ZGV feature extraction method based on local entropy reconstruction optimization multiple synchronous compression algorithm
Through local entropy reconstruction, the multi-synchronous compression algorithm is optimized, and the problem of insufficient accuracy in ZGV signal feature extraction is solved, high-precision ZGV signal feature extraction is realized, energy leakage is reduced, the accuracy and clarity of spectrum estimation is improved, and the algorithm usage process is simplified.
Patent Information
- Application Number
- CN202510248262.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-04
- Publication Date
- 2025-07-25
AI Technical Summary
The prior art has insufficient accuracy in the ZGV signal feature extraction, resulting in limited accuracy of ZGV-based measurement technology. Traditional methods such as STFT and SST have energy leakage problems, and manual debugging of time window parameters is time-consuming and lacks objective evaluation standards.
The Bayesian cost function is constructed, optimized window function length, and high-precision time-frequency graph extraction is performed through short-term Fourier transform, instantaneous frequency estimation, synchronous compression transformation, iteration, Rényi entropy value calculation and Bayesian optimization.
It significantly reduces energy leakage, improves spectrum estimation accuracy and clarity, simplifies the algorithm process, improves the accuracy and reliability of ZGV signal feature extraction, and is suitable for weak non-stationary signal feature extraction in various occasions.
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Figure CN120372260A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a method for extracting ZGV features, specifically to a method for extracting ZGV features based on local entropy reconstruction optimized multi-synchronous compression algorithm, belonging to the technical field of signal feature extraction. Background Art
[0002] With the continuous progress of the aviation industry, increasingly stringent requirements have been put forward for the performance and lifespan of aircraft. Accurately monitoring the stress distribution and damage defects of aircraft panels is crucial for preventing structural failures, monitoring fuselage fatigue damage, and extending service life, which is a highly challenging and significant task. In recent years, the mechanical property measurement method based on zero group velocity (ZGV) Lamb waves has gradually become a research hotspot due to its high sensitivity and high resolution characteristics, and is expected to develop into a new generation of high-precision mechanical structure health monitoring technology.
[0003] Based on the characteristics of ZGV Lamb waves, researchers have developed a series of measurement techniques. For example, Liu Bin et al. proposed a method for detecting defects in honeycomb structures based on zero group velocity feature analysis in patent CN116735712A. This method realizes relatively accurate detection of defects in honeycomb structures by comparing the ZGV frequency distribution in the theoretically defect-free state with the local ZGV frequency distribution at the actual measurement points. However, the specific algorithms and processes for ZGV frequency extraction in this method have not been deeply explored, which is one of the important reasons why the defect detection accuracy is difficult to further improve. Therefore, in order to further improve the accuracy and reliability of defect detection, it is urgent to develop more accurate ZGV feature extraction techniques.
[0004] Both existing theoretical simulations and experimental results indicate that the ZGV wave is a non-stationary signal. The simple Fourier transform has certain limitations in extracting its features. In the industrial field, bearing fault signals are also a common type of non-stationary signal. Liao Shuming et al. proposed a rolling bearing fault diagnosis method based on the Synchrosqueezing Transform (SST) and the improved CMT model in patent CN118395081A. The method of Liao Shuming et al. first uses SST to extract the time-frequency information in the rolling bearing, then trains the improved CMT (Convolutional Neural Networks Meets Visual Transformers, CMT) model, and finally inputs the time-frequency information of the bearing vibration signal collected on-site into the model to achieve real-time fault diagnosis. Although this method is applicable to the extraction of non-stationary signals in rotating machinery bearings, considering that the frequency of the ZGV signal is usually in the megahertz range, much higher than the kilohertz range corresponding to bearing faults; in addition, this method requires a large amount of training sets, and it is relatively difficult to collect training data in the emerging field of ZGV measurement. Based on the above reasons, it can be concluded that the existing mature algorithms (such as SST) should be further improved according to the characteristics of ZGV measurement.
[0005] For the analysis of non-stationary signals, time-frequency images are usually used for visual representation. The Short-Time Fourier Transform (STFT), as a classic time-frequency analysis method, and its subsequent development such as the Synchrosqueezing Transform (SST), can effectively characterize the time-frequency information of signals. However, these methods all have certain limitations when dealing with ZGV signals. Specifically, the time-frequency image extracted by STFT has a serious energy leakage phenomenon, resulting in inaccurate representation of the ZGV signal frequency, showing a fluctuation of about 0.1 MHz up and down. This error level is unacceptable for high-precision mechanical property measurements. Although SST and second-order SST (2nd-order SST) have improved this problem to a certain extent and can show the trend of frequency changing with time, there is still obvious energy leakage. In addition, the traditional Synchrosqueezing Transform (SST) method relies on a manually set time window, and the choice of the time window directly affects the accuracy of the transformation result. Moreover, manually debugging the time window parameters is not only time-consuming but also lacks an objective evaluation standard for the quality of the extraction results. Summary of the Invention
[0006] The present invention aims to solve the problem of limited accuracy of the ZGV-based measurement technology caused by insufficient ZGV feature extraction accuracy, and to achieve more accurate and reliable feature extraction of ZGV signals. Furthermore, a ZGV feature extraction method based on local entropy reconstruction optimized multiple synchrosqueezing algorithm is proposed.
[0007] The technical solution adopted by the present invention to solve the above problems is as follows:
[0008] A ZGV feature extraction method based on local entropy reconstruction optimized multiple synchrosqueezing algorithm, and the ZGV feature extraction method based on local entropy reconstruction optimized multiple synchrosqueezing algorithm is realized through the following steps:
[0009] Step 1: For signals with time-varying features, perform preliminary extraction using the short-time Fourier transform;
[0010] Step 2: Estimate the instantaneous frequency corresponding to the short-time Fourier transform result;
[0011] Step 3: Use the instantaneous frequency estimated in Step 2 and the short-time Fourier transform result obtained in Step 1 for synchrosqueezing transform to perform time squeezing and reassignment;
[0012] Step 4: Iterate the synchrosqueezing transform result obtained in Step 3;
[0013] Step 5: Calculate the Rényi entropy value and reconstruction accuracy of the transform result obtained in Step 4 to evaluate the transform result;
[0014] Step 6: Construct a Bayesian cost function using the Rényi entropy and reconstruction accuracy calculated in Step 5, and perform Bayesian optimization on the cost function to obtain the globally optimized window function length;
[0015] Step 7: Use the globally optimized window function length obtained in Step 6 as the window length of the Gaussian window function to obtain a new window function, and then perform a new operation of the short-time Fourier transform on the new window function to obtain a high-precision time-frequency diagram.
[0016] Furthermore, the specific content of using the short-time Fourier transform for preliminary extraction in Step 1 includes:
[0017] Suppose there is a square-integrable signal:
[0018]
[0019] Window it with a square-integrable even real window function g(t), and its short-time Fourier transform is as follows:
[0020]
[0021] Suppose The amplitude A(t) and phase within the research time change small enough to neglect the high-order terms of the Taylor expansion and neglect o(A'(t)) and Approximately consider that:
[0022]
[0023] Substitute Equation (3) into Equation (2) to obtain:
[0024]
[0025] In Equation (4) represents the Fourier transform of the window function with respect to of.
[0026] Furthermore, the specific steps for estimating the instantaneous frequency corresponding to the short-time Fourier transform result in Step 2 are as follows:
[0027] Take the partial derivative with respect to time t under the approximation of the obtained short-time Fourier transform result, noting that o(A'(t)) and i.e., A(t) and are approximately considered constants, and the approximate partial derivative:
[0028]
[0029] Construct an instantaneous frequency estimation formula to estimate the instantaneous frequency corresponding to the short-time Fourier result:
[0030]
[0031] Substitute Equation (5) into Equation (6) to obtain:
[0032]
[0033] Furthermore, the specific steps for the synchrosqueezing transform in Step 3 are as follows:
[0034] Use the estimated instantaneous frequency and the short-time Fourier transform result G(t,ω) for the synchrosqueezing transform, perform time squeezing and reassignment to concentrate the energy of the zero-group velocity Lamb wave:
[0035]
[0036] In Equation (8), η is the corresponding frequency of the synchrosqueezing transform result.
