thereby realizing automatic detection and quantitative description of the energy concentration frequency band in the time-frequency graph.

[0051] Step 4: Estimate the instantaneous frequency, that is, construct a variational instantaneous frequency estimator to reduce the false peak interference in the high-energy region.

[0052] Specifically, firstly, the partial derivative with respect to time is calculated for the time-frequency coefficient, and the estimated value of the instantaneous frequency is obtained. On this basis, a variational instantaneous frequency estimator is constructed as shown in formula (1):

[0053]

[0054] In the formula, G is the time-frequency coefficient, is the estimated value of the instantaneous frequency, is the instantaneous frequency position on the vertical coordinate axis of the time-frequency spectrum, is the estimated value of the instantaneous frequency corresponding to the local minimum value of the function in the parentheses, and the regularization parameter is used to suppress the false peak. In formula (1), is the local maximum value of the time-frequency coefficient in the high-energy region at each time; is a regularization term used to smooth the instantaneous frequency curve. If the energy of a frequency point in the neighborhood is high but deviates too far from the current frequency, the regularization term will set the current energy point to 0, and then a point with the highest energy and the smallest regularization term in the high-energy region is selected as the estimated value of the instantaneous frequency, so as to "punish" the possible jump of the instantaneous frequency band, thereby avoiding the false peak.

[0055] Step 5: Refine the frequency band. The time-frequency spectrum is synchronously compressed and transformed by using the estimated value of the instantaneous frequency obtained in formula (1), and a refined frequency band is obtained.

[0056] Step 6: Extract the instantaneous frequency curve. The maximum value method is used to extract the instantaneous frequency curve for each compressed high-energy region.

[0057] Compared with the prior art, the design provided by the embodiment of the present application has the following advantages: (1) the instantaneous frequency curve of the response signal with time-varying characteristics can be extracted; (2) the proposed high-energy region locking method and variational instantaneous frequency estimation element can improve the interference of false peaks in the time-frequency diagram, thereby effectively improving the identification accuracy of the instantaneous frequency; and (3) the identification of the structural modal parameters can be completed only by using the output response of the structure, and the method is particularly suitable for the working modal analysis problem.

[0058] The method can be specifically used for instantaneous frequency identification in the case that the time-varying engineering structure contains false peaks.

[0059] Based on the same inventive concept, the present application further provides a computer device, which comprises one or more processors and a memory for storing one or more computer programs; the program comprises program instructions, and the processor is configured to execute the program instructions stored in the memory. The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The processor is the computing core and control core of the terminal, and is configured to implement one or more instructions, and is specifically configured to load and execute one or more instructions in the computer storage medium to implement the above method.

[0060] It should be further noted that based on the same inventive concept, the present application also provides a computer storage medium, which stores a computer program, and the computer program is run by a processor to execute the above method. The storage medium can adopt any combination of one or more computer readable media. The computer readable medium can be a computer readable signal medium or a computer readable storage medium. The computer readable storage medium may, for example, but is not limited to, an electrical, magnetic, optical, infrared, or semiconductor system, device or apparatus, or any combination of the above. More specific examples (non-exhaustive list) of the computer readable storage medium include: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, the computer readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device or apparatus.

[0061] It should be noted that unless otherwise defined, technical or scientific terms used in the present application should be understood as having the common meaning in the field of the present application to those having ordinary skill in the art. The terms "first", "second" and similar terms used in the present application do not denote any order, quantity or importance, but are only used to distinguish different components. The terms "include" or "contain" and similar terms mean that the elements or objects before the terms cover the elements or objects listed after the terms and their equivalents, and do not exclude other elements or objects. The terms "connected" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to represent relative positional relationships, and when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0062] The above is only the preferred embodiment of the present application, and does not limit other forms of the present application. Any skilled person in the art can modify or change the above disclosed technical content to equivalent embodiments. However, any simple modification, equivalent change and modification of the above embodiments without departing from the technical solution of the present application, and according to the technical essence of the present application, still belongs to the protection scope of the technical solution of the present application.

[0063] The present application is not limited to the above-mentioned best mode, and anyone can derive other various forms of time-varying structure instantaneous frequency identification methods based on variational synchronous compression transformation under the inspiration of the present application. Any equivalent changes and modifications made within the scope of the present application should be included in the scope of the present application.

Claims

1. A method for identifying the instantaneous frequency of a time-varying structure based on variational synchronous compression transform, characterized in that, include: Acquire vibration response signals of time-varying engineering structures; The vibration response signal is subjected to signal extension processing; The time-frequency transformation of the extended vibration response signal is performed to obtain the time-frequency spectrum and time-frequency coefficients. The high-energy region corresponding to the time-varying structural characteristic frequency band is locked from the time spectrum to eliminate interference points caused by test noise; Based on the time-frequency coefficients in the high-energy region, the instantaneous frequency is estimated by a variational optimization method that introduces a regularized smoothing term, which is used to suppress spurious peak interference. Based on the instantaneous frequency estimate, the time-frequency coefficients are synchronously compressed and transformed to obtain a refined frequency band; Extract the instantaneous frequency curve of the time-varying engineering structure from the refined frequency band.

2. The instantaneous frequency identification method for time-varying structures based on variational synchronous compression transform according to claim 1, characterized in that: The signal extension processing is implemented using an autoregressive model to eliminate the endpoint effect in the time-frequency transformation process.

3. The instantaneous frequency identification method for time-varying structures based on variational synchronous compression transform according to claim 1, characterized in that: The specific process of locking the high-energy region corresponding to the time-varying structural characteristic frequency band includes: The time-frequency coefficient matrix is ​​normalized and Gaussian smoothed to initially eliminate some test noise; The Canny edge detection algorithm is used to locate the boundaries of energy abrupt changes in the time spectrum. A closed profile is formed by connecting the broken parts in the boundary through morphological closing operations; The region formed by the closed contour is filled, and isolated time-frequency interference regions with an area smaller than a preset value are removed to obtain the high-energy region.

4. The instantaneous frequency identification method for time-varying structures based on variational synchronous compression transform according to claim 1, characterized in that: The variational optimization method estimates the instantaneous frequency by minimizing an objective function, which consists of two terms: the first term is the negative of the absolute value of the time-frequency coefficient; the second term is the product of the regularization parameter and the square of the difference between the instantaneous frequency location and the estimated instantaneous frequency.

5. The instantaneous frequency identification method for time-varying structures based on variational synchronous compression transform according to claim 1, characterized in that: The regularization smoothing term achieves smooth constraint on the instantaneous frequency trajectory by penalizing high-energy time-frequency points that deviate too far from the instantaneous frequency estimate, thus avoiding abnormal jumps in the instantaneous frequency curve.

6. The instantaneous frequency identification method for time-varying structures based on variational synchronous compression transform according to claim 1, characterized in that: The time-frequency transformation is a short-time Fourier transform.

7. The instantaneous frequency identification method for time-varying structures based on variational synchronous compression transform according to claim 1, characterized in that: The instantaneous frequency curve of the time-varying engineering structure is extracted from the refined frequency band using the maximum value method.

8. The instantaneous frequency identification method for time-varying structures based on variational synchronous compression transform according to claim 1, characterized in that: The method only requires collecting the vibration response output signal of the time-varying engineering structure, without needing to collect the excitation input signal of the structure, and is suitable for the working modal analysis of time-varying engineering structures.

9. The instantaneous frequency identification method for time-varying structures based on variational synchronous compression transform according to claim 1, characterized in that: The time-varying engineering structure is a civil engineering structure.

10. A time-varying structure instantaneous frequency identification system based on variational synchronous compression transform, characterized in that, The system includes a processor, a memory, and a data acquisition device. The processor executes a computer program stored in the memory, and, in conjunction with the data acquisition device, implements the instantaneous frequency identification method for time-varying engineering structures as described in claim 1. The system further includes: The signal acquisition module is used to acquire vibration response signals of time-varying engineering structures through the data acquisition device; The signal extension module is used to perform signal extension processing on the vibration response signal; The time-frequency conversion module is used to perform time-frequency conversion on the extended vibration response signal to obtain the time spectrum and time-frequency coefficients. A high-energy region locking module is used to lock the high-energy region corresponding to the time-varying structural characteristic frequency band from the time spectrum and eliminate interference points caused by test noise. The variational optimization module is used to estimate the instantaneous frequency based on the time-frequency coefficients in the high-energy region by introducing a variational optimization method with a regularized smoothing term, wherein the regularized smoothing term is used to suppress spurious peak interference. The synchronous compression module is used to perform synchronous compression transformation on the time-frequency coefficients based on the instantaneous frequency estimate to obtain a refined frequency band; The frequency extraction module is used to extract the instantaneous frequency curve of the time-varying engineering structure from the refined frequency band.

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