Underdetermined time-varying operational modal parameter identification method and device based on statistical characteristic variable window length

Abstract

The application discloses a kind of underdetermined time-varying operating modal parameter identification method and device based on statistical characteristic variable window length, comprising: obtaining the response signal sequence of structure vibration under the set environment excitation and processing, obtain the processed response signal subsequence in current sliding window, extract time-frequency feature matrix to the processed response signal subsequence in current sliding window, and extract principal component matrix from time-frequency feature matrix using principal component analysis, determine lag period using autocorrelation function analysis;Modal parameters of current sliding window are estimated according to the time-frequency feature matrix of current sliding window, lag period and principal component matrix;Statistical characteristics of current sliding window are calculated and adaptive window length adjustment strategy is designed, to obtain the window length of next sliding window;The next sliding window is used as the current sliding window, and the above steps are repeated, and the underdetermined time-varying operating modal parameter can be accurately identified.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of operational modal parameter identification, and in particular to an underdetermined time-varying operational modal parameter identification method and device based on statistical feature variable window length. BACKGROUND

[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 mainly target 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 operating conditions or time stages. For example, the dynamic response of a bridge under different loads will change with the change of load position and load size; the change of rotating speed in rotating machinery will cause the change of modal frequency, damping ratio, and modal shape. These time-varying characteristics make it difficult 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, due to limited number of sensors, the number of modes often exceeds the observability, making the identification problem more complex. For example, in the case of complex structure, limited sensor placement, or cost constraints, how to accurately extract the modal frequency, modal damping ratio, and modal shape of the system from limited measurement data becomes a difficult problem. Traditional time-varying modal identification methods based on fixed sliding window process data in segments to cope with the time-varying characteristics of the system, but this method has the problems of fixed window size, response lag, and insufficient precision, especially in the case of rapid or drastic changes, it cannot timely capture the dynamic characteristics of the system.

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

[0005] The present application aims to provide an underdetermined time-varying operational modal parameter identification method and device based on statistical feature variable window length to solve the above technical problems.

[0006] In a first aspect, the present application provides an underdetermined time-varying operational modal parameter identification method based on statistical feature variable window length, comprising the following steps:

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

[0008] S2, processing a response signal sub-sequence in the current sliding window to obtain a processed response signal sub-sequence in the current sliding window, extracting a time-frequency feature matrix of the current sliding window from the processed response signal sub-sequence in the current sliding window, extracting a principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window by principal component analysis, and analyzing the processed response signal sub-sequence in the current sliding window by autocorrelation function analysis to determine a lag period of the current sliding window;

[0009] S3, combining 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, 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;

[0010] S4, calculating a statistical feature of the current sliding window based on the processed response signal sub-sequence in the current sliding window, designing an adaptive window length adjustment strategy according to the statistical feature of the current sliding window and the adjustment factor to obtain a window length of a next sliding window, taking the next sliding window as the current sliding window and repeating steps S2-S4 until a range of the current sliding window exceeds a range of a total length of the response signal sequence.

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

[0012] normalizing each time point of the response signal sub-sequence in the current sliding window to obtain a normalized signal value of each time point in the current sliding window, as shown in the following formula:

[0013]

[0014] wherein the response signal sub-sequence in the current sliding window is i represents the number of the sliding window, n m is the number of sensors, L i represents the window length of the current sliding window, is a set of real numbers, x(t) is a response signal sub-sequence X in the current sliding window, μ1 represents the mean of the response signal of all time steps in the response signal sub-sequence X in the current sliding window, σ1 represents the standard deviation of the response signal of all time steps in the response signal sub-sequence X in the current sliding window, (i) (i) (i) is a normalized signal value of the t-th time step in the current sliding window;

[0015] The normalized signal value of each time in the current sliding window is denoised using wavelet transform to obtain the processed response signal of each time in the current sliding window, as shown in the following formula:

[0016]

[0017] wherein W represents wavelet transform, W -1 represents inverse wavelet transform, x denoised (t) represents the processed response signal of the t-th 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 sub-sequence in the current sliding window.

