Structural parameter solving method based on complete modal decomposition and random forest response surface fitting

Abstract

The present invention discloses a method for solving structural parameters based on complete modal decomposition and random forest response surface fitting. First, obtain the estimated values of the structural natural vibration frequencies and the number of dominant frequencies. Secondly, obtain the minimum frequency difference, design a frequency overlap criterion and combine it with VMD to determine the number of decomposition components K, and perform noise reduction processing on the K + 1 components including the obtained K IMF components and the residual term respectively. Then, use the variable-speed GWO algorithm combined with the FIR band-pass filter to perform complete division on the noise-reduced and reconstructed signal, set the objective function by comprehensively considering the correlation coefficient, mutual approximate entropy and envelope spectrum entropy, determine the weights of different factors and obtain the optimal segmentation frequency, and solve the damping ratio based on the single-mode attenuation signals of each order. Finally, use the random forest to fit the response surface and combine the modal frequencies to solve the structural elastic modulus and Poisson's ratio. The present invention can accurately identify the modal structure parameters in an environment with strong noise and dense modes, and improve the accuracy, robustness, reliability and practicability of the algorithm.

Description

Technical Field

[0001] The present invention relates to the field of mechanical structure parameter identification, and particularly to a method for solving structure parameters based on complete modal decomposition and random forest response surface fitting. Background Art

[0002] Modal parameter identification is an important means to study the inherent dynamic characteristics of a system. Modal parameters mainly include modal frequency, damping ratio, elastic modulus, Poisson's ratio, etc. Common modal parameter identification methods include time-domain methods (Ibrahim time-domain (ITD), eigensystem realization algorithm (ERA), and stochastic subspace identification (SSI)), frequency-domain methods (peak picking method and frequency-domain decomposition method), and time-frequency domain methods (empirical mode decomposition (EMD), singular spectrum analysis (SSA), analytical mode decomposition (AMD), variational mode decomposition (VMD), and singular value decomposition (SVD), etc.). The above methods have obvious effects on the identification of modal parameters of stationary signals, but have poor effects on the processing of strong noise and dense modal signals. How to overcome the deficiencies of existing algorithms and improve the accuracy of modal structure parameter identification is the focus of future research.

[0003] The complete modal decomposition using time-frequency domain methods combined with optimization algorithms can significantly improve the identification accuracy of modal frequency and damping ratio in the presence of strong noise and dense modal signals; the random forest response surface fitting algorithm can accurately obtain parameters such as the elastic modulus and Poisson's ratio of the structure. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for solving structure parameters based on complete modal decomposition and random forest response surface fitting, which can accurately identify modal structure parameters in an environment of strong noise and dense modes, and improve the accuracy, robustness, reliability, and practicability of the algorithm.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions:

[0006] A method for solving structure parameters based on complete modal decomposition and random forest response surface fitting, the method comprising:

[0007] Step S1, obtaining an estimated value of the main frequency number of the structure and an estimated value of the natural vibration frequency, and estimating the frequency division range and the minimum frequency difference between adjacent frequencies according to the spectrogram;

[0008] Step S2, constructing a frequency overlap criterion and its threshold based on the minimum frequency difference between adjacent frequencies obtained in Step S1, and determining the optimal component number K and the main frequency number of VMD decomposition according to the frequency overlap criterion;

[0009] Step S3: Decompose the original modal signal based on the optimal component value K obtained in Step S2, perform noise reduction processing on each of the K + 1 signal components including the K IMF components and the residual term obtained by VMD decomposition, and reconstruct the K + 1 denoised signal components to obtain a denoised and reconstructed signal;

[0010] Step S4: Use the variable-speed GWO algorithm combined with an FIR band-pass filter to perform a complete partition on the denoised and reconstructed signal obtained in Step S3. Continuously adjust the segmentation value of the band-pass filter using the variable-speed GWO algorithm to obtain the optimal segmentation frequency. The optimization objective function comprehensively considers the correlation coefficient, mutual approximate entropy, and envelope spectrum entropy, and uses the entropy weight method to determine the weights of different factors and obtain the optimal segmentation frequency;

[0011] Step S5: Obtain a single-modal complete decay signal based on the optimal segmentation frequency obtained in Step S4, and calculate the modal frequency and damping ratio;

[0012] Step S6: Based on the modal frequency obtained in Step S5, use the random forest to fit the response surface to obtain the structural elastic modulus and Poisson's ratio.

[0013] Preferably, Step S1 includes:

[0014] Step S101: Use the autoregressive power spectrum AR model combined with the automatic peak picking algorithm to obtain the estimated value of the structural main frequency number and the estimated value of the natural vibration frequency The autoregressive power spectrum P AR (e jω ) of the signal y(n) is calculated by the following formula:

[0015]

[0016] where p R is the order of the AR model; n = 1 , 2,..., N represents the nth data point; N is the signal data length; is the variance of y(n); is the corresponding model parameter; r R (k R ) is the autocorrelation function;

[0017] Step S102: Estimate the frequency segmentation range and the minimum frequency difference between adjacent frequencies respectively satisfy:

[0018]

[0019] where and are the estimated values of the ith and jth frequencies respectively; min{·} represents taking the minimum value.

[0020] Preferably, step S2 includes:

[0021] Step S201, the VMD decomposition process is as follows:

[0022] Under the constraint that the sum of each intrinsic mode function is equal to the original input signal y(t), k intrinsic mode functions u k (t) are sought such that the sum of the estimated bandwidths of each intrinsic mode function is minimized; decompose the original input signal:

[0023]

[0024] where y(t) is the multi-component signal to be decomposed; u k (t) is the single-component signal obtained after VMD decomposition; A k (t) is the instantaneous amplitude of u k (t); is the instantaneous phase of u k (t); the constraint variational model expression of VMD decomposition is as follows:

[0025]

[0026] where {u k} = {u1,..., u K} and {ω k} = {ω1,..., ω K} are all modal sequences and their center frequencies respectively; δ(t) is the Dirac distribution; is the derivative with respect to time; * is the convolution operation; is the L 2 norm of the vector; is the instantaneous frequency; the last term of VMD decomposition is the residual term, satisfying:

[0027]

[0028] where ru(t) is the residual term; K is the number of VMD decomposition modes;

[0029] Step S202, based on the minimum frequency difference between adjacent frequencies obtained in step S1 Construct a frequency overlap criterion and its threshold, and the constructed frequency overlap criterion is as follows:

[0030]

[0031] where ω lIt represents the center frequency of the l-th component obtained by VMD decomposition; r represents the center frequency overlap ratio; a threshold for setting the frequency overlap criterion is set. If the change in r is greater than the threshold, it is considered that modal cracking occurs; otherwise, it is considered that the VMD decomposition meets the requirements. The maximum value among all the component numbers K that meet the threshold requirements is selected as the optimal number of VMD decomposition components.

[0032] Step S203. Based on the optimal number of VMD decomposition components K determined in step S202, the main frequency number is:

[0033] n * = K + 1 (8).

[0034] Preferably, the step S3 includes:

[0035] Step S301. Based on the optimal number of VMD decomposition components K obtained in step S2, the original modal signal is decomposed, and the K + 1 components including the K IMF components and the residual term obtained by VMD decomposition are respectively denoised by SVD.

[0036] Step S302. Select the order of the effective rank of SVD denoising to be twice the number of main frequencies in the source vibration signal, and reconstruct the K + 1 denoised signal components to obtain y f (t).

[0037] Preferably, the step S4 includes:

[0038] Step S401. The denoised and reconstructed signal obtained in step S3 is completely partitioned by using the variable-speed GWO algorithm in combination with the FIR band-pass filter; based on the structural main frequency number n * obtained in step S2 and the corresponding natural vibration frequency estimation value establish the variable-speed GWO optimization parameters as where D i = [d i1 , d i2 is the left and right segmentation frequencies of the i-th mode, i = 1, 2,..., n * - 1; d i2 - d i1 is the boundary frequency segmentation bandwidth of the i-th mode; the left and right cut-off frequencies of the FIR band-pass filter determined based on the variable-speed GWO algorithm satisfy:

[0039]

[0040] Based on equation (9), respectively filter according to the left and right cut-off frequencies of the first n * - 1 order by using the FIR band-pass filter and determine the corresponding optimal left and right cut-off frequencies according to the optimization objective function of the variable-speed GWO algorithm;

[0041] For the first n *After the -1st order left and right cut-off frequencies and their corresponding single-modal time-domain signals are determined, for the nth * order single-modal time-domain signal, the calculation formula is as follows:

[0042]

[0043] Step S402: Optimize the objective function using the variable-speed GWO algorithm, comprehensively consider the correlation coefficient, cross-approximate entropy, and envelope spectrum entropy, and use the entropy weight method to determine the weights of different factors and obtain the optimal segmentation frequency. The relevant calculation process is as follows:

[0044] The update formulas for the velocity and position components are as follows:

[0045]

[0046] In the formula, is the moving speed of the gray wolf population; is the inertia factor; c VSGWO1 , c VSGWO2 and c VSGWO3 are the learning factors respectively; r VSGWO1 =random(0,1), r VSGWO2 =random(0,1) and r VSGWO3 =random(0,1) are random numbers respectively; is the current position of the gray wolf; t GWO is the number of iterations; and are intermediate auxiliary variables respectively;

[0047] The optimization objective function is set to comprehensively consider the correlation coefficient, cross-approximate entropy, and envelope spectrum entropy, and use the entropy weight method to determine the weights of different factors and obtain the optimal segmentation frequency. For the ith single-frequency signal y f (t) of the noise-reduced reconstructed signal y i (t), calculate its envelope spectrum entropy and its correlation coefficient and cross-approximate entropy with the signal y ri (t)=y f (t)-y i (t) respectively, i = 1, 2,..., n * .

[0048] Preferably, for the ith single-frequency signal y f (t) of the noise-reduced reconstructed signal y i (t), calculate its envelope spectrum entropy and its correlation coefficient and cross-approximate entropy with the signal y ri (t)=y f (t)-y i (t) respectively. The relevant calculation process is as follows:

[0049] (1) The calculation process of the correlation coefficient is as follows:

[0050]

[0051] In the formula, Cov(·) represents the covariance of the variable; Var[·] is the variance of the signal; re(·) is the correlation coefficient of the signal; the larger the correlation coefficient, the greater the correlation between the two signals.

[0052] (2) The calculation process of the mutual approximate entropy is as follows:

[0053] Standardize the sequences y i (t) and y j (t) (i = 1, 2,..., n * ; j = 1, 2,..., n * ; i ≠ j) respectively, that is:

[0054]

[0055] In the formula, SD(·) represents the standard deviation of the variable; i n and i m respectively represent the i n and i m th data points, and i n = 1, 2,..., N; i m = 1, 2,..., N; i n ≠ i m ; mean(·) represents taking the average of the variable; then take the similarity tolerance as ry = 0.2C ov (y i , y j ), and calculate the mutual approximate entropy of the new sequence {y i * (i n ), y j * (i m )} as the mutual approximate entropy of the original sequence {y i (i n ), y j (i m )};

[0056] For a time series containing N data points, first calculate the N×N binary distance matrix D t , and the element in the i t th row and i n th column of D m is denoted as d inim , and its expression is as follows:

[0057]

[0058] Using matrix D t The elements in it are used to calculate the component correlation coefficients and

[0059]

[0060] Based on the results of equations (16) and (17), the results of summing the product of each row of the diagonal lines are accumulated and then the average value is obtained, that is, and Furthermore, the mutual approximate entropy formula is obtained as follows:

[0061]

[0062] In the formula, CrossApEn(2, ry) is the mutual approximate entropy;

[0063] (3) Calculate the envelope spectrum entropy of the component y i (t) obtained by signal decomposition;

[0064] (4) Use the entropy weight method to determine the weights of different factors.

[0065] Preferably, the specific steps of using the entropy weight method to determine the weights of different factors include:

[0066] First, make the evaluation indexes homogeneous and standardized to obtain the standardized matrix χ = {X1, X2,..., X α} and the weight vector ω τ = {W1, W2,..., W β}, where α and β are the dimensions of the data to be evaluated and the number of evaluation indexes respectively;

[0067] Secondly, make the index attributes in the original data set homogeneous to obtain the matrix E, and construct the weighted normalized matrix Z, which is obtained by multiplying E by ω τ :

[0068]

[0069] In the formula: is the weight of the jω-th attribute, and the index weights are determined by the entropy weight method. The specific process of the entropy weight method is as follows:

[0070] Calculate each element in the probability matrix P as follows:

[0071]

[0072] Calculate the entropy of each index respectively as follows:

[0073]

[0074] The calculation of each weight coefficient is as follows:

[0075]

[0076] Then, calculate the distances of each sample index from the positive and negative ideal solutions, that is, calculate the degrees of closeness of each evaluation object to the optimal solution and the worst solution:

[0077] The calculation formula for the positive ideal solution is as follows:

[0078]

[0079] The calculation formula for the negative ideal solution is as follows:

[0080]

[0081] The calculation formula for the distance of each sample index from the positive ideal solution is as follows:

[0082]

[0083] The calculation formula for the distance of each sample index from the negative ideal solution is as follows:

[0084]

[0085] Finally, calculate the degree of closeness of each evaluation object to the optimal solution and according to sort by size and give the evaluation results;

[0086]

[0087] In the formula: The closer to 1, the better the sample score.

[0088] Preferably, the step S5 includes:

[0089] Step S501, obtain the complete modal decay signal y i (t), i = 1, 2,..., n * , use the Hilbert transform to obtain the envelope spectrum, and at the same time calculate the cross-correlation function based on the NExT method. The process is as follows:

[0090] When the external excitation f kd (t) acts on the system k d at point, the cross-correlation function corresponding to the i p th point and the j p th point is calculated as follows:

[0091] In the formula, is the ip The r-th d modal shape of the measurement point; Denote the constant term related to the excitation point k d and the modal order r d ; For the j-th p measurement point, the s-th d modal shape; Denote the constant term related to the excitation point k d and the modal order s d ; For the eigenvalue of the r-th d modal shape; For the eigenvalue of the s-th d modal shape; N d Is the system degree of freedom; p d , q d and τ all represent the system time delay; E[·] represents the cross-correlation function of the variable;

[0092] Step S502, Obtain the modal frequency and damping ratio by fitting the envelope of the cross-correlation function based on the least squares method.

[0093] Preferably, the step S6 includes:

[0094] Construct a data set Θ from the modal simulation results of the μ groups of structures with different elastic moduli and Poisson's ratios calculated by the finite element software Patran, and use the random forest algorithm to fit the data set Θ with the elastic modulus and Poisson's ratio as the abscissa and the modal frequency as the ordinate, and match with the experimental modal results to obtain the elastic modulus and Poisson's ratio of the structure;

[0095] Step S601, Use the random forest to fit the response surface, and the specific process is as follows:

[0096] (1) Encode the μ groups of modal simulation result data Θ calculated by the finite element software Patran as the input of the random forest algorithm;

[0097] (2) Use the Bootstrap method to randomly draw the training set and the test set from the data set Θ with replacement; and use the training set as the root node to split and train multiple regression trees;

[0098] (3) Split the nodes in the regression tree according to the principle of the minimum mean square error until they cannot be further split, and repeat this operation to generate multiple regression trees, and form these trees into a forest Among them, Is a random variable; ρ is a sample; T is the number of regression trees;

[0099] (4) Construct a series of independent and identically distributed decision trees and vote to determine the final category of the sample, and the obtained prediction result is as follows:

[0100]

[0101] Where: ν(ρ) is the classification prediction result of the random forest combination; is the decision tree classification model; Y T is the output variable of the random forest; I(·) is the indicator function; is the value of Y when the variable reaches the maximum value T ;

[0102] (5) Based on the random forest model, with the structural elastic modulus and Poisson's ratio as the abscissa and the modal frequency as the ordinate, fit the response surface;

[0103] Step S602, based on the modal frequencies obtained in step S5, the response surface fitted in step S601, and the experimental modal results, obtain the structural elastic modulus and Poisson's ratio.

[0104] The beneficial effects of the present invention are:

[0105] 1. The present invention uses the autoregressive power spectrum AR model to avoid spectral leakage, can effectively process noisy signals or non-stationary signals, and at the same time, combined with the automatic peak picking algorithm, can obtain accurate estimates of the structural main frequency number and natural vibration frequency;

[0106] 2. By constructing a frequency overlap criterion and its threshold using the minimum frequency difference between adjacent frequencies, and at the same time combining VMD and the frequency overlap criterion to determine the optimal component values, the modal order determination problem is effectively solved, and the recognition accuracy for dense modes in a strong interference environment is very high;

[0107] 3. The present invention decomposes the original modal signal based on the optimal number of components, and performs noise reduction processing on all IMF components and residual terms obtained by VMD decomposition using SVD respectively, which can effectively avoid the modal loss phenomenon caused by the existence of VMD decomposition residual terms. At the same time, noise reduction for each component can achieve the maximum reduction of energy loss caused by noise reduction processing while ensuring the original characteristics of the modal signal, improving the noise reduction effect of the algorithm;

[0108] 4. The present invention introduces the velocity component of the traditional particle swarm optimization algorithm into the grey wolf optimization algorithm to form a variable-speed GWO optimization algorithm, which combines the advantages of the grey wolf optimization algorithm with strong local search ability and the particle swarm optimization algorithm with fast convergence speed and strong global search ability. At the same time, the optimization objective function is set to comprehensively consider the correlation coefficient, mutual approximate entropy, and envelope spectrum entropy, and the entropy weight method is used to determine the weights of different factors, which can significantly improve the performance of the optimization algorithm and the optimization results.

[0109] 5. The present invention uses a variable-speed GWO algorithm combined with an FIR band-pass filter to perform a complete division of the single-mode cut-off frequency, which can obtain an optimized modal frequency segmentation result, effectively improve the dense modal identification accuracy, and obtain an accurate single-mode decaying vibration signal;

[0110] 6. The present invention uses a random forest to fit the response surface to obtain the structural elastic modulus and Poisson's ratio. The random forest is not prone to overfitting, has strong capabilities in dealing with high-dimensional data and imbalanced data, and can obtain a high response surface fitting accuracy. Description of the Drawings

[0111] Figure 1 It is a schematic flow chart of the structural parameter solving method based on complete modal decomposition and random forest response surface fitting provided in Embodiment 1;

[0112] Figure 2 It is the bearing housing used in Embodiment 1, where a is the physical drawing of the bearing housing, and b is the geometric modeling drawing of the bearing housing modal test;

[0113] Figure 3 It is the original time-domain vibration signal and power spectrum diagram of the modal test provided in Embodiment 1, where a is the original time-domain vibration signal, and b is the AR autoregressive power spectrum diagram;

[0114] Figure 4 It is the influence diagram of the number of VMD components provided in Embodiment 1, where a represents the influence diagram of the number of VMD components on the maximum value of the central frequency repetition ratio, and b represents the influence diagram of the number of VMD components on the energy loss coefficient;

[0115] Figure 5 It is the AR autoregressive power spectrum diagram obtained based on VMD and combined with the optimal number of components provided in Embodiment 1;

[0116] Figure 6 It is the time-domain vibration signal and power spectrum diagram of SVD noise reduction and reconstruction provided in Embodiment 1, where a is the SVD noise reduction and reconstruction time-domain signal, and b is the AR autoregressive power spectrum diagram;

[0117] Figure 7 It is the optimized objective function value based on the variable-speed GWO provided in Embodiment 1;

[0118] Figure 8 It is the first-order modal decay signal and power spectrum diagram obtained based on the optimal segmentation frequency provided in Embodiment 1, where a is the first-order modal time-domain decay signal, and b is the first-order modal AR autoregressive power spectrum diagram;

[0119] Figure 9The second-order modal decay signal and power spectrum diagram obtained based on the optimal segmentation frequency provided in Embodiment 1, where a is the second-order modal time-domain decay signal and b is the second-order modal AR autoregressive power spectrum diagram;

[0120] Figure 10 The third-order modal decay signal and power spectrum diagram obtained based on the optimal segmentation frequency provided in Embodiment 1, where a is the third-order modal time-domain decay signal and b is the third-order modal AR autoregressive power spectrum diagram;

[0121] Figure 11 The fourth-order modal decay signal and power spectrum diagram obtained based on the optimal segmentation frequency provided in Embodiment 1, where a is the fourth-order modal time-domain decay signal and b is the fourth-order modal AR autoregressive power spectrum diagram;

[0122] Figure 12 The fifth-order modal decay signal and power spectrum diagram obtained based on the optimal segmentation frequency provided in Embodiment 1, where a is the fifth-order modal time-domain decay signal and b is the fifth-order modal AR autoregressive power spectrum diagram;

[0123] Figure 13 The sixth-order modal decay signal and power spectrum diagram obtained based on the optimal segmentation frequency provided in Embodiment 1, where a is the sixth-order modal time-domain decay signal and b is the sixth-order modal AR autoregressive power spectrum diagram;

[0124] Figure 14 The random forest response surface fitting result provided in Embodiment 1. Detailed implementation manners

[0125] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0126] Embodiment 1

[0127] See Figures 1 - 14 , this embodiment provides a method for solving structural parameters based on complete modal decomposition and random forest response surface fitting. The flow of this method is as Figure 1 shown. In this embodiment, the free modal test of the bearing housing is taken as an example to verify the algorithm performance. Figure 2 In Figure 2 , a shows the physical diagram of the bearing housing, and b in

[0128] Step S1. Obtain the estimated value of the main frequency number and the estimated value of the natural vibration frequency of the structure by using the autoregressive power spectrum AR model in combination with the automatic peak picking algorithm and the estimated value of the natural vibration frequency Estimate the frequency division range according to the spectrogram and the minimum frequency difference between adjacent frequencies

[0129] Specifically, in this embodiment, the step S1 includes:

[0130] Step S101. Obtain the estimated value of the main frequency number and the estimated value of the natural vibration frequency of the structure by using the autoregressive power spectrum AR model in combination with the automatic peak picking algorithm and the estimated value of the natural vibration frequency The autoregressive power spectrum P AR (e jω ) of the signal y(n) can be calculated by the following formula:

[0131]

[0132] In the formula, p R is the order of the AR model; n (n = 1, 2,..., N) is the nth data point; N is the signal data length; represents the variance of the white noise sequence; is the corresponding model parameter; r R (k R ) is the autocorrelation function; the original time-domain signal of the modal test and its AR autoregressive power spectrum are as Figure 3 shown; the estimated main frequency number The estimated values of the natural vibration frequencies are respectively and

[0133] Step S102. Estimate the frequency division range according to the spectrogram and the minimum frequency difference between adjacent frequencies respectively satisfy:

[0134]

[0135] In the formula, and are the estimated values of the ith and jth frequencies respectively; min{·} represents taking the minimum value; in this embodiment, the minimum frequency difference between adjacent frequencies

[0136] Step S2. Based on the minimum frequency difference between adjacent frequencies obtained in step S1 Construct the frequency overlap criterion and its threshold, use VMD and the frequency overlap criterion to determine the optimal component value K of the VMD decomposition, and determine that the main frequency number is n *= K + 1;

[0137] Specifically, in this embodiment, step S2 includes:

[0138] Step S201, the VMD decomposition process is as follows:

[0139] Under the constraint that the sum of each intrinsic mode function is equal to the original input signal y(t), k intrinsic mode functions u k (t) are sought such that the sum of the estimated bandwidths of each intrinsic mode function is minimized; the original input signal is decomposed:

[0140]

[0141] where y(t) is the multi-component signal to be decomposed; u k (t) is the single-component signal obtained after VMD decomposition; A k (t) is the instantaneous amplitude of u k (t); is the instantaneous phase of u k (t); the constraint variational model expression of VMD decomposition is as follows:

[0142]

[0143] where {u k} = {u1,..., u K} and {ω k} = {ω1,..., ω K} are all modal sequences and their center frequencies respectively; δ(t) is the Dirac distribution; is the derivative with respect to time; * is the convolution operation; ||·||2 is the L 2 norm of the vector; is the instantaneous frequency; the last term of VMD decomposition is the residual term, satisfying:

[0144]

[0145] where ru(t) is the residual term; K is the number of VMD decomposition modes;

[0146] Step S202, based on step S1, obtain the minimum frequency difference between adjacent frequencies Construct a frequency overlap criterion and its threshold, and the constructed frequency overlap criterion is as follows:

[0147]

[0148] where ω lrepresents the central frequency of the \(l\)-th component of VMD decomposition; \(r\) represents the central frequency overlap ratio; the threshold for setting the frequency overlap criterion is 1. If the change in \(r\) is greater than 1, modal splitting is considered to occur; otherwise, the VMD decomposition is considered to meet the requirements. The maximum value among all the number of components \(K\) that meet the threshold requirements is selected as the optimal number of VMD decomposition components; according to Figure 4 as can be seen from a in, in this embodiment, taking \(K = 5\) can obtain the optimal VMD decomposition result, and the relevant numerical values are shown in Table 1;

[0149] Table 1 Maximum central frequency repetition ratio

[0150] Number of components 2 3 4 5 6 7 8 Replication ratio 0 1 1 1 136 88 884 Number of components 9 10 11 12 13 14 15 Replication ratio 401 7 99 1014 10038 944 30 Number of components 16 17 18 19 20 Replication ratio 935 3858 8667 961 78

[0151] Figure 4 b in shows the curve of the energy loss coefficient changing with the number of components; the corresponding results are shown in Table 2:

[0152] Table 2 Energy loss coefficient

[0153] Number of components 2 3 4 5 6 7 8 Loss coefficient 0.0745 0.0502 0.0307 0.0124 0.0121 0.0076 0.0075 Number of components 9 10 11 12 13 14 15 Loss coefficient 0.0064 0.0060 0.0045 0.0041 0.0040 0.0031 0.0029 Number of components 16 17 18 19 20 Loss coefficient 0.0024 0.0022 0.0023 0.0018 0.0017

[0154] Step S203. Based on step S202, the determined dominant frequency number is:

[0155] n * = K + 1 (8)

[0156] Step S3. Based on the optimal number of components \(K\) obtained in step S2, the original modal signal is decomposed. The \(K + 1\) components including the \(K\) IMF components and the residual term obtained by VMD decomposition are respectively denoised by SVD. The order of the effective rank of SVD denoising is selected to be twice the number of dominant frequency numbers in the source vibration signal. The \(K + 1\) denoised signal components are reconstructed to obtain \(y\) f (t);

[0157] Specifically, in this embodiment, this step S3 includes:

[0158] Step S301. Based on the optimal number of components \(K\) obtained in step S2, the original modal signal is decomposed, Figure 5 shows the AR autoregressive power spectrum diagram obtained based on VMD and combined with the optimal number of components \(K\). From Figure 5 compared with Figure 3 b in, it can be seen that due to the existence of the residual term, VMD will cause modal loss, which will bring large errors to the modal parameter identification results. The comparison of modal loss results is shown in Table 3:

[0159] Table 3 Comparison of modal loss results

[0160]

[0161] To avoid the phenomenon of modal loss, in the subsequent processing, the K + 1 components including the K IMF components and the residual term obtained by VMD decomposition are respectively denoised using SVD. The basic principle of SVD denoising is as follows:

[0162] For the k-th noisy component u k (t) among the K + 1 components, perform phase space reconstruction and construct it into a p×q order Hankel matrix:

[0163]

[0164] where N = p + q - 1, and p ≥q. Perform singular value decomposition on H m to obtain:

[0165] H m = U∑V T (10)

[0166] where U and V are unitary matrices of p×p and q×q respectively; ∑ is a p×q diagonal matrix that satisfies the following equation:

[0167] ∑ = diag(λ1, λ2,..., λ s ) (11)

[0168] where λ1, λ2,..., λ s are the singular values of matrix H m , and λ1 ≥ λ2 ≥... ≥ λ s ≥ 0;

[0169] Use the first r s orders of larger singular values to represent the true signal, and the subsequent s - r s orders of smaller singular values to represent the noise signal; perform inverse operations on the matrix components corresponding to the first r orders of singular values to obtain the best approximation matrix m of H Add and average the anti-diagonal elements in the matrix to obtain the denoised signal;

[0170] Step S302: Select the order of the effective rank of SVD denoising to be twice the number of main frequencies in the source vibration signal, and reconstruct the K + 1 denoised signal components to obtain y f (t); Figure 6 Figure a in Figure 6 shows the reconstructed time-domain signal based on SVD denoising, Figure 6 Figure b in Figure 5 shows the AR autoregressive power spectrum diagram corresponding to Figure 3As can be seen from the comparison with b, comprehensively considering the residual signal for VMD based on the optimal number of components can effectively avoid the phenomenon of mode loss and obtain a better denoising effect. The comparison results are shown in Table 4:

[0171] Table 4 Comparison of Mode Loss Results

[0172]

[0173] Step S4: Use the variable-speed GWO algorithm combined with the FIR band-pass filter to perform a complete partition on the denoised and reconstructed signal obtained in step S3. Continuously adjust the segmentation value of the band-pass filter using the variable-speed GWO algorithm to obtain the optimal segmentation frequency. The optimization objective function comprehensively considers the correlation coefficient, mutual approximate entropy, and envelope spectrum entropy, and uses the entropy weight method to determine the weights of different factors and obtain the optimal segmentation frequency;

[0174] Specifically, in this embodiment, step S4 includes:

[0175] Step S402: Use the variable-speed GWO algorithm combined with the FIR band-pass filter to perform a complete partition on the denoised and reconstructed signal obtained in step S3; Based on step S2, the structural main frequency number can be obtained as n * and the estimated value of the natural vibration frequency Establish the variable-speed GWO optimization parameters as D = pD1, D2,..., D n*-1 , where D i =[d i1 , d i2 (i = 1, 2,...., n * -1) is the left and right segmentation frequencies of the i-th order mode; d i2 -d i1 is the boundary frequency segmentation bandwidth of the i-th order mode; The left and right cut-off frequencies of the FIR filter determined based on the variable-speed GWO algorithm satisfy:

[0176]

[0177] Based on Equation (12), filter according to the left and right cut-off frequencies of the first n * -1 order using the FIR band-pass filter and determine the corresponding optimal left and right cut-off frequencies according to the optimization objective function of the variable-speed GWO algorithm. The expression of the FIR band-pass filter is as follows:

[0178]

[0179] In the formula, y(n) is the filter input; y r (n) is the filter output; h(k) is the filter coefficient; N J is the filter order;

[0180] Pending the first n *After the -1st order left and right cut-off frequencies and the corresponding single-mode time-domain signals are determined, for the nth * order single-mode time-domain signal, the calculation formula is as follows:

[0181]

[0182] Step S402: Optimize the objective function using the variable-speed GWO algorithm, comprehensively consider the correlation coefficient, mutual approximate entropy, and envelope spectrum entropy, and use the entropy weight method to determine the weights of different factors and obtain the optimal segmentation frequency. The relevant calculation process is as follows:

[0183] The variable-speed GWO algorithm combines the advantages of the strong local search ability of the gray wolf optimization algorithm and the fast convergence speed and strong global search ability of the particle swarm optimization algorithm. It introduces the velocity component of the traditional particle swarm optimization algorithm into the gray wolf optimization algorithm to form a variable-speed gray wolf optimization algorithm. The updated formulas for the fused velocity and position components are as follows:

[0184]

[0185] In the formula, is the moving speed of the gray wolf population; ζ is the inertia factor; c VSGWO1 , c VSGWO2 and c VSGWO3 are learning factors respectively; r VSGWO1 = random(0,1), r VSGWO2 = random(0,1) and r VSGWO3 = random(0,1) are random numbers respectively; is the current position of the gray wolf; t GWO is the number of iterations; and are intermediate auxiliary variables respectively;

[0186] The optimization process of the objective function based on the variable-speed GWO is as Figure 7 shown, and the optimized values of different modes are shown in Table 5:

[0187] Table 5 Optimized values of the objective function for different modes

[0188] Modal order 1 2 3 4 5 6 Objective function value 1.8526e-09 1.0567e-06 1.3494e-09 3.4882-09 3.2264-08 3.7036e-09

[0189] The optimized objective function is set to comprehensively consider the correlation coefficient, mutual approximate entropy, and envelope spectrum entropy, and use the entropy weight method to determine the weights of different factors and obtain the optimal segmentation frequency. For the ith single-frequency signal yi(t) (i = 1, 2,...., n f ) of the noise-reduced reconstructed signal y * (t), calculate its envelope spectrum entropy and its correlation with the signal y ri (t) = y f (t) - yi (t)’s correlation coefficient and mutual approximate entropy, and the related calculation process is as follows: (1) The correlation coefficient calculation process is as follows:

[0190]

[0191] In the formula, Cov(·) is the signal covariance; Var[·] is the variance of the signal; re(·) is the correlation coefficient of the signal; the larger the correlation coefficient, the greater the correlation between the two signals;

[0192] (2) The mutual approximate entropy calculation process is as follows:

[0193] If the amplitudes of the sequences y i (t) and y j (t) (i = 1, 2,..., n * ; j = 1, 2,..., n * ; i ≠ j) differ greatly, it is best to standardize the sequences y i (t) and y j (t) respectively, that is:

[0194]

[0195] In the formula, i n and i m respectively represent the i n and i m th data points, and i n = 1, 2,..., N; i m = 1, 2,..., N; i n ≠ i m ; mean(·) represents taking the average of the variable; then take the similarity tolerance ry = 0.2C ov (y i , y j ), and calculate the mutual approximate entropy of the new sequence {y i * (i n ), y j * (i m )} as the mutual approximate entropy of the original sequence {y i (i n ), y j (i m )};

[0196] For a time series containing N data points, first calculate the N×N binary distance matrix D t , and the element in the i t th row and i n th column of D m is denoted as d inim , and its expression is as follows:

[0197]

[0198] Using the elements in matrix D t , the component correlation coefficients can be conveniently calculated and

[0199]

[0200] Based on the results of equations (20) and (21), sum up the results of the summation of each diagonal line and then calculate the average value to obtain and Furthermore, the mutual approximate entropy formula can be obtained as follows:

[0201]

[0202] In the formula, CrossApEn(2, ry) is the mutual approximate entropy;

[0203] (3) Calculate the component y i (t) (i = 1, 2,..., n * ) envelope spectrum entropy;

[0204] (4) Use the entropy weight method to determine the weights of different factors

[0205] First, make the evaluation indicators homogeneous, standardize them, and obtain the standardized matrix χ = {X1, X2,..., X α} and the weight vector ω τ = {W1, W2,..., W β}, where α and β are the dimensions of the data to be evaluated and the number of evaluation indicators respectively;

[0206] Secondly, make the indicator attributes in the original dataset homogeneous to obtain the matrix E, and construct the weighted normalized matrix Z. Z is obtained by multiplying E with ω τ as follows:

[0207]

[0208] In the formula: is the weight (importance degree) of the j ω th attribute. The indicator weights are determined by the entropy weight method. The specific process of the entropy weight method is as follows:

[0209] Calculate each element in the probability matrix P as follows:

[0210]

[0211] Calculate the entropy of each indicator respectively as follows:

[0212]

[0213] The calculation of each weight coefficient is as follows:

[0214]

[0215] Then, calculate the distances of each sample index from the positive and negative ideal solutions, that is, calculate the closeness of each evaluation object to the optimal solution and the worst solution:

[0216] The calculation formula for the positive ideal solution is as follows:

[0217]

[0218] The calculation formula for the negative ideal solution is as follows:

[0219]

[0220] The calculation formula for the distance of each sample index from the positive ideal solution is as follows:

[0221]

[0222] The calculation formula for the distance of each sample index from the negative ideal solution is as follows:

[0223]

[0224] Finally, calculate the closeness of each evaluation object to the optimal solution and according to sort by size and give the evaluation result;

[0225]

[0226] In the formula: The closer to 1, the better the sample score; The weights of each sample index are shown in Table 6:

[0227] Table 6 Weights of Each Sample Index

[0228] Sample index Correlation coefficient Mutual approximate entropy Envelope spectrum entropy Weight 0.6732 0.1245 0.2023

[0229] Step S5. Obtain the complete modal decay signal y i (t) (i = 1, 2,...., n * ) by using the optimal segmentation frequency obtained in step S4, and obtain the envelope spectrum by using the Hilbert transform. At the same time, obtain the modal frequency and damping ratio based on the Natural Excitation Technique (NExT) method and the least squares method;

[0230] Specifically, in this embodiment, this step S5 includes:

[0231] Step S501: Obtain the complete modal decay signal y based on the optimal segmentation frequency obtained in step S4 i (t) (i = 1, 2,...., n * ), and calculate the envelope spectrum using the Hilbert transform. At the same time, calculate the cross-correlation function based on the NExT method as follows:

[0232] When the external excitation f kd (t) acts on the system at point k d , the cross-correlation function corresponding to the i-th point and the j-th point is calculated as follows:

[0233] In the formula, is the r-th p modal shape of the i-th measurement point of the structure d ; represents the constant term related to the excitation point k d and the modal order r d ; is the s-th p modal shape of the j-th measurement point of the structure d ; represents the constant term related to the excitation point k d and the modal order s d ; λ rd is the eigenvalue of the r-th d modal shape; is the eigenvalue of the s-th d modal shape; N d is the degree of freedom of the system; p d , q d and τ all represent the system time delay; E[·] represents the cross-correlation function of the variable; The complete modal decay signals of each order obtained based on the optimal segmentation frequency and their corresponding AR autoregressive power spectra are as Figures 8 - 13 shown; The optimal segmentation frequencies of each order are shown in Table 7:

[0234] Table 7 Optimal segmentation frequency bandwidth of each order

[0235] Modal order 1 2 3 4 5 Frequency bandwidth 10.4323 12.0741 14.6987 36.4313 26.1941 Left cut-off frequency 290.3119 511.1822 539.9800 1336.0760 1744.3150 Right cut-off frequency 300.7442 523.2563 554.6787 1372.5073 1770.5091

[0236] Step S502: Fit the envelope of the cross-correlation function based on the least squares method to obtain the modal frequency and damping ratio;

[0237] The identification results of the optimal modal frequencies and damping ratios of each order are shown in Table 8:

[0238] Table 8 Identification results of modal frequencies of each order

[0239] Modal order 1 2 3 4 5 6 Modal frequency 295.8021 517.2863 548.3121 1354.8045 1757.4623 1891.2932

[0240] The identification results and errors of each order damping ratio are shown in Table 9:

[0241] Table 9 Identification Results of Each Order Damping Ratio

[0242]

[0243] Step S6: Based on the modal frequencies obtained in Step S5, use random forest to fit the response surface to obtain the structural elastic modulus and Poisson's ratio;

[0244] Specifically, in this embodiment, this Step S6:

[0245] Fit the μ-group modal simulation result data set Θ calculated based on Patran, and combine with the experimental modal results to match and obtain the structural elastic modulus and Poisson's ratio;

[0246] Step S601: Use random forest to fit the response surface, and the specific process is as follows:

[0247] (1) Encode the μ-group modal simulation result data Θ calculated based on Patran as the input of the random forest algorithm;

[0248] (2) Use the Bootstrap method to randomly draw 70% as the training set and 30% as the test set from the data set Θ with replacement; and use the training set as the root node to split and train multiple regression trees;

[0249] (3) Split the nodes in the regression tree according to the principle of the minimum mean square error until they cannot be further split, and repeat this operation to generate multiple regression trees, and form these trees into a forest Among them, is a random variable; ρ is a sample; T is the number of regression trees;

[0250] (4) Construct a series of independent and identically distributed decision trees and conduct voting to determine the final category of the sample, and the obtained prediction results are as follows:

[0251]

[0252] In the formula: ν(ρ) is the combined classification prediction result of the random forest; is the decision tree classification model; Y T is the output variable of the random forest; I(·) is the indicator function; is the value of Y when the variable reaches the maximum value T ;

[0253] (5) Based on the random forest model, use the structural elastic modulus and Poisson's ratio as the abscissa and the modal frequency as the ordinate to fit the response surface; the response surface fitting result is as Figure 14 shown, and the fitting accuracy of each order response surface is shown in Table 10:

[0254] Fitting accuracy of response surfaces of each order in Table 10

[0255] Modal order 1 2 3 4 5 6 Root mean square error RMSE 0.0015 0.0008 0.0013 0.0002 0.0001 0.0002 Fitting accuracy R2 0.9847 0.9864 0.9760 0.9119 0.9951 0.9924

[0256] Step S602: Based on the modal frequencies obtained in step S5, the response surface fitted in step S601, and the experimental modal results, obtain the structural elastic modulus and Poisson's ratio.

[0257] Supplementary data

[0258] Where the present invention is not described in detail are all well-known techniques to those skilled in the art.

[0259] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention through logical analysis, reasoning, or limited experiments based on the concept of the present invention on the basis of the prior art shall fall within the protection scope determined by the claims.

Claims

1. A method for solving structural parameters based on complete modal decomposition and random forest response surface fitting, characterized in that, The method includes: Step S1: Obtain the estimated value of the structural main frequency number and the estimated value of the natural vibration frequency, and estimate the frequency division range and the minimum frequency difference between adjacent frequencies according to the spectrogram; Step S2: Construct a frequency overlapping criterion and its threshold based on the minimum frequency difference between adjacent frequencies obtained in Step S1, and determine the optimal component number K and the main frequency number of the VMD decomposition according to the frequency overlapping criterion; Step S3: Decompose the original modal signal based on the optimal component number K obtained in Step S2, perform noise reduction processing on the K + 1 signal components including the K IMF components and the residual term obtained by the VMD decomposition respectively, and reconstruct the K + 1 noise-reduced signal components to obtain a noise-reduced reconstructed signal; Step S4: Use the variable-speed GWO algorithm combined with the FIR band-pass filter to perform a complete division on the noise-reduced reconstructed signal obtained in Step S3. Continuously adjust the division value of the band-pass filter using the variable-speed GWO algorithm to obtain the optimal division frequency. The optimization objective function comprehensively considers the correlation coefficient, mutual approximate entropy, and envelope spectrum entropy, and uses the entropy weight method to determine the weights of different factors and obtain the optimal division frequency; Step S5: Obtain the single-modal complete attenuation signal based on the optimal division frequency obtained in Step S4, and calculate the modal frequency and damping ratio; Step S6: Based on the modal frequency obtained in Step S5, use the random forest to fit the response surface to obtain the structural elastic modulus and Poisson's ratio; specifically including: Construct a dataset Θ from the modal simulation results of the μ groups of different structural elastic moduli and Poisson's ratios calculated by the finite element software Patran, and use the random forest algorithