Statistical characteristic variable window length-based under-timing variable working mode parameter identification method and device

Abstract

The invention discloses an under-timing variable working mode parameter identification method and device based on statistical characteristic variable window length, and the method comprises the steps: obtaining and processing a response signal sequence of structural vibration under the excitation of a set environment, and obtaining a processed response signal subsequence in a current sliding window, extracting a time-frequency characteristic matrix from the processed response signal sub-sequence in the current sliding window, extracting a principal component matrix from the time-frequency characteristic matrix by adopting principal component analysis, and analyzing and determining a hysteresis period by adopting an autocorrelation function; according to the time-frequency characteristic matrix, the hysteresis period and the principal component matrix of the current sliding window, estimating to obtain modal parameters of the current sliding window; calculating to obtain the statistical characteristics of the current sliding window and designing a self-adaptive window length adjustment strategy to obtain the window length of the next sliding window; and taking the next sliding window as the current sliding window, and repeating the steps. According to the method, the under-timing variable working mode parameters can be accurately identified.

Description

Technical Field

[0001] The present invention relates to the field of working modal parameter identification, and in particular to a method and a device for identifying under-timed variable working modal parameters based on statistical feature variable window length. Background Art

[0002] In practical engineering applications, modal parameter identification of dynamic systems faces many challenges, especially under time-varying and underdetermined conditions. Traditional modal parameter identification techniques are mainly aimed at time-invariant systems, assuming that the modal parameters of the system remain stable throughout the observation process. However, many engineering systems, such as bridges, rotating machinery, and transportation systems, often exhibit time-varying characteristics under different working conditions or time stages. For example, the dynamic response of a bridge under different loads will change with changes in load position and load size; speed changes in rotating machinery will cause changes in modal frequency, damping ratio, and modal vibration shape. These time-varying characteristics make it impossible for traditional modal identification methods to accurately adapt to rapidly changing system states.

[0003] Under underdetermined conditions, modal parameter identification faces even greater challenges. In practical applications, the number of modes often exceeds the observable degree due to the limited number of sensors, making the identification problem more complicated. For example, in the case of complex structures, limited sensor layout or tight costs, how to accurately extract the system's modal frequency, modal damping ratio and modal vibration shape from limited measurement data becomes a difficult problem. The traditional time-varying modal identification method based on a fixed sliding window responds to the time-varying characteristics of the system by segmenting the data, but this method has problems such as fixed window size, delayed response and insufficient accuracy. Especially in the case of rapid or drastic changes, it is impossible to capture the dynamic characteristics of the system in a timely manner.

[0004] In addition, existing time-varying modal parameter identification techniques mostly rely on rough assumptions and simple statistical analysis, which makes it difficult to deal with the information loss caused by complex dynamic changes and underdetermined conditions. In practical applications, the modal parameters of the system not only change with time, but may also be affected by external disturbances, changes in operating conditions, etc., which makes real-time and accurate modal parameter identification a challenging task. Summary of the invention

[0005] The purpose of this application is to propose a method and device for identifying under-timed variable working modal parameters based on statistical feature variable window length in response to the above-mentioned technical problems.

[0006] In a first aspect, the present invention provides a method for identifying under-timed variable working modal parameters based on statistical feature variable window length, comprising the following steps:

[0007] S1, obtaining a response signal sequence of the structural vibration under a set environmental excitation, setting the number of the sliding window in the response signal sequence, the initial window length, the minimum window length, the maximum window length and the adjustment factor, taking the first sliding window as the current sliding window, and the initial window length as the window length of the first sliding window;

[0008] S2, processing the response signal subsequence in the current sliding window in the response signal sequence to obtain the processed response signal subsequence in the current sliding window, extracting the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, and using principal component analysis to extract the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window, using an autocorrelation function to analyze the processed response signal subsequence in the current sliding window, and determining the lag period of the current sliding window;

[0009] S3, combining the time-frequency feature matrix, lag period and principal component matrix of the current sliding window to construct the third-order tensor of the current sliding window, performing CP decomposition on the third-order tensor of the current sliding window to obtain the modal response matrix of the current sliding window, and estimating the modal parameters of the current sliding window according to the modal response matrix of the current sliding window;

[0010] S4, based on the processed response signal subsequence in the current sliding window, calculate the statistical characteristics of the current sliding window, design an adaptive window length adjustment strategy according to the statistical characteristics of the current sliding window and the adjustment factor, and obtain the window length of the next sliding window; use the next sliding window as the current sliding window and repeat steps S2-S4 until the range of the current sliding window exceeds the range of the total length of the response signal sequence.

[0011] Preferably, processing the response signal subsequence in the current sliding window in the response signal sequence to obtain the processed response signal subsequence in the current sliding window specifically includes:

[0012] The response signal at each moment in the response signal subsequence within the current sliding window in the response signal sequence is standardized to obtain the signal value after the standardized processing at each moment in the current sliding window, as shown in the following formula:

[0013]

[0014] Among them, the response signal subsequence in the current sliding window is i represents the number of the sliding window, n m is the number of sensors, L i Indicates the current sliding window length, is a set of real numbers, x(t) is the response signal subsequence X in the current sliding window (i) The response signal of the tth time step in , μ1 represents the response signal subsequence X in the current sliding window (i) The mean of the response signals of all time steps in , σ1 represents the response signal subsequence X in the current sliding window (i) The standard deviation of the response signal at all time steps in , Represents the standardized signal value of the tth time step in the current sliding window;

[0015] The wavelet transform is used to denoise the standardized signal value at each moment in the current sliding window to obtain the processed response signal at each moment in the current sliding window, as shown in the following formula:

[0016]

[0017] Where W represents wavelet transform, W -1 represents the inverse wavelet transform, x denoised (t) represents the processed response signal of the tth time step in the current sliding window, and the processed response signals of all time steps in the current sliding window constitute a processed response signal subsequence in the current sliding window.

[0018] Preferably, extracting the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, extracting the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window using principal component analysis, analyzing the processed response signal subsequence in the current sliding window using an autocorrelation function, and determining the lag period of the current sliding window, specifically includes:

[0019] The wavelet transform time-frequency analysis method is used to extract the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, as shown in the following formula:

[0020]

[0021] Among them, x denoised (t) represents the processed response signal of the tth time step in the current sliding window, ψ represents the mother wavelet, a represents the scale, b represents the translation parameter, and W ψ Represents the time-frequency feature matrix of the current sliding window;

[0022] The time-frequency feature matrix of the current sliding window is input into the principal component analysis algorithm, and the eigenvector matrix and the principal component matrix are obtained by calculating the covariance matrix and performing eigendecomposition, as shown in the following formula:

[0023] Y=W ψ M;

[0024] Where Y represents the principal component matrix, and M represents the eigenvector matrix;

[0025] The autocorrelation function is used to analyze the periodic characteristics of the processed response signal subsequence in the current sliding window to obtain the autocorrelation function curve, as shown in the following formula:

[0026]

[0027] Among them, ACF(l) represents the peak value corresponding to different lag periods in the autocorrelation function curve, L i represents the window length of the current sliding window, l represents the lag period, and μ2 represents the mean of the processed response signals of all time steps in the current sliding window;

[0028] Determine each lag period l of the current sliding window according to the significant peak in the autocorrelation function curve g , where g = 1, 2…, s, s represents the total number of lag periods of the current sliding window.

[0029] Preferably, step S3 specifically includes:

[0030] Initialize a third-order tensor X , for each lag period l g For a third-order tensor X Fill the third dimension, assuming that the time-frequency feature matrix W of the current sliding window ψ is an N×m matrix, then the time-frequency feature corresponding to each time step t is X[t,:], and for each lag period l g , from the time-frequency feature matrix W of the current sliding window ψ Extract a length L i +1 for the data snippet:

[0031] X l =X[t+l g ,:];

[0032] Among them, X l Represents a data segment, t=1,2,...,L i , L i Indicates the current sliding window length;

[0033] Then fill the third-order tensor to get the filled third-order tensor:

[0034] X[t,j,l g ]=Wavelet Feature(X l ,j);

[0035] Among them, X[t,j,l g ] represents the third-order tensor after filling, j represents the frequency dimension from the principal component matrix, and Wavelet Feature represents the data segment X through wavelet transform. l Extract features in frequency dimension j;

[0036] Perform CP decomposition on the filled third-order tensor to obtain the modal vibration matrix Φ, modal response matrix Q, and modal weight matrix Θ, as shown in the following formula:

[0037]

[0038] in, represents the outer product multiplication of vectors, and R represents the rank of CP decomposition;

[0039] The column vectors in the modal response matrix are processed by Fourier transform to estimate the modal parameters of the current sliding window, where the modal parameters of the current sliding window include the natural frequency.

[0040] Preferably, the statistical features of the current sliding window are calculated based on the processed response signal subsequence in the current sliding window, specifically including:

[0041] Estimate the probability density of the processed response signal subsequence in the current sliding window. First, select an interval to divide the value range of the processed response signal subsequence in the current sliding window. Assume that the number of intervals is N. bins , the width of each interval is Δx, and the frequency of each interval is obtained by bucketing the processed response signal subsequence in the current sliding window, and then standardized into probability density, as shown in the following formula:

[0042]

[0043] Among them, p(x denoised (t)) represents the processed response signal x at the tth time step in the current sliding window denoised The probability density at (t), L i represents the current sliding window length, u represents the uth interval, h(x denoised (t)-x denoised (u)) represents the indicator function, when x denoised (t) falls within the interval [x denoised (u),x denoised (u)+Δx], the indicator function is 1, otherwise the indicator function is 0;

[0044] The standard deviation σ2 of the processed response signal of all time steps in the current sliding window is estimated according to the probability density, as shown in the following formula:

[0045]

[0046] The skewness γ is calculated using the following formula:

[0047]

[0048] Among them, E[(x denoised (t)-μ2) 3 ] represents the third-order central moment of the processed response signal subsequence in the current sliding window. When the skewness γ=0, the processed response signal subsequence in the current sliding window is symmetrically distributed; when γ>0, the distribution of the processed response signal subsequence in the current sliding window is positively skewed; when γ<0, the distribution of the processed response signal subsequence in the current sliding window is negatively skewed;

[0049] The kurtosis δ is calculated using the following formula:

[0050]

[0051] Among them, E[(x denoised (t)-μ2) 4 ] is the fourth-order central moment of the processed response signal subsequence in the current sliding window. When the kurtosis δ=0, the distribution shape of the processed response signal subsequence in the current sliding window is similar to the normal distribution. When δ>0, the distribution of the processed response signal subsequence in the current sliding window is sharper than the normal distribution. When δ<0, the distribution of the processed response signal subsequence in the current sliding window is flatter than the normal distribution.

[0052] For the processed response signal subsequence in the current sliding window, the self-mutual information of the processed response signal subsequence in the current sliding window between different time periods is calculated by selecting the time delay τ, as shown in the following formula:

[0053]

[0054] Among them, x denoised (t+τ) represents the processed response signal at the t+τth time step in the current sliding window, p(x c ,x o ) represents the joint probability distribution of the processed response signal subsequence in the current sliding window at time steps t and t+τ, p(x c ) and p(x o ) represent the processed response signal subsequences in the current sliding window at time step x c and x o The probability density of .

[0055] Preferably, an adaptive window length adjustment strategy is designed according to the statistical characteristics of the current sliding window to obtain the window length of the next sliding window, specifically including:

[0056] Combining probability density, kurtosis, skewness and self-mutual information, the adaptive window length adjustment strategy is designed as shown in the following formula:

[0057]

[0058] Among them, L i+1 represents the window length of the next sliding window, and α, β1, β2, and β3 represent adjustment factors.

[0059] In a second aspect, the present invention provides a method for identifying under-timed variable working modal parameters based on statistical feature variable window length, comprising:

[0060] The data acquisition module is configured to acquire a response signal sequence of the structural vibration under a set environmental excitation, set the number of the sliding window in the response signal sequence, the initial window length, the minimum window length, the maximum window length and the adjustment factor, and use the first sliding window as the current sliding window and the initial window length as the window length of the first sliding window;

[0061] The data processing module is configured to process the response signal subsequence in the current sliding window in the response signal sequence to obtain the processed response signal subsequence in the current sliding window, extract the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, and use principal component analysis to extract the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window, and use autocorrelation function to analyze the processed response signal subsequence in the current sliding window to determine the lag period of the current sliding window;

[0062] The modal parameter identification module is configured to combine the time-frequency feature matrix, the lag period and the principal component matrix of the current sliding window to construct the third-order tensor of the current sliding window, perform CP decomposition on the third-order tensor of the current sliding window to obtain the modal response matrix of the current sliding window, and estimate the modal parameters of the current sliding window according to the modal response matrix of the current sliding window;

[0063] The window length adjustment module is configured to calculate the statistical characteristics of the current sliding window based on the processed response signal subsequence in the current sliding window, design an adaptive window length adjustment strategy according to the statistical characteristics of the current sliding window and the adjustment factor, and obtain the window length of the next sliding window; use the next sliding window as the current sliding window and repeatedly execute the data processing module to the window length adjustment module until the range of the current sliding window exceeds the range of the total length of the response signal sequence.

[0064] In a third aspect, the present invention provides an electronic device comprising one or more processors; a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the method described in any implementation manner in the first aspect.

[0065] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in any implementation manner in the first aspect.

[0066] In a fifth aspect, the present invention provides a computer program product, comprising a computer program, which, when executed by a processor, implements the method described in any implementation manner in the first aspect.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] (1) The under-time-varying working modal parameter identification method based on statistical characteristic variable window length proposed by the present invention dynamically adjusts the window length by introducing statistical characteristics such as signal kurtosis, skewness, mutual information, etc., so as to adapt to the changing characteristics of the signal in real time. This adaptive window length adjustment strategy can effectively cope with the dynamic changes of signals in time-varying systems, and is particularly suitable for real-time monitoring and modal identification of large-scale structures (such as bridges, wind turbines, etc.).

[0069] (2) The underdetermined variable working modal parameter identification method based on statistical feature variable window length proposed in the present invention is particularly aimed at the situation where the number of sensors is less than the number of modes to be identified. It can accurately extract modal information under underdetermined conditions, solving the problem of incomplete modal information identification due to insufficient sensors in traditional methods.

[0070] (3) The under-timed variable working modal parameter identification method based on statistical feature variable window length proposed in this invention explores and analyzes the complex structure and dynamic characteristics in multi-dimensional time series data by integrating signal normalization, wavelet denoising, dynamic sliding window, wavelet transform and tensor decomposition. It is particularly suitable for processing large, high-dimensional and time-dependent data sets, such as vehicle dynamics systems, bridges and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0072] Figure 1A flow chart of an under-timed variable working modal parameter identification method based on a statistical feature variable window length according to an embodiment of the present application;

[0073] Figure 2 A comparison diagram of the modal vibration shapes identified at 200.625s by the under-timed variable working modal parameter identification method based on statistical feature variable window length according to an embodiment of the present application;

[0074] Figure 3 A comparison diagram of the modal vibration shapes identified in 500s by the under-time variable working modal parameter identification method based on statistical feature variable window length according to an embodiment of the present application;

[0075] Figure 4 A schematic diagram of a dual-entity model calculation process of an under-timed variable working modal parameter identification method based on a statistical feature variable window length according to an embodiment of the present application;

[0076] Figure 5 A comparison diagram of the natural frequency variation curve identified by the under-time-varying working modal parameter identification method based on statistical characteristic variable window length according to an embodiment of the present application and the theoretical natural frequency variation curve of the three-degree-of-freedom time-varying structure;

[0077] Figure 6 A curve diagram of MAC value variation of a three-degree-of-freedom time-varying system identified by an under-time-varying working modal parameter identification method based on a statistical feature variable window length according to an embodiment of the present application;

[0078] Figure 7 It is a schematic diagram of an under-timed variable working modal parameter identification device based on a statistical feature variable window length according to an embodiment of the present application;

[0079] Figure 8 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0081] Figure 1 An under-timed variable working modal parameter identification method based on a statistical feature variable window length provided in an embodiment of the present application is shown, comprising the following steps:

[0082] S1, obtain the response signal sequence of the structural vibration under the set environmental excitation, set the sliding window number, initial window length, minimum window length, maximum window length and adjustment factor in the response signal sequence, take the first sliding window as the current sliding window, and the initial window length as the window length of the first sliding window.

[0083] Specifically, a response signal sequence of the linear structure vibration of the selected sensor (the number of sensors is less than the number of degrees of freedom) measuring point under the set environmental excitation is obtained, the length of the response signal sequence is T, and the number of the sliding window in the response signal sequence, the initial window length, the minimum window length, the maximum window length and the adjustment factor are set. The number i of the sliding window increases from 1 in sequence according to the sliding step length of the sliding window. In the embodiment of the present application, the sliding step length of the sliding window defaults to 1. In other embodiments, the sliding step length of the sliding window can select other values.

[0084] S2, processing the response signal subsequence within the current sliding window in the response signal sequence to obtain the processed response signal subsequence within the current sliding window, extracting the time-frequency feature matrix of the current sliding window from the processed response signal subsequence within the current sliding window, and using principal component analysis to extract the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window, using autocorrelation function to analyze the processed response signal subsequence within the current sliding window to determine the lag period of the current sliding window.

[0085] In a specific embodiment, processing a response signal subsequence in a current sliding window in a response signal sequence to obtain a processed response signal subsequence in the current sliding window specifically includes:

[0086] The response signal at each moment in the response signal subsequence within the current sliding window in the response signal sequence is standardized to obtain the signal value after the standardized processing at each moment in the current sliding window, as shown in the following formula:

[0087]

[0088] Among them, the response signal subsequence in the current sliding window is i represents the number of the sliding window, n m is the number of sensors, L i Indicates the current sliding window length, is a set of real numbers, x(t) is the response signal subsequence X in the current sliding window (i) The response signal of the tth time step in , μ1 represents the response signal subsequence X in the current sliding window (i)The mean of the response signals of all time steps in , σ1 represents the response signal subsequence X in the current sliding window (i) The standard deviation of the response signal at all time steps in , Represents the standardized signal value of the tth time step in the current sliding window;

[0089] The wavelet transform is used to denoise the standardized signal value at each moment in the current sliding window to obtain the processed response signal at each moment in the current sliding window, as shown in the following formula:

[0090]

[0091] Where W represents wavelet transform, W -1 represents the inverse wavelet transform, x denoised (t) represents the processed response signal of the tth time step in the current sliding window, and the processed response signals of all time steps in the current sliding window constitute a processed response signal subsequence in the current sliding window.

[0092] In a specific embodiment, extracting the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, extracting the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window using principal component analysis, analyzing the processed response signal subsequence in the current sliding window using an autocorrelation function, and determining the lag period of the current sliding window, specifically includes:

[0093] The wavelet transform time-frequency analysis method is used to extract the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, as shown in the following formula:

[0094]

[0095] Among them, x denoised (t) represents the processed response signal of the tth time step in the current sliding window, ψ represents the mother wavelet, a represents the scale, b represents the translation parameter, and W ψ Represents the time-frequency feature matrix of the current sliding window;

[0096] The time-frequency feature matrix of the current sliding window is input into the principal component analysis algorithm, and the eigenvector matrix and the principal component matrix are obtained by calculating the covariance matrix and performing eigendecomposition, as shown in the following formula:

[0097] Y=W ψ M;

[0098] Where Y represents the principal component matrix, and M represents the eigenvector matrix;

[0099] The autocorrelation function is used to analyze the periodic characteristics of the processed response signal subsequence in the current sliding window to obtain the autocorrelation function curve, as shown in the following formula:

[0100]

[0101] Among them, ACF(l) represents the peak value corresponding to different lag periods in the autocorrelation function curve, L i represents the window length of the current sliding window, l represents the lag period, and μ2 represents the mean of the processed response signals of all time steps in the current sliding window;

[0102] Determine each lag period l of the current sliding window according to the significant peak in the autocorrelation function curve g , where g = 1, 2…, s, s represents the total number of lag periods of the current sliding window.

[0103] Specifically, the response signal subsequence in the current sliding window is first standardized, and then the signal is denoised using wavelet transform to retain the main components of the signal and remove high-frequency noise. By extracting the time spectrum features through the wavelet transform time-frequency analysis method, not only can the amplitude information of the signal be obtained, but also the frequency characteristics of the signal changing over time can be captured. The use of wavelet transform to extract the multi-scale features of the signal is particularly effective for non-stationary signals. Finally, principal component analysis (PCA) is used to extract the principal component features from the time-frequency features of the signal and the autocorrelation function (ACF) analysis is used to determine the lag period of the current sliding window.

[0104] S3, the time-frequency feature matrix, lag period and principal component matrix of the current sliding window are combined to construct the third-order tensor of the current sliding window, the third-order tensor of the current sliding window is decomposed by CP to obtain the modal response matrix of the current sliding window, and the modal parameters of the current sliding window are estimated according to the modal response matrix of the current sliding window.

[0105] In a specific embodiment, step S3 specifically includes:

[0106] Initialize a third-order tensor X , for each lag period l g For a third-order tensor X Fill the third dimension, assuming that the time-frequency feature matrix W of the current sliding window ψ is an N×m matrix, then the time-frequency feature corresponding to each time step t is X[t,:], and for each lag period l g , from the time-frequency feature matrix W of the current sliding window ψ Extract a length L i +1 for the data snippet:

[0107] X l =X[t+l g ,:];

[0108] Among them, X l Represents a data segment, t=1,2,...,L i , L i Indicates the current sliding window length;

[0109] Then fill the third-order tensor to get the filled third-order tensor:

[0110] X [t,j,l g ]=Wavelet Feature(X l ,j);

[0111] in, X [t,j,l g ] represents the third-order tensor after filling, j represents the frequency dimension from the principal component matrix, and Wavelet Feature represents the data segment X through wavelet transform. l Extract features in frequency dimension j;

[0112] Perform CP decomposition on the filled third-order tensor to obtain the modal vibration matrix Φ, modal response matrix Q, and modal weight matrix Θ, as shown in the following formula:

[0113]

[0114] in, represents the outer product multiplication of vectors, and R represents the rank of CP decomposition;

[0115] The column vectors in the modal response matrix are processed by Fourier transform to estimate the modal parameters of the current sliding window, where the modal parameters of the current sliding window include the natural frequency.

[0116] Specifically, the first dimension uses the time step t, the second dimension uses the frequency dimension of the current sliding window extracted from the principal component matrix, and the lag period is calculated based on the autocorrelation function (ACF), which is used to extract the time dependence of the signal and define the length of the data segment. g It is the time window parameter used to split the time-frequency feature matrix of the current sliding window. The length of the window is L i +1, used to construct the third dimension of the third-order tensor, thereby obtaining the filled third-order tensor, and performing CP decomposition on the filled third-order tensor to obtain three factor matrices Φ, Q, and Θ; is the mode shape matrix, Q∈R N×Ris the modal response matrix. The column vectors in the modal response matrix can be processed by Fourier transform to estimate the natural frequency w corresponding to each mode. i , you can get the modal parameters of the current sliding window.

[0117] S4, based on the processed response signal subsequence in the current sliding window, calculate the statistical characteristics of the current sliding window, design an adaptive window length adjustment strategy according to the statistical characteristics of the current sliding window and the adjustment factor, and obtain the window length of the next sliding window; use the next sliding window as the current sliding window and repeat steps S2-S4 until the range of the current sliding window exceeds the range of the total length of the response signal sequence.

[0118] In a specific embodiment, the statistical features of the current sliding window are calculated based on the processed response signal subsequence in the current sliding window, specifically including:

[0119] Estimate the probability density of the processed response signal subsequence in the current sliding window. First, select an interval to divide the value range of the processed response signal subsequence in the current sliding window. Assume that the number of intervals is N. bins , the width of each interval is Δx, and the frequency of each interval is obtained by bucketing the processed response signal subsequence in the current sliding window, and then standardized into probability density, as shown in the following formula:

[0120]

[0121] Among them, p(x denoised (t)) represents the processed response signal x at the tth time step in the current sliding window denoised The probability density at (t), L i represents the current sliding window length, u represents the uth interval, h(x denoised (t)-x denoised (u)) represents the indicator function, when x denoised (t) falls within the interval [x denoised (u),x denoised (u)+Δx], the indicator function is 1, otherwise the indicator function is 0;

[0122] The standard deviation σ2 of the processed response signal of all time steps in the current sliding window is estimated according to the probability density, as shown in the following formula:

[0123]

[0124] The skewness γ is calculated using the following formula:

[0125]

[0126] Among them, E[(x denoised (t)-μ2) 3 ] represents the third-order central moment of the processed response signal subsequence in the current sliding window. When the skewness γ=0, the processed response signal subsequence in the current sliding window is symmetrically distributed; when γ>0, the distribution of the processed response signal subsequence in the current sliding window is positively skewed; when γ<0, the distribution of the processed response signal subsequence in the current sliding window is negatively skewed;

[0127] The kurtosis δ is calculated using the following formula:

[0128]

[0129] Among them, E[(x denoised (t)-μ2) 4 ] is the fourth-order central moment of the processed response signal subsequence in the current sliding window. When the kurtosis δ=0, the distribution shape of the processed response signal subsequence in the current sliding window is similar to the normal distribution. When δ>0, the distribution of the processed response signal subsequence in the current sliding window is sharper than the normal distribution. When δ<0, the distribution of the processed response signal subsequence in the current sliding window is flatter than the normal distribution.

[0130] For the processed response signal subsequence in the current sliding window, the self-mutual information of the processed response signal subsequence in the current sliding window between different time periods is calculated by selecting the time delay τ, as shown in the following formula:

[0131]

[0132] Among them, x denoised (t+τ) represents the processed response signal at the t+τth time step in the current sliding window, p(x c ,x o ) represents the joint probability distribution of the processed response signal subsequence in the current sliding window at time steps t and t+τ, p(x c ) and p(x o ) represent the processed response signal subsequences in the current sliding window at time step x c and x o The probability density of .

[0133] In a specific embodiment, an adaptive window length adjustment strategy is designed according to the statistical characteristics of the current sliding window to obtain the window length of the next sliding window, specifically including:

[0134] Combining probability density, kurtosis, skewness and self-mutual information, the adaptive window length adjustment strategy is designed as shown in the following formula:

[0135]

[0136] Among them, L i+1 represents the window length of the next sliding window, and α, β1, β2, and β3 represent adjustment factors.

[0137] Specifically, the statistical features include probability density, kurtosis, skewness and self-mutual information, which are used to describe the continuous time series signal x in the current sliding window. denoised (t) Estimate the probability density and select an appropriate interval to divide the value range of the signal. By performing a bucket design on the signal data, the frequency of each interval is obtained and then standardized to the probability density. According to the calculated probability density, the standard deviation σ2 of the signal is estimated, which reflects the volatility of the signal. The skewness can measure the asymmetry of the signal distribution. The kurtosis can measure the sharpness of the signal distribution. The mutual information of the signal between different time periods can measure the time correlation of the signal and reflect the time dependence of the signal. α, β1, β2 and β3 are adjusted, therefore, they are used to control the weights of each feature in the window size adjustment.

[0138] In one embodiment, if the signal has a strong correlation in time (larger self-mutual information, i.e., I>0.5), small fluctuations (smaller standard deviation), and a relatively stable distribution (smaller skewness and kurtosis, i.e., γ→0, δ<3), the window can be increased to capture more global information; if the signal changes rapidly (smaller self-mutual information, larger standard deviation) and has strong asymmetry or sharp peaks (larger skewness and kurtosis), the window should be reduced to better capture local changes.

[0139] After the window length of the next sliding window is adjusted, the current sliding window slides forward to the next (i+1) sliding window, and the modal parameters in the next sliding window are calculated; that is, the next sliding window is used as the current sliding window (i=i+1) and steps S2-S4 are repeated until the range of the current sliding window exceeds the range of the total length of the response signal sequence, that is, when i>TL i +1, then stop repeating steps S2-S4, and finally obtain the modal parameters of each sliding window.

[0140] A linear time-varying three-degree-of-freedom spring oscillator system is used below to verify the under-time-varying working modal parameter identification method based on statistical characteristic variable window length proposed in the embodiment of the present application.

[0141] Assume that the sampling frequency f is 40 Hz, the sampling interval Δt is 0.025 s, and the sampling time is t=2000 s.

[0142] Assume that the initial conditions of the three-degree-of-freedom displacements of the three-degree-of-freedom spring oscillator system are all zero, apply Gaussian white noise excitation to the first block, and set the mass of the first block to:

[0143]

[0144] Among them, m1 represents the mass of the first block, m2 represents the mass of the second block, m3 represents the mass of the third block, m2=m3=1kg, the stiffness of the first block, the second block and the third block are: k1=1000N / m, k2=1000N / m, k3=1000N / m; the damping of the first block, the second block and the third block are:

[0145] c1=0.01Ns / m, c2=0.01Ns / m, c3=0.01Ns / m.

[0146] Then the three-degree-of-freedom spring oscillator system was experimented. The response signal was obtained by simulation using MATLAB / Newmark-β. The sampling frequency of the response signal was 40Hz, the sampling time was t=2000s, and the sampling interval was 0.025s. The Gaussian white noise excitation applied by the first object and the simulated response signal are shown in Figure 2 shown.

[0147] In this experiment, the modal assurance criterion (MAC) and the relative error of modal natural frequency are used to compare and evaluate the under-time varying operating modal parameter identification methods of linear time-varying structures.

[0148] The formula of the modal confidence criterion is as follows:

[0149]

[0150] in, and They represent the estimated modal vibration shape vector of the i-th order and the true modal vibration shape vector, respectively, and the MAC value varies between 0 and 1. The larger the MAC value (closer to 1), the better the vibration shape.

[0151] The formula for the natural frequency relative error evaluation method is as follows:

[0152]

[0153] Among them, ω q With ω q-theory denote the qth-order estimated modal natural frequency and the theoretical natural frequency, ζ q The closer the value is to 0, the more accurate the identified natural frequency is.

[0154] The MAC values ​​of the three-degree-of-freedom spring oscillator system in this experiment at 230s and 720s are shown in Tables 1 and 2, and the relative error results of the natural frequency are shown in Table 3. The instantaneous vibration modes identified by the under-time-varying working modal parameter identification method based on statistical characteristic variable window length at different times of 200.625s and 500s and the comparison results of the natural vibration modes of the three-degree-of-freedom time-varying system are shown in Tables 1 and 2. Figure 3 and Figure 4 As shown, Figure 5 and Figure 6 They are the comparison results of the natural frequency curve and the identification frequency curve at different times and the MAC curve change curve at different times. Figure 3-6 It can be seen that the under-time-varying working modal parameter identification method based on statistical characteristic variable window length proposed in the embodiment of the present application can well realize the identification of modal parameters under under-time-varying conditions. Not only is the relative error of the natural frequency small, but the identified vibration mode is also better.

[0155] Table 1 Confidence criteria of each modal at 230s

[0156]

[0157] Table 2 Confidence criteria of each modal at 720s

[0158]

[0159] Table 3 Natural frequency errors of each order

[0160]

[0161] Further references Figure 7 As an implementation of the methods shown in the above figures, the present application provides an embodiment of an under-timed variable working modal parameter identification device based on a statistical feature variable window length, and the device embodiment is similar to Figure 1 Corresponding to the method embodiment shown, the device can be specifically applied to various electronic devices.

[0162] The embodiment of the present application further proposes a method for identifying under-timed variable working modal parameters based on statistical feature variable window length, comprising:

[0163] The data acquisition module 1 is configured to acquire a response signal sequence of the structural vibration under a set environmental excitation, set the number of the sliding window in the response signal sequence, the initial window length, the minimum window length, the maximum window length and the adjustment factor, and use the first sliding window as the current sliding window and the initial window length as the window length of the first sliding window;

[0164] The data processing module 2 is configured to process the response signal subsequence in the current sliding window in the response signal sequence to obtain the processed response signal subsequence in the current sliding window, extract the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, and use principal component analysis to extract the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window, and use autocorrelation function to analyze the processed response signal subsequence in the current sliding window to determine the lag period of the current sliding window;

[0165] The modal parameter identification module 3 is configured to combine the time-frequency feature matrix, the lag period and the principal component matrix of the current sliding window to construct the third-order tensor of the current sliding window, perform CP decomposition on the third-order tensor of the current sliding window to obtain the modal response matrix of the current sliding window, and estimate the modal parameters of the current sliding window according to the modal response matrix of the current sliding window;

[0166] The window length adjustment module 4 is configured to calculate the statistical characteristics of the current sliding window based on the processed response signal subsequence in the current sliding window, design an adaptive window length adjustment strategy according to the statistical characteristics of the current sliding window and the adjustment factor, and obtain the window length of the next sliding window; take the next sliding window as the current sliding window and repeatedly execute the data processing module to the window length adjustment module until the range of the current sliding window exceeds the range of the total length of the response signal sequence.

[0167] Figure 8 Schematic diagram of the hardware structure of the electronic device provided by the embodiment of the present invention. Figure 8 As shown, the electronic device of this embodiment includes: a processor 801 and a memory 802; wherein the memory 802 is used to store computer-executable instructions; the processor 801 is used to execute the computer-executable instructions stored in the memory to implement the various steps performed by the electronic device in the above embodiment. For details, please refer to the relevant description in the above method embodiment.

[0168] Optionally, the memory 802 may be independent or integrated with the processor 801 .

[0169] When the memory 802 is independently provided, the electronic device further includes a bus 803 for connecting the memory 802 and the processor 801 .

[0170] The embodiment of the present invention further provides a computer storage medium, in which computer execution instructions are stored. When the processor 801 executes the computer execution instructions, the above method is implemented.

[0171] The embodiment of the present invention further provides a computer program product, including a computer program. When the computer program is executed by the processor 801, the above method is implemented.

[0172] In the embodiments provided by the present invention, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic, for example, the division of modules is only a logical function division, and there may be other division methods in actual implementation, such as multiple modules can be combined or integrated into another system, or some features can be ignored or not executed. Another point, the mutual coupling or direct coupling or communication connection shown or discussed can be an indirect coupling or communication connection through some interfaces, devices or modules, which can be electrical, mechanical or other forms.

[0173] The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the modules may be selected according to actual needs to implement the solution of this embodiment.

[0174] In addition, each functional module in each embodiment of the present invention may be integrated into one processing unit, each module may exist physically separately, or two or more modules may be integrated into one unit. The unit formed by the above modules may be implemented in the form of hardware or in the form of hardware plus software functional units.

[0175] The above-mentioned integrated module implemented in the form of a software function module can be stored in a computer-readable storage medium. The above-mentioned software function module is stored in a storage medium, including a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor 801 to perform some steps of the methods of various embodiments of the present application.

[0176] It should be understood that the processor 801 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), etc. A general-purpose processor may be a microprocessor or the processor 801 may be any conventional processor 801, etc. The steps of the method disclosed in the invention may be directly embodied in the hardware processor 801 for execution, or may be executed by a combination of hardware and software modules in the processor 801.

[0177] The memory 802 may include a high-speed RAM memory, and may also include a non-volatile storage NVM, such as at least one disk memory, and may also be a USB flash drive, a mobile hard disk, a read-only memory, a magnetic disk or an optical disk.

[0178] The bus 803 may be an Industry Standard Architecture (ISA), a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus 803 may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, the bus 803 in the drawings of the present application is not limited to only one bus 803 or one type of bus 803.

[0179] The above storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk. The storage medium can be any available medium that can be accessed by a general or special purpose computer.

[0180] An exemplary storage medium is coupled to the processor 801, so that the processor 801 can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor 801. The processor 801 and the storage medium can be located in an application specific integrated circuit (ASIC). Of course, the processor 801 and the storage medium can also exist as discrete components in an electronic device or a main control device.

[0181] Those skilled in the art can understand that all or part of the steps of implementing the above-mentioned method embodiments can be completed by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, the steps of the above-mentioned method embodiments are executed; and the aforementioned storage medium includes: ROM, RAM, disk or optical disk and other media that can store program codes.

[0182] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for identifying under-timed variable working modal parameters based on statistical feature variable window length, characterized in that: The following steps are involved: S1, obtaining a response signal sequence of the structural vibration under a set environmental excitation, setting the number of the sliding window in the response signal sequence, the initial window length, the minimum window length, the maximum window length and the adjustment factor, taking the first sliding window as the current sliding window, and the initial window length as the window length of the first sliding window; S2, processing the response signal subsequence in the current sliding window of the response signal sequence to obtain a processed response signal subsequence in the current sliding window, extracting the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, and using principal component analysis to extract the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window, and using an autocorrelation function to analyze the processed response signal subsequence in the current sliding window to determine the lag period of the current sliding window; S3, combining the time-frequency feature matrix, lag period and principal component matrix of the current sliding window to construct a third-order tensor of the current sliding window, performing CP decomposition on the third-order tensor of the current sliding window to obtain a modal response matrix of the current sliding window, and estimating modal parameters of the current sliding window according to the modal response matrix of the current sliding window; S4, calculating the statistical characteristics of the current sliding window based on the processed response signal subsequence within the current sliding window, designing an adaptive window length adjustment strategy according to the statistical characteristics of the current sliding window and the adjustment factor, and obtaining the window length of the next sliding window; taking the next sliding window as the current sliding window and repeating steps S2-S4 until the range of the current sliding window exceeds the range of the total length of the response signal sequence.

2. The under-time variable working modal parameter identification method based on statistical feature variable window length according to claim 1 is characterized in that: Processing a response signal subsequence in a current sliding window in the response signal sequence to obtain a processed response signal subsequence in the current sliding window specifically includes: The response signal at each moment in the response signal subsequence within the current sliding window in the response signal sequence is standardized to obtain the signal value after the standardized processing at each moment in the current sliding window, as shown in the following formula: Among them, the response signal subsequence in the current sliding window is i represents the number of the sliding window, n m is the number of sensors, L i Indicates the current sliding window length, is a set of real numbers, x(t) is the response signal subsequence X in the current sliding window (i) The response signal of the tth time step in , μ1 represents the response signal subsequence X in the current sliding window (i) The mean of the response signals of all time steps in , σ1 represents the response signal subsequence X in the current sliding window (i) The standard deviation of the response signal at all time steps in , Represents the standardized signal value of the tth time step in the current sliding window; The wavelet transform is used to denoise the standardized signal value at each moment in the current sliding window to obtain the processed response signal at each moment in the current sliding window, as shown in the following formula: Where W represents wavelet transform, W -1 represents the inverse wavelet transform, x denoised (t) represents the processed response signal of the tth time step in the current sliding window, and the processed response signals of all time steps in the current sliding window constitute a processed response signal subsequence in the current sliding window.

3. The under-time variable working modal parameter identification method based on statistical feature variable window length according to claim 1 is characterized in that: Extracting the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, extracting the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window using principal component analysis, analyzing the processed response signal subsequence in the current sliding window using an autocorrelation function, and determining the lag period of the current sliding window, specifically including: The wavelet transform time-frequency analysis method is used to extract the time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, as shown in the following formula: Among them, x denoised (t) represents the processed response signal of the tth time step in the current sliding window, ψ represents the mother wavelet, a represents the scale, b represents the translation parameter, and W ψ Represents the time-frequency feature matrix of the current sliding window; The time-frequency feature matrix of the current sliding window is input into the principal component analysis algorithm, and the eigenvector matrix and the principal component matrix are obtained by calculating the covariance matrix and performing eigendecomposition, as shown in the following formula: Y=W ψ M; Where Y represents the principal component matrix, and M represents the eigenvector matrix; The autocorrelation function is used to analyze the periodic characteristics of the processed response signal subsequence in the current sliding window to obtain an autocorrelation function curve, as shown in the following formula: Among them, ACF(l) represents the peak value corresponding to different lag periods in the autocorrelation function curve, L i represents the window length of the current sliding window, l represents the lag period, and μ2 represents the mean of the processed response signals of all time steps in the current sliding window; Determine each lag period l of the current sliding window according to the significant peak in the autocorrelation function curve g , where g = 1, 2…, s, s represents the total number of lag periods of the current sliding window.

4. The under-time variable working modal parameter identification method based on statistical feature variable window length according to claim 3 is characterized in that: Step S3 specifically includes: Initialize a third-order tensor For each lag period l g For the third-order tensor The third dimension is filled, assuming that the time-frequency feature matrix W of the current sliding window ψ is an N×m matrix, then the time-frequency feature corresponding to each time step t is X[t,:], and for each lag period l g , from the time-frequency feature matrix W of the current sliding window ψ Extract a length L i +1 for the data snippet: X l =X[t+l g ,:]; Among them, X l Represents a data segment, t=1,2,...,L i , L i Indicates the current sliding window length; Then fill the third-order tensor to get the filled third-order tensor: in, represents the third-order tensor after filling, j represents the frequency dimension from the principal component matrix, and Wavelet Feature represents the data segment X through wavelet transform. l Extract features on the frequency dimension j; The filled third-order tensor is subjected to CP decomposition to obtain the modal vibration matrix Φ, the modal response matrix Q, and the modal weight matrix Θ, as shown in the following formula: in, represents the outer product multiplication of vectors, and R represents the rank of CP decomposition; The column vectors in the modal response matrix are processed by Fourier transform to estimate the modal parameters of the current sliding window, where the modal parameters of the current sliding window include the natural frequency.

5. The under-time variable working modal parameter identification method based on statistical feature variable window length according to claim 1 is characterized in that: The statistical features of the current sliding window are calculated based on the processed response signal subsequence in the current sliding window, specifically including: The probability density of the processed response signal subsequence in the current sliding window is estimated. First, an interval is selected to divide the value range of the processed response signal subsequence in the current sliding window. Assume that the number of intervals is N. bins , the width of each interval is Δx, and the frequency of each interval is obtained by performing bucket design on the processed response signal subsequence in the current sliding window, and then standardized into probability density, as shown in the following formula: Among them, p(x denoised (t)) represents the processed response signal x at the tth time step in the current sliding window denoised The probability density at (t), L i represents the current sliding window length, u represents the uth interval, h(x denoised (t)-x denoised (u)) represents the indicator function, when x denoised (t) falls within the interval [x denoised (u),x denoised (u)+Δx], the indicator function is 1, otherwise the indicator function is 0; The standard deviation σ2 of the processed response signal of all time steps in the current sliding window is estimated according to the probability density, as shown in the following formula: The skewness γ is calculated using the following formula: Among them, E[(x denoised (t)-μ2) 3 ] represents the third-order central moment of the processed response signal subsequence in the current sliding window. When the skewness γ=0, the processed response signal subsequence in the current sliding window is symmetrically distributed; when γ>0, the distribution of the processed response signal subsequence in the current sliding window is positively skewed; when γ<0, the distribution of the processed response signal subsequence in the current sliding window is negatively skewed; The kurtosis δ is calculated using the following formula: Among them, E[(x denoised (t)-μ2) 4 ] is the fourth-order central moment of the processed response signal subsequence in the current sliding window. When the kurtosis δ=0, the distribution shape of the processed response signal subsequence in the current sliding window is similar to the normal distribution. When δ>0, the distribution of the processed response signal subsequence in the current sliding window is sharper than the normal distribution. When δ<0, the distribution of the processed response signal subsequence in the current sliding window is flatter than the normal distribution. For the processed response signal subsequence in the current sliding window, the self-mutual information of the processed response signal subsequence in the current sliding window between different time periods is calculated by selecting the time delay τ, as shown in the following formula: Among them, x denoised (t+τ) represents the processed response signal at the t+τth time step in the current sliding window, p(x c ,x o ) represents the joint probability distribution of the processed response signal subsequence in the current sliding window at time steps t and t+τ, p(x c ) and p(x o ) represent the processed response signal subsequences in the current sliding window at time step x c and x o The probability density of .

6. The under-time variable working modal parameter identification method based on statistical feature variable window length according to claim 5 is characterized in that: Designing an adaptive window length adjustment strategy according to the statistical characteristics of the current sliding window to obtain the window length of the next sliding window, specifically including: The adaptive window length adjustment strategy is designed by combining the probability density, kurtosis, skewness and self-mutual information, as shown in the following formula: Among them, L i+1 represents the window length of the next sliding window, and α, β1, β2, and β3 represent adjustment factors.

7. A method for identifying under-timed variable working modal parameters based on statistical characteristic variable window length, characterized in that: include: A data acquisition module is configured to acquire a response signal sequence of the structural vibration under a set environmental excitation, set the number of the sliding window in the response signal sequence, the initial window length, the minimum window length, the maximum window length and the adjustment factor, and use the first sliding window as the current sliding window, and the initial window length as the window length of the first sliding window; a data processing module configured to process a response signal subsequence in a current sliding window in the response signal sequence to obtain a processed response signal subsequence in the current sliding window, extract a time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, extract a principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window using principal component analysis, analyze the processed response signal subsequence in the current sliding window using an autocorrelation function, and determine a lag period of the current sliding window; A modal parameter identification module is configured to combine the time-frequency feature matrix, the lag period and the principal component matrix of the current sliding window to construct a third-order tensor of the current sliding window, perform CP decomposition on the third-order tensor of the current sliding window to obtain a modal response matrix of the current sliding window, and estimate the modal parameters of the current sliding window according to the modal response matrix of the current sliding window; The window length adjustment module is configured to calculate the statistical characteristics of the current sliding window based on the processed response signal subsequence in the current sliding window, design an adaptive window length adjustment strategy according to the statistical characteristics of the current sliding window and the adjustment factor, and obtain the window length of the next sliding window; use the next sliding window as the current sliding window and repeatedly execute the data processing module to the window length adjustment module until the range of the current sliding window exceeds the range of the total length of the response signal sequence.

8. An electronic device, comprising: one or more processors; a storage device for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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