[0018] As preferred, the time-frequency feature matrix of the current sliding window is extracted from the processed response signal sub-sequence in the current sliding window, and the principal component matrix of the current sliding window is extracted from the time-frequency feature matrix of the current sliding window using principal component analysis, and the autocorrelation function is used to analyze the processed response signal sub-sequence in the current sliding window to determine the lag period of the current sliding window, specifically including:

[0019] The time-frequency feature matrix of the current sliding window is extracted from the processed response signal sub-sequence in the current sliding window using wavelet transform time-frequency analysis method, as shown in the following formula:

[0020]

[0021] wherein x denoised (t) represents the processed response signal of the t-th time step in the current sliding window, ψ represents the mother wavelet, a represents the scale, b represents the translation parameter, 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 eigenvalue decomposition, as shown in the following formula:

[0023] ​​​Y = W ψ M;

[0024] wherein Y represents a principal component matrix, and M represents an eigenvector matrix;

[0025] The periodicity feature of the processed response signal subsequence in the current sliding window is analyzed by using the autocorrelation function to obtain an autocorrelation function curve, as shown in the following formula:

[0026]

[0027] wherein ACF(l) represents a 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 a lag period, and μ2 represents the mean value of the processed response signal of all time steps in the current sliding window;

[0028] The significant peak value in the autocorrelation function curve is used to determine each lag period l g of the current sliding window, wherein g = 1, 2,..., s, and s represents the total number of lag periods of the current sliding window.

[0029] As preferred, step S3 specifically comprises:

[0030] initializing a third-order tensor X for each lag period l g filling the third dimension of the third-order tensor X , assuming that the time-frequency feature matrix W ψ of the current sliding window 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 , a data segment with a length of L i + 1 is extracted from the time-frequency feature matrix W ψ of the current sliding window:

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

[0032] wherein X l represents the data segment, t = 1, 2,..., L i , and L i represents the window length of the current sliding window;

[0033] Then the third-order tensor is filled to obtain a filled third-order tensor:

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

[0035] wherein X[t,j,l g ] represents the filled third-order tensor, j represents the frequency dimension from the principal component matrix, Wavelet Feature represents the data segment X l extracting features on the frequency dimension j;

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

[0037]

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

[0039] processing the column vectors in the modal response matrix by Fourier transform to estimate the modal parameters of the current sliding window, the modal parameters of the current sliding window including the natural frequency.

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

[0041] performing probability density estimation on the processed response signal subsequence within the current sliding window, first selecting an interval to divide the value range of the processed response signal subsequence within the current sliding window, assuming that the number of intervals is N bins , and the width of each interval is Δx, and by performing bucket design on the processed response signal subsequence within the current sliding window, the frequency of each interval is obtained, and then normalized to the probability density, as shown in the following formula:

[0042]

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

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

[0045]

[0046] Skewness γ is calculated using the following formula:

[0047]

[0048] where E[(x denoised (t)-μ2) 3 ] is the third central moment of the processed response signal subsequence in the current sliding window, when 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] Kurtosis δ is calculated using the following formula:

[0050]

[0051] where E[(x denoised (t)-μ2) 4 ] is the fourth central moment of the processed response signal subsequence in the current sliding window, when kurtosis δ = 0, the shape of the distribution of the processed response signal subsequence in the current sliding window is similar to the normal distribution, δ > 0, the distribution of the processed response signal subsequence in the current sliding window is more peaked than the normal distribution, and 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, by selecting a time delay τ, the self mutual information between different time periods of the processed response signal subsequence in the current sliding window is calculated, as shown in the following formula:

[0053]

[0054] where x denoised (t+τ) represents the processed response signal at the t+τ 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 probability density of the processed response signal subsequence in the current sliding window at time steps x c and x o , respectively.

[0055] As preferred, the 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, and specifically includes:

[0056] The adaptive window length adjustment strategy is designed in combination with the probability density, kurtosis, skewness and mutual information, and is shown in the following formula:

[0057]

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

[0059] In the second aspect, the application provides an underdetermined time-varying operational modal parameter identification method based on statistical characteristic variable window length, which includes:

[0060] The data acquisition module is configured to acquire a response signal sequence of structure vibration under a set environment excitation, set the number of sliding windows, the initial window length, the minimum window length and the maximum window length and the adjustment factor in the response signal sequence, take the first sliding window as the current sliding window, and take 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, extract the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window by principal component analysis, and analyze the processed response signal subsequence in the current sliding window by autocorrelation function 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 the adaptive window length adjustment strategy according to the statistical characteristics of the current sliding window and the adjustment factor to obtain the window length of the next sliding window, take the next sliding window as the current sliding window and repeat the execution of 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 application provides an electronic device, comprising one or more processors; a memory device 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 as described in any implementation manner of the first aspect.

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

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

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

[0068] (1) The underdetermined time-varying operating modal parameter identification method based on statistical characteristic variable window length proposed in the present application dynamically adjusts the window length by introducing the kurtosis, skewness, mutual information and other statistical characteristics of the signal, so as to adapt to the change characteristics of the signal in real time. Through this adaptive window length adjustment strategy, the dynamic changes of the signal in the time-varying system can be effectively dealt with, and it is especially suitable for real-time monitoring and modal identification of large-scale structures (such as bridges, wind turbines, etc.).

[0069] (2) The underdetermined time-varying operating modal parameter identification method based on statistical characteristic variable window length proposed in the present application is especially suitable for the case where the number of sensors is less than the number of modes to be identified, and can accurately extract modal information under the underdetermined condition, solving the problem of incomplete identification of modal information caused by insufficient sensors in the traditional method.

[0070] (3) The underdetermined time-varying operating modal parameter identification method based on statistical characteristic variable window length proposed in the present application integrates signal standardization, wavelet denoising, dynamic sliding window, wavelet transform and tensor decomposition technologies to explore and analyze the complex structure and dynamic characteristics in multi-dimensional time series data. It is especially suitable for processing large, high-dimensional and time-dependent data sets, such as vehicle dynamics systems, bridges, etc. BRIEF DESCRIPTION OF DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0072] Figure 1Flowchart of the statistical characteristic variable window length based underdetermined time-varying operational modal parameter identification method of the embodiment of the present application;

[0073] Figure 2 Comparison chart of modal shapes identified by the statistical characteristic variable window length based underdetermined time-varying operational modal parameter identification method of the embodiment of the present application at 200.625s;

[0074] Figure 3 Comparison chart of modal shapes identified by the statistical characteristic variable window length based underdetermined time-varying operational modal parameter identification method of the embodiment of the present application at 500s;

[0075] Figure 4 Flowchart of the double entity model calculation of the statistical characteristic variable window length based underdetermined time-varying operational modal parameter identification method of the embodiment of the present application;

[0076] Figure 5 Comparison chart of the natural frequency variation curve identified by the statistical characteristic variable window length based underdetermined time-varying operational modal parameter identification method of the embodiment of the present application and the theoretical natural frequency variation curve of the three-degree-of-freedom time-varying structure;

[0077] Figure 6 MAC value variation curve chart of the three-degree-of-freedom time-varying system identified by the statistical characteristic variable window length based underdetermined time-varying operational modal parameter identification method of the embodiment of the present application;

[0078] Figure 7 Schematic diagram of the statistical characteristic variable window length based underdetermined time-varying operational modal parameter identification device of the embodiment of the present application;

[0079] Figure 8 The hardware structure schematic diagram of the electronic device provided by the embodiment of the present application is shown. DETAILED DESCRIPTION

[0080] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0081] Figure 1 A statistical characteristic variable window length based underdetermined time-varying operational modal parameter identification method provided by the embodiment of the present application is shown, which comprises the following steps:

[0082] S1, obtaining a response signal sequence of linear structure vibration under a set environmental excitation, setting a number of sliding windows in the response signal sequence, an initial window length, a minimum window length and a maximum window length and an adjustment factor, taking a first sliding window as a current sliding window, and taking the initial window length as a window length of the first sliding window.

[0083] Specifically, a response signal sequence of linear structure vibration of selected sensors (a number of sensors is less than a number of degrees of freedom) under a set environmental excitation is obtained, a length of the response signal sequence is T, and a number of sliding windows in the response signal sequence, an initial window length, a minimum window length and a maximum window length and an adjustment factor are set. The number i of the sliding windows is sequentially increased by a sliding step of the sliding windows from 1, and in the embodiment of the application, the sliding step of the sliding windows is 1 by default, and in other embodiments, the sliding step of the sliding windows can be selected as other values.

[0084] S2, processing a response signal subsequence in the current sliding window in the response signal sequence to obtain a processed response signal subsequence in the current sliding window, extracting a time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, extracting a principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window by principal component analysis, and determining a lag period of the current sliding window by autocorrelation function analysis on the processed response signal subsequence in the current sliding window.