[0037] Furthermore, the specific iterative expression in Step 4 is as follows:
[0038] Let Ts(t,η) = Ts [1](t, η), the iterative process is as follows:
[0039]
[0040] Take the difference between the current result and the previous result. When the difference is less than the convergence threshold or the iteration upper limit is reached, the transformation result is obtained.
[0041] Furthermore, the calculation of the Rényi entropy value described in step 5 specifically includes:
[0042] To determine the degree of energy concentration of the transformation result, calculate the local Rényi entropy
[0043]
[0044] In formula (10), θ is time, β is the interval size near time θ, and λ is the Rényi entropy order, generally taking λ = 3.
[0045] Furthermore, the calculation of the reconstruction accuracy described in step 5 specifically includes:
[0046] Calculate the local reconstruction quality factor
[0047]
[0048] In the formula, x β (θ) = [x(θ), x(θ + 1),..., x(θ + 2β)], is the reconstructed signal obtained by the inverse Fourier transform of Ts [N] (t, η).
[0049] Furthermore, the expression for constructing the Bayesian cost function described in step 6 is as follows:
[0050]
[0051] Furthermore, the expression for Bayesian optimization of the cost function described in step 6 is as follows:
[0052]
[0053] In formula (13), l * (θ) is the window function length of global optimization.
[0054] Furthermore, the expression for obtaining a new window function by taking the globally optimized window function length as the window length of the Gaussian window function described in step 7 is as follows:
[0055]
[0056] In Equation (14),
[0057] The beneficial effects of the present invention are as follows:
[0058] 1. The present invention constructs a cost function based on energy concentration and signal reconstruction accuracy for Bayesian optimization, and can obtain the globally optimal window function length, which significantly reduces the energy leakage in signal extraction of zero group velocity waves and significantly weakens the energy leakage phenomenon in signal feature extraction.
[0059] 2. The present invention redistributes the energy in the Short-Time Fourier Transform (STFT) spectrogram to a more accurate time-frequency position, improving the accuracy and clarity of spectral estimation. In addition, by automatically generating the optimization result by comparing the original signal and the reconstructed signal, the number of parameters that need to be manually adjusted by the user is reduced, the usage process of the algorithm is simplified, the efficiency is improved, and the extraction of weak non-stationary signal features is applicable to a variety of different occasions. BRIEF DESCRIPTION OF THE DRAWINGS
[0060] Figure 1 is a schematic flow chart of the ZGV feature extraction method based on the local entropy reconstruction optimized multiple synchronous compression algorithm of the present invention;
[0061] Figure 2 is a schematic diagram of the ZGV frequency at different time periods of the same signal;
[0062] Figure 3 is a schematic diagram of the frequency-wave number dispersion curve of a 6061 aluminum alloy plate with a thickness of 3 mm;
[0063] Figure 4 is a schematic diagram of the time-frequency image of a non-stationary signal;
[0064] Figure 5 is a schematic diagram of the result of processing a signal containing noise;
[0065] Figure 6 is a schematic diagram of the time-frequency image obtained after the present invention processes a section of signal. DETAILED DESCRIPTION OF THE INVENTION
[0066] DETAILED DESCRIPTION OF THE INVENTION 1: In combination with Figure 1-6 This embodiment is described. The ZGV feature extraction method based on the local entropy reconstruction optimized multiple synchronous compression algorithm in this embodiment is implemented through the following steps:
[0067] Step 1: For a signal with time-varying characteristics, perform preliminary extraction using the short-time Fourier transform;
[0068] Suppose there is a square-integrable signal:
[0069]
[0070] Window the signal with a square-integrable even real window function \(g(t)\), and its short-time Fourier transform is as follows:
[0071]
[0072] Suppose During the research time, the amplitude \(A(t)\) and phase change small enough. Neglect the high-order terms of the Taylor expansion, neglect \(o(A'(t))\) and Approximately consider that:
[0073]
[0074] Substitute Equation (3) into Equation (2), and we get:
[0075]
[0076] In Equation (4) represents the Fourier transform of the window function with respect to .
[0077] Step 2: Estimate the instantaneous frequency corresponding to the short-time Fourier transform result;
[0078] Take the partial derivative with respect to time \(t\) under the approximation of the obtained short-time Fourier transform result. Note that \(o(A'(t))\) and i.e., \(A(t)\) and are approximately considered as constants. The approximate partial derivative is:
[0079]
[0080] Construct an instantaneous frequency estimation formula to estimate the instantaneous frequency corresponding to the short-time Fourier result:
[0081]
[0082] Substitute Equation (5) into Equation (6), and we get:
[0083] It can be seen that the constructed estimation formula is reasonable.
[0084] Step 3: Use the instantaneous frequency estimated in Step 2 and the short-time Fourier transform result obtained in Step 1 for synchrosqueezing transform to perform time squeezing and reassignment;
[0085] Use the estimated instantaneous frequency and the short-time Fourier transform result \(G(t,\omega)\) for synchrosqueezing transform to perform time squeezing and reassignment, so that the energy of the zero group velocity Lamb wave is concentrated:
[0086]
[0087] In Equation (8), η is the corresponding frequency of the synchrosqueezing transform result.
[0088] Step 4: Iterate the synchrosqueezing transform result obtained in Step 3, that is, iterate the result of Equation (8);
[0089] Let Ts(t,η) = Ts [1] (t,η), and the iteration process is as follows:
[0090]
[0091] Subtract the current result from the previous result. When the difference is less than the convergence threshold or the iteration upper limit is reached, the transform result is obtained.
[0092] Step 5: Calculate the Rényi entropy value and the reconstruction accuracy of the transform result obtained in Step 4, and evaluate the transform result;
[0093] The calculation of the Rényi entropy value specifically includes:
[0094] To determine the level of energy concentration of the transform result, calculate the local Rényi entropy
[0095]
[0096] In Equation (10), θ is time, β is the interval size near time θ, and λ is the Rényi entropy order, generally taking λ = 3.
[0097] The calculation of the reconstruction accuracy specifically includes:
[0098] Calculate the local reconstruction quality factor
[0099]
[0100] where x β (θ) = [x(θ), x(θ + 1),..., x(θ + 2β)], is the reconstructed signal obtained by the inverse Fourier transform of Ts [N] (t,η).
[0101] Step 6: Use the Rényi entropy and the reconstruction accuracy calculated in Step 5 to construct a Bayesian cost function, and perform Bayesian optimization on the cost function to obtain the globally optimized window function length;
[0102] Use Equations (11) and (12) to construct a Bayesian cost function, and the expression of the constructed Bayesian cost function is as follows:
[0103]
[0104] The Bayesian optimization expression for the cost function is as follows:
[0105]
[0106] In Equation (13), l * (θ) is the window function length for global optimization.
[0107] Step 7: Use the window function length for global optimization obtained in Step 6 as the window length of the Gaussian window function to obtain a new window function. Then, perform a new operation on the new window function using the short-time Fourier transform to obtain a high-precision time-frequency diagram;
[0108] The operation of using the window function length for global optimization as the window length of the Gaussian window function to obtain a new window function means using the result of Equation (13) as the window length of the Gaussian window function to obtain a new window function. The expression is as follows:
[0109]
[0110] In Equation (14),
[0111] Then, substitute the window function of Equation (14) into Equation (4) to perform a new operation, and finally obtain a high-precision time-frequency diagram, which fully characterizes the non-stationary characteristics of the signal and ensures higher signal reconstruction quality (RQF) and lower Rényi entropy value of the result.
[0112] The present invention aims to accurately extract the ZGV characteristics. For this purpose, the method adopted not only needs to accurately reflect the non-stationary characteristics of the ZGV signal but also should have good noise recognition ability for subsequent signal identification and rejection.
[0113] The zero group velocity (ZGV) Lamb wave has non-stationary characteristics. By segmenting and intercepting the same signal and performing Fourier transform separately, it can be observed that there are significant differences in the ZGV frequencies of different time segments, as Figure 2 shown. Therefore, accurately characterizing the dynamic characteristics of the ZGV signal changing with time is the key prerequisite for analyzing and accurately extracting the ZGV signal characteristics.
[0114] From a theoretical perspective:
[0115] For an isotropic elastic material thin plate, according to the Rayleigh-Brill formula, the relationship between its frequency f and wave number k can be characterized by the following dispersion equation:
[0116]
[0117] In Equation (15), f is the guided wave frequency, h is the half-thickness of the plate, k is the wave number, c L and c T are the longitudinal wave velocity and the transverse wave velocity, respectively.
[0118] Taking a 6061 aluminum alloy plate with a thickness of 3 mm as an example, its dispersion curve is calculated by Equation (15) as Figure 3 shown. Figure 3 In the left region, a local minimum of the frequency can be observed. Figure 3 On the right is the locally enlarged schematic diagram of the observed local minimum of the frequency. It can be seen from the figure that the forward waveguide of the S1 mode and the backward waveguide of the S2b mode interfere in space, and a zero group velocity Lamb wave of the S1 mode appears. The curve of the S1 mode shows a zero point of the derivative of the angular velocity with respect to the wave number. According to the group velocity formula:
[0119]
[0120] In Equation (16), v g is the group velocity, ω is the angular frequency, and k is the wave number. At the local minimum of the frequency, the group velocity is zero, and a zero group velocity Lamb wave is generated in the plate at this time.
[0121] The simulation and experimental results show that the zero group velocity Lamb wave exhibits time-varying characteristics in the time-frequency characteristics, and its frequency will change slightly with time, which causes interference to the feature extraction of the zero group velocity Lamb wave.
[0122] As Figure 4 shown, for the analysis of non-stationary signals, a time-frequency image is used for visual representation. The time-domain signal is subjected to a short-time Fourier transform operation, and the ZGV Lamb wave frequency is about 1 MHz. Figure 4 (a) is the processing result of the Short-Time Fourier Transform (STFT). It is found that the energy is concentrated within ±0.1 MHz of the theoretical ZGV frequency, which will cause a large fluctuation in the extracted ZGV frequency; there is a serious energy leakage phenomenon in the time-frequency image extracted by STFT, resulting in inaccurate representation of the ZGV signal frequency, showing a fluctuation of about ±0.1 MHz. This error level is unacceptable for high-precision mechanical property measurements. Figure 4 (b) is the processing result of the Synchrosqueezing Transform (SST), Figure 4 (c) is the processing result of the second-order SST; although SST and the second-order SST (2nd-order SST) improve this problem to a certain extent and can show the trend of the frequency changing with time, there is still obvious energy leakage. Figure 4(d) is the treatment result of the present invention, and it can be observed that the energy concentration is greatly improved.
[0123] like Figure 5 As shown, the noisy signal was processed and the signal resolution ability of the algorithm was tested.
[0124] The normalized expression of noise is:
[0125] y=sin(2π×1MHz×(t+0.2×sin(t))) (17)
[0126] Figure 5 (a) is the result of STFT processing of noisy signals, which cannot distinguish between noise and ZGV signals; Figure 5 (b) and Figure 5 (c) The processing results of SST and second-order SST on noisy signals respectively; Figure 5 (d) is the processing result of the present invention, which successfully distinguishes the ZGV signal (yellow curve) and the noise (light blue curve). When processing a signal containing noise with a frequency close to that of the ZGV signal, the algorithm proposed by the present invention also achieves better performance and can successfully distinguish the signal from the noise component.
[0127] like Figure 6 As shown, a time-frequency diagram is obtained by processing a section of signal using the local entropy reconstruction optimization multiple synchronous compression algorithm of the present invention. In order to verify the effectiveness of the algorithm, we verified the distortion of the time-frequency diagram: first, the time-frequency diagram was inverse Fourier transformed and the signal was reconstructed; then the reconstructed signal (represented by the red dotted line) was compared with the original signal (represented by the blue solid line). The experimental results show that the reconstructed signal is highly consistent with the original signal. This observation shows that the distortion introduced by the signal processing algorithm proposed in the present invention is extremely small, thereby verifying the rationality and effectiveness of the algorithm.
[0128] Rényi entropy is a generalized form of the classic Shannon entropy. As a generalized entropy measure, it has important application value in time-frequency analysis. Rényi entropy can quantitatively characterize the compactness (Concentration) or diffusion (Diffusion) of signal energy in the time-frequency domain. Specifically, when the signal energy is highly concentrated on the time-frequency plane (such as a narrowband signal or a signal with clear modulation characteristics), the corresponding Rényi entropy value is small; conversely, when the signal energy is diffusely distributed on the time-frequency plane, the Rényi entropy value will increase. Therefore, the Rényi entropy can be used to quantitatively measure the time-frequency concentration. In the ZGV feature extraction based on time-frequency analysis, when the Rényi entropy value corresponding to the time-frequency graph generated by the algorithm is small, it reflects that the energy concentration of the time-frequency graph is high. At this time, the extracted ZGV information is usually more accurate and reliable than the time-frequency graph with a larger Rényi entropy value.
[0129] As shown in the following table, the table shows the ZGV frequencies obtained by each method, their standard deviations, and the corresponding Rényi entropy of the time-frequency diagram. The calculation of the standard deviation of the ZGV frequency is based on the weighted average of the time-frequency diagram, with the weight being the amplitude of the corresponding element points of each frequency, and the standard deviation is quantified using the weighted average standard deviation formula.
[0130]
[0131] The results show that the Rényi entropy value of the present invention is significantly lower than that of other methods, and the corresponding standard deviation of the ZGV frequency is also the smallest. According to the characteristics of the Rényi entropy, a lower entropy value indicates that the energy distribution of the extracted ZGV signal is more concentrated and less diffusive. For the same signal, the method proposed in this method obtains a lower Rényi entropy value while ensuring a higher signal reconstruction quality (RQF), indicating that it is superior to other methods. It has achieved better performance than traditional time-frequency transformation methods, thus realizing more accurate and reliable feature extraction of ZGV signals. Therefore, based on the above analysis, this method has advantages in ZGV signal extraction and better extraction effects.
[0132] The ZGV feature extraction method of the present invention based on local entropy reconstruction optimization of the multi-synchronous compression algorithm proposes an evaluation criterion based on the signal reconstruction accuracy (Reconstruction Quality Factor, RQF) and Rényi entropy. Through the Bayesian optimization algorithm, global search is carried out to determine the optimal time window length at each time point, and the optimization results are iteratively updated into the algorithm. This method can achieve adaptive global optimal time window selection and perform multi-synchronous compression transformation, thus realizing accurate extraction of zero group velocity Lamb wave features.
[0133] The above is only a preferred embodiment of the present invention and does not impose any form of limitation on the present invention. Although the present invention has been disclosed above with a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the equivalent embodiments by using the above-disclosed technical content within the scope of the technical solution of the present invention. However, as long as it does not depart from the content of the technical solution of the present invention and is based on the technical essence of the present invention, any simple modification, equivalent replacement, and improvement of the above embodiments still fall within the protection scope of the technical solution of the present invention.
Claims
1. A method for extracting ZGV features based on local entropy reconstruction and optimized multi-synchronous compression algorithm, characterized in that: The ZGV feature extraction method based on the locally entropy - reconstructed and optimized multi - synchronous compression algorithm is implemented through the following steps: Step 1: For signals with time - varying features, perform preliminary extraction using the short - time Fourier transform; Step 2: Estimate the instantaneous frequency corresponding to the short - time Fourier transform result; Step 3: Use the instantaneous frequency estimated in Step 2 and the short - time Fourier transform result obtained in Step 1 for synchronous compression transform to perform time squeezing and reassignment; Step 4: Iterate the synchronous compression transform result obtained in Step 3; Step 5: Calculate the Rényi entropy value and reconstruction accuracy of the transform result obtained in Step 4, and evaluate the transform result; Step 6: Construct a Bayesian cost function using the Rényi entropy and reconstruction accuracy calculated in Step 5, and perform Bayesian optimization on the cost function to obtain the globally optimized window function length; Step 7: Use the globally optimized window function length obtained in Step 6 as the window length of the Gaussian window function to obtain a new window function, and then perform a new operation of the short - time Fourier transform on the new window function to obtain a high - precision time - frequency diagram.
2. The ZGV feature extraction method based on the locally entropy-reconstructed optimized multi-synchronous compression algorithm according to claim 1, wherein: The specific content of the preliminary extraction using the short - time Fourier transform in Step 1 includes: Suppose there is a square - integrable signal: Window it with a square - integrable even real - valued window function g(t), and its short - time Fourier transform is as follows: Hypothesis During the research time, the amplitude A(t) and phase change small enough, neglect the high-order terms of Taylor expansion, neglect o(A'(t)) and Approximately consider that: Substitute Equation (3) into Equation (2) to get: In Equation (4) represents the Fourier transform of the window function with respect to .
3. The ZGV feature extraction method based on the locally entropy-reconstructed and optimized multi-synchronous compression algorithm according to claim 2, characterized in that: The specific content of estimating the instantaneous frequency corresponding to the short - time Fourier transform result in Step 2 includes: Take the partial derivative with respect to time t under the approximation of the obtained short-time Fourier transform result. Note that o(A'(t)) is ignored and that is, A(t) and are approximately considered constants. The approximate partial derivative is: Construct an instantaneous frequency estimation formula to estimate the instantaneous frequency corresponding to the short - time Fourier result: Substitute Equation (5) into Equation (6) to get:
4. The ZGV feature extraction method based on the locally-entropy-reconstruction-optimized multi-synchronous compression algorithm according to claim 3, wherein: The specific content of the synchronous compression transform in Step 3 includes: The estimated instantaneous frequency and the short-time Fourier transform result G(t, ω) are used for synchrosqueezing transform to perform time-squeezing reassignment, concentrating the energy of the zero-group-velocity Lamb wave: In Equation (8), η is the corresponding frequency of the synchronous squeezing transform result.
5. The ZGV feature extraction method based on the optimized multi-synchronous compression algorithm by local entropy reconstruction according to claim 4, characterized in that: The specific expression of the iteration in Step 4 is as follows: Let \(T_s(t,\eta)=T_s\) [1] (t,\eta), and the iterative process is as follows: Take the difference between the current result and the previous result. When the difference is less than the convergence threshold or reaches the iteration upper limit, the transform result is obtained.
6. The ZGV feature extraction method based on the locally entropy reconstructed optimized multi-synchronous compression algorithm according to claim 5, wherein: The specific content of the Rényi entropy value calculation in Step 5 includes: To determine the degree of energy concentration of the transformation result, the local Rényi entropy is calculated In formula (10) is time, and β is time The interval size near, λ is the Rényi entropy order, and generally λ = 3 is taken.
7. The ZGV feature extraction method based on the locally entropy-reconstructed and optimized multi-synchronous compression algorithm according to claim 6, wherein: The specific content of the reconstruction accuracy calculation in Step 5 includes: Find the local reconstruction quality factor In the formula is Ts [N] (t, η) is the reconstructed signal obtained by inverse Fourier transform.
8. The ZGV feature extraction method based on the locally entropy-reconstructed and optimized multi-synchronous compression algorithm according to claim 7, wherein: The expression of constructing the Bayesian cost function in Step 6 is as follows:
9. The ZGV feature extraction method based on the locally-entropy-reconstruction-optimized multi-synchronous compression algorithm according to claim 8, wherein: The expression of performing Bayesian optimization on the cost function in Step 6 is as follows: In formula (13) is the globally optimized window function length.
10. The ZGV feature extraction method based on the locally entropy-reconstructed optimized multi-synchronous compression algorithm according to claim 9, characterized in that: The expression of using the globally optimized window function length as the window length of the Gaussian window function to obtain a new window function in Step 7 is as follows: In formula (14),