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

[0086] Standardizing a response signal at each time in the response signal subsequence in the current sliding window in the response signal sequence to obtain a signal value after standardization at each time in the current sliding window, as shown in the following formula:

[0087]

[0088] wherein the response signal subsequence in the current sliding window is i represents the number of the sliding window, and n represents the number of the time steps. m L represents the number of the sensors, and L represents the number of the time steps. i L represents the number of the time steps. X represents a real number set, x(t) represents a response signal at the tth time step in the response signal subsequence X in the current sliding window, and μ1 represents a mean value of the response signal subsequence X in the current sliding window. (i) (i) ​the mean of the response signals in all time steps, σ1 represents the response signal sub-sequence X in the current sliding window (i) the standard deviation of the response signals in all time steps, denotes the normalized signal value of the tth time step in the current sliding window;

[0089] The normalized signal value of each time in the current sliding window is denoted using wavelet transform for denoising processing, and the processed response signal of each time in the current sliding window is obtained, as shown in the following formula:

[0090]

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

[0092] In specific embodiments, the time-frequency feature matrix of the current sliding window is extracted from the processed response signal sub-sequence in the current sliding window, and the principal component matrix of the current sliding window is extracted from the time-frequency feature matrix of the current sliding window using principal component analysis, and the autocorrelation function is used to analyze the processed response signal sub-sequence in the current sliding window to determine the lag period of the current sliding window, specifically including:

[0093] The time-frequency feature matrix of the current sliding window is extracted from the processed response signal sub-sequence in the current sliding window using wavelet transform time-frequency analysis method, as shown in the following formula:

[0094]

[0095] wherein 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, W ψ denotes 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 eigenvalue decomposition, as shown in the following formula:

[0097] Y=W ψ M;

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

[0099] The periodicity characteristics of the processed response signal subsequence in the current sliding window are analyzed by using the autocorrelation function to obtain an autocorrelation function curve, as shown in the following formula:

[0100]

[0101] Wherein, 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 signal of all time steps in the current sliding window.

[0102] The significant peak value in the autocorrelation function curve is used to determine each lag period l g of the current sliding window, wherein g = 1, 2…, s, and 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 normalized, and then the wavelet transform is used for denoising processing to retain the main components of the signal and remove high-frequency noise. The time-frequency characteristics are extracted by the wavelet transform time-frequency analysis method, which can not only obtain the amplitude information of the signal, but also capture the frequency characteristics of the signal changing with time. The multi-scale characteristics of the signal are extracted by using the wavelet transform, which is particularly effective for non-stationary signals. Finally, the principal component analysis (PCA) is used to extract the principal component features from the time-frequency characteristics of the signal, and the autocorrelation function (ACF) is used to analyze and determine the lag period of the current sliding window.

[0104] S3, the time-frequency feature matrix, the lag period and the principal component matrix of the current sliding window are combined to construct a third-order tensor of the current sliding window, the third-order tensor of the current sliding window is CP decomposed to obtain a 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 specific embodiments, step S3 specifically includes:

[0106] Initializing a third-order tensor X for each lag period l g The third dimension of the third-order tensor X is filled, assuming that the time-frequency feature matrix W ψ of the current sliding window is an Nxm matrix, then the time-frequency feature corresponding to each time step t is X[t, :], and for each lag period l g , a data segment with a length of L ψ +1 is extracted from the time-frequency feature matrix W i of the current sliding window:

[0107] X l = X[t+1 g ,:];

[0108] wherein, X l represents a data segment, t = 1, 2,..., L i , L i represents a window length of a current sliding window;

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

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

[0111] wherein, X [t,j,l g ] represents the filled third-order tensor, j represents a frequency dimension from a principal component matrix, and Wavelet Feature represents extracting a feature on the frequency dimension j of the data segment X l through wavelet transform;

[0112] CP-decompose the filled third-order tensor to obtain a modal shape matrix Φ, a modal response matrix Q, and a modal weight matrix Θ, as shown in the following formula:

[0113]

[0114] wherein, represents an outer product multiplication of vectors, and R represents a rank of CP-decomposition;

[0115] Process column vectors in the modal response matrix through Fourier transform to estimate modal parameters of the current sliding window, the modal parameters of the current sliding window including an inherent frequency.

[0116] Specifically, the first dimension uses a time step t, the second dimension uses a frequency dimension from a principal component matrix for extracting the current sliding window, and a lag period calculation is based on an autocorrelation function (ACF), which is used to extract a time dependence of a signal and defines a length of a data segment. The lag period l g is a time window parameter used to segment a time-frequency feature matrix of the current sliding window, the length of the window is L i + 1, which is used to construct a third dimension of the third-order tensor, thereby obtaining the filled third-order tensor, and CP-decomposing the filled third-order tensor to obtain three factor matrices Φ, Q, and Θ after decomposition; is a modal shape matrix, Q ∈ R N×Ris the modal response matrix, the column vector in the modal response matrix can estimate the natural frequency w corresponding to each mode through Fourier transform processing i , the modal parameters of the current sliding window are obtained.

[0117] S4, the statistical characteristics of the current sliding window are calculated based on the processed response signal subsequence in the current sliding window, the adaptive window length adjustment strategy is designed according to the statistical characteristics of the current sliding window and the adjustment factor, and the window length of the next sliding window is obtained; the next sliding window is taken as the current sliding window 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.

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

[0119] The probability density of the processed response signal subsequence in the current sliding window is estimated, first selecting an interval to divide the value range of the processed response signal subsequence in the current sliding window, assuming that the number of intervals is N bins , the width of each interval is Δx, and the frequency of each interval is obtained by bucket design of the processed response signal subsequence in the current sliding window, and then standardized to probability density, as shown in the following formula:

[0120]

[0121] where p(x denoised (t)) represents the probability density of the processed response signal x denoised (t) at the t-th time step in the current sliding window, L i represents the window length of the current sliding window, u represents the u-th interval, and h(x denoised (t)-x denoised (u)) represents an indicator function, which is 1 when x denoised (t) falls within the interval [x denoised (u), x denoised (u)+Δx], 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] wherein E[(x denoised (t)-μ2) 3 ] represents the third central moment of the processed response signal subsequence within the current sliding window, when the skewness γ = 0, the processed response signal subsequence within the current sliding window is symmetrically distributed; when γ > 0, the distribution of the processed response signal subsequence within the current sliding window is positively skewed; when γ < 0, the distribution of the processed response signal subsequence within the current sliding window is negatively skewed;

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

[0128]

[0129] wherein E[(x denoised (t)-μ2) 4 ] is the fourth central moment of the processed response signal subsequence within the current sliding window, when the kurtosis δ = 0, the distribution shape of the processed response signal subsequence within the current sliding window is similar to the normal distribution, δ > 0, the distribution of the processed response signal subsequence within the current sliding window is more acute than the normal distribution, when δ < 0, the distribution of the processed response signal subsequence within the current sliding window is more flat than the normal distribution;

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

[0131]

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

[0133] In specific embodiments, 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, which specifically includes:

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

[0135]

[0136] wherein, L i+1 represents the window length of the next sliding window, and a, b1, b2 and b3 represent adjustment factors.

[0137] Specifically, the statistical features include probability density, kurtosis, skewness and self mutual information, and the probability density of the continuous time series signal x denoised (t) in the current sliding window is estimated, an appropriate interval is selected to divide the value range of the signal, and the frequency of each interval is obtained by bucketing the signal data, and then normalized 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. Skewness can measure the asymmetry of signal distribution. The kurtosis can measure the sharpness of the signal distribution. The self mutual information between signals at different time periods can measure the time correlation of the signal, reflecting the time dependence of the signal. a, b1, b2 and b3 are adjustment factors, so as to control the weight of each feature in the window size adjustment.

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

[0139] After the window length adjustment of the next sliding window is completed, the current sliding window is slid 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 taken as the current sliding window (i=i+1) and steps S2-S4 are repeated until the range of the current sliding window exceeds the total length of the response signal sequence, i.e. when i>T-L i +1, the repetition of steps S2-S4 is stopped, and the modal parameters of each sliding window are finally obtained.

[0140] The linear time-varying three-degree-of-freedom spring oscillator system is used below to verify the underdetermined time-varying operational modal parameter identification method based on statistical feature variable window length proposed in the embodiments of the present application.

[0141] It is assumed that the sampling frequency f is 40 Hz, the sampling interval At is 0.025 s, and the sampling time t is 2000 s.

[0142] The initial conditions of three degrees of freedom displacement of a three degrees of freedom spring oscillator system are all zero, a Gaussian white noise excitation is applied to the first mass, and the mass of the first mass is set as:

[0143]

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

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

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

[0147] The experiment compares and evaluates the underdetermined time-varying operating modal parameter identification method of linear time-varying structure by modal assurance criterion (MAC) and relative error of modal natural frequency.

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

[0149]

[0150] Wherein, And Respectively represent the estimated modal shape vector of the i-th order and the real modal shape vector, and the MAC value changes between 0 and 1. The larger the MAC value (close to 1), the better the mode.

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

[0152]

[0153] Wherein, ω q And ω q-theory Respectively represent the estimated modal natural frequency of the q-th order and the theoretical natural frequency, and the value of ζ q The closer to 0, the more accurate the identified natural frequency.

[0154] The MAC value results of the three-degree-of-freedom spring oscillator system in the experiment at 230s and 720s are shown in Table 1 and Table 2, and the relative error results of the natural frequency are shown in Table 3. The comparison results of the instantaneous mode shapes identified by the underdetermined time-varying operational modal parameter identification method based on the statistical characteristic variable window length proposed in the embodiments of the present application and the inherent mode shapes of the three-degree-of-freedom time-varying system at different time points of 200.625s and 500s are shown in Figure 3 and Figure 4 respectively, Figure 5 and Figure 6 are the comparison results of the inherent frequency curves and the identified frequency curves at different times and the MAC curve variation curves at different times respectively. From Table 1-4 and Figures 3-6 it can be seen that the underdetermined time-varying operational modal parameter identification method based on the statistical characteristic variable window length proposed in the embodiments of the present application can well realize the identification of modal parameters under the condition of underdetermined time-varying, not only the relative error of the natural frequency is small, but also the identified mode shape is good.

[0155] Table 1 Confidence Coefficient of Each Order Mode at 230s

[0156]

[0157] Table 2 Confidence Coefficient of Each Order Mode at 720s

[0158]

[0159] Table 3 Error of Each Order Natural Frequency

[0160]

[0161] Further referring to Figure 7 , as an implementation of the method shown in the above figures, the present application provides an embodiment of an underdetermined time-varying operational modal parameter identification device based on the statistical characteristic variable window length, which corresponds to the method embodiment shown in Figure 1 , and the device can be specifically applied to various electronic devices.

[0162] The embodiments of the present application also propose an underdetermined time-varying operational modal parameter identification method based on the statistical characteristic variable window length, comprising:

[0163] A data acquisition module 1 is configured to acquire a response signal sequence of structure vibration under a set environment excitation, set the number of sliding windows, the initial window length, the minimum window length and the maximum window length in the response signal sequence and an adjustment factor, take the first sliding window as the current sliding window, and take the initial window length as the window length of the first sliding window;

[0164] The data processing module 2 is 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 by using principal component analysis, analyze the processed response signal subsequence in the current sliding window by using autocorrelation function analysis, and determine a lag period of the current sliding window.

[0165] The modal parameter identification module 3 is configured to combine the time-frequency feature matrix of the current sliding window, the lag period and the principal component matrix 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 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 a statistical feature 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 feature of the current sliding window and an adjustment factor to obtain a window length of a next sliding window, take the next sliding window as the current sliding window and repeat the execution of 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 A hardware structure schematic diagram of an electronic device provided by the embodiment of the present application is shown in FIG. 1. Figure 8 As shown in FIG. 1, the electronic device of the embodiment includes a processor 801 and a memory 802; the memory 802 is used to store computer execution instructions; the processor 801 is used to execute the computer execution instructions stored by the memory to realize each step executed by the electronic device in the above-mentioned embodiment. For details, please refer to the related description in the foregoing method embodiment.

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

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

[0170] The embodiment of the present application further provides a computer storage medium, and the computer storage medium stores computer execution instructions; when the processor 801 executes the computer execution instructions, the method described above is realized.

[0171] The embodiment of the present application further provides a computer program product comprising a computer program, which, when executed by the processor 801, implements the method as above.

[0172] In the embodiments of the present application, it should be understood that the disclosed device and method can be implemented in other manners. For example, the described device embodiments are merely schematic. For example, the division of the modules is merely logical function division. There can be another division manner for the actual implementation. For example, a plurality of modules or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed mutual couplings or direct couplings or communication connections can be indirect couplings or communication connections through some interfaces, devices or modules, and can be electrical, mechanical or in other forms.

[0173] The modules illustrated as separated components can or can not be physical separated, and the components illustrated as modules can or can not be physical units, i.e., can be located in one place or can be distributed on a plurality of network units. In actual implementation, some or all of the modules can be selected according to actual needs to implement the embodiments of the present application.

[0174] In addition, the various function modules in the various embodiments of the present application can be integrated in one processing unit, or each module can be a physical unit, or two or more modules can be integrated in one unit. The units formed by the above modules can be implemented in the form of hardware, or in the form of hardware plus software function units.

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

[0176] It should be understood that the processor 801 can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), or the like. The general-purpose processor can be a microprocessor, or the processor 801 can also be any conventional processor, etc. The steps of the methods disclosed in the present application can be directly embodied as the processor 801 executing hardware, or a combination of hardware and software modules in the processor 801 executing.

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

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

[0179] The storage medium described above can be realized 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 storage, flash memory, magnetic disk or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose 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 can write information to the storage medium. Of course, the storage medium can also be an integral part 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 host device.

[0181] Those of ordinary skill in the art can understand that all or part of the steps of the above-mentioned method embodiments can be completed by program instruction-related hardware. The foregoing 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 foregoing storage medium includes various storage media that can store program codes, such as ROM, RAM, magnetic disk or optical disk, etc.

[0182] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for underdetermined time-varying operational modal parameter identification based on statistical characteristic variable window length, characterized in that, The method comprises the following steps: S1, obtaining a response signal sequence of structural vibration under a set environmental excitation, setting a number of sliding windows, an initial window length, a minimum window length, a maximum window length and an adjustment factor in the response signal sequence, taking a first sliding window as a current sliding window, and taking the initial window length as the window length of the first sliding window; S2, processing a response signal subsequence in the current sliding window to obtain a processed response signal subsequence in the current sliding window, extracting a time-frequency feature matrix of the current sliding window from the processed response signal subsequence in the current sliding window, and extracting a principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window by principal component analysis, and determining a lag period of the current sliding window by autocorrelation function analysis on the processed response signal subsequence in the current sliding window; S3, combining 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, 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 a statistical feature of the current sliding window based on the processed response signal subsequence in the current sliding window, designing an adaptive window length adjustment strategy according to the statistical feature of the current sliding window and the adjustment factor to obtain a window length of a 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; The statistical feature of the current sliding window calculated based on the processed response signal subsequence in the current sliding window specifically comprises: The probability density of the processed response signal subsequence in the current sliding window is estimated as follows: ； where p(x denoised (t)) represents the probability density of the processed response signal x denoised (t) at the t-th time step within the current sliding window, N bins is the number of intervals, Δx is the width of each interval, L i represents the window length of the current sliding window, u represents the u-th interval, h(x denoised (t) - x denoised (u)) represents an indicator function, when x denoised (t) falls in the interval [x denoised (u),x denoised (u)+Δx] is 1, otherwise the indicator function is 0; The standard deviation σ2 of the processed response signal at all time steps in the current sliding window is estimated according to the probability density as follows: ; where p2represents the mean of the processed response signal for all time steps within the current sliding window; The skewness γ is calculated as follows: ； E[(x denoised (t)-μ2) 3 ] represents the third central moment of the processed response signal subsequence within the current sliding window. The kurtosis δ is calculated as follows: ； E[(x denoised (t)-μ2) 4 ] is the fourth order central moment of the processed response signal subsequence within the current sliding window; For the processed response signal subsequence in the current sliding window, the self mutual information between different time periods of the processed response signal subsequence in the current sliding window is calculated by selecting a time delay τ as follows: ； where x denoised (t + τ) represents the processed response signal at time step t + τ within the current sliding window, p(x c , x o ) represents the joint probability distribution of the processed response signal sub-sequence within the current sliding window at time steps t and t + τ, p(x c ) and p(x o ) represent the probability densities of the processed response signal sub-sequence within the current sliding window at time steps x c and x o , respectively; According to the statistical characteristics of the current sliding window and an adjustment factor, an adaptive window length adjustment strategy is designed to obtain the window length of the next sliding window, and specifically includes: ; wherein L i+1 denotes the window length of the next sliding window, and a, b1, b2, and b3 denote adjustment factors.

2. The underdetermined time-varying operational modal parameter identification method based on variable window length according to statistical characteristics of claim 1, characterized in that, The response signal subsequence in the current sliding window in the response signal sequence is processed to obtain a processed response signal subsequence in the current sliding window, specifically comprising: The response signal at each time in the response signal subsequence in the current sliding window in the response signal sequence is normalized to obtain a standardized signal value at each time in the current sliding window as follows: ； wherein X denotes a response signal sub-sequence within a current sliding window i denotes a number of the sliding window, n m is a number of sensors, L i denotes a window length of the current sliding window, is a real number set, x(t) denotes a response signal at a t-th time step in the response signal sub-sequence X (i) within the current sliding window, μ1 denotes a mean of the response signals at all time steps in the response signal sub-sequence X (i) within the current sliding window, σ1 denotes a standard deviation of the response signals at all time steps in the response signal sub-sequence X (i) within the current sliding window, denotes a signal value after normalization at the t-th time step within the current sliding window; The denoising processing is performed on each time point of the normalized signal value in the current sliding window using the wavelet transform to obtain a processed response signal at each time point in the current sliding window, as shown in the following formula: ； where W denotes a wavelet transform, W -1 denotes an inverse wavelet transform, x denoised (t) denotes a processed response signal at the t-th time step within the current sliding window, and the processed response signals at all time steps within the current sliding window constitute a sub-sequence of processed response signals within the current sliding window.

3. The underdetermined time-varying operational modal parameter identification method based on variable window length according to statistical characteristics of claim 1, characterized in that, The time-frequency feature matrix of the current sliding window is extracted from the processed response signal subsequence in the current sliding window, and the principal component matrix of the current sliding window is extracted from the time-frequency feature matrix of the current sliding window using principal component analysis, and the autocorrelation function is used to analyze the processed response signal subsequence in the current sliding window to determine the lag period of the current sliding window, specifically including: The time-frequency feature matrix of the current sliding window is extracted from the processed response signal subsequence in the current sliding window using the wavelet transform time-frequency analysis method, as shown in the following formula: ； where x denoised (t) denotes the processed response signal at the tth time step within the current sliding window, ψ denotes the mother wavelet, a denotes the scale, b denotes the translation parameter, W ψ denotes 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 characteristic vector matrix and the principal component matrix are obtained by calculating the covariance matrix and performing eigenvalue decomposition, as shown in the following formula: Y = W ψ M; Wherein, Y represents the principal component matrix, and M represents the characteristic vector matrix; The autocorrelation function curve is obtained by analyzing the periodic characteristics of the processed response signal subsequence in the current sliding window using the autocorrelation function, as shown in the following formula: ； wherein 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 within the current sliding window. determining each lag period l of the current sliding window according to a significant peak value 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. A method for underdetermined time-varying operational modal parameter identification based on variable window length of statistical characteristics, characterized in that, Including: The data acquisition module is configured to acquire a response signal sequence of structural vibration under a set environmental excitation, set the number of sliding windows, the initial window length, the minimum window length, the maximum window length and the adjustment factor in the response signal sequence, and take the first sliding window as the current sliding window, and take the initial window length as the window length of the first sliding window; The data processing module is configured to process the response signal subsequence in the current sliding window in the response signal sequence to obtain a 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 extract the principal component matrix of the current sliding window from the time-frequency feature matrix of the current sliding window using principal component analysis, and analyze the processed response signal subsequence in the current sliding window using the autocorrelation function to determine the lag period of the current sliding window; 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 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. a window length adjustment module configured to calculate a statistical feature of the current sliding window based on the processed response signal subsequence within the current sliding window, design an adaptive window length adjustment strategy according to the statistical feature of the current sliding window and an adjustment factor, and obtain a window length of a next sliding window; take the next sliding window as the current sliding window and repeat the execution of 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; calculating a statistical feature of the current sliding window based on the processed response signal subsequence within the current sliding window, specifically comprising: performing a probability density estimation on the processed response signal subsequence within the current sliding window, as shown in the following formula: ； where p(x denoised (t)) represents the probability density of the processed response signal x denoised (t) at the t-th time step within the current sliding window, N bins is the number of intervals, and Δx is the width of each interval, L i represents the window length of the current sliding window, u represents the u-th interval, and h(x denoised (t) - x denoised (u)) represents an indicator function, which is 1 when x denoised (t) falls in the interval [x denoised (u),x denoised (u)+Δx] is 1, otherwise the indicator function is 0; estimating the standard deviation σ2 of the processed response signal at all time steps within the current sliding window according to the probability density, as shown in the following formula: ; where μ2represents the mean of the processed response signal of all time steps within the current sliding window; calculating the skewness γ by using the following formula: ； E[(x denoised (t)-μ2) 3 ] represents the third central moment of the processed response signal subsequence within the current sliding window. calculating the kurtosis δ by using the following formula: ； E[(x denoised (t)-μ2) 4 is the fourth order central moment of the processed response signal subsequence within the current sliding window; for the processed response signal subsequence within the current sliding window, calculating the self mutual information between different time periods of the processed response signal subsequence within the current sliding window by selecting a time delay τ, as shown in the following formula: ； where x denoised (t+τ) represents the processed response signal at time step t+τ within the current sliding window, p(x c ,x o ) represents the joint probability distribution of the processed response signal sub-sequence within the current sliding window at time steps t and t+τ, p(x c ) and p(x o ) represent the probability densities of the processed response signal sub-sequence within the current sliding window at time steps x c and x o , respectively; According to the statistical characteristics of the current sliding window, an adaptive window length adjustment strategy is designed to obtain the window length of the next sliding window, specifically including: ; where L i+1 denotes the window length of the next sliding window, and a, b1, b2, and b3 denote adjustment factors.

5. 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 of any one of claims 1-3.

6. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the method of any one of claims 1-3.

7. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to implement the method of any one of claims 1-3. The computer program is executed by the processor to implement the method of any one of claims 1-3.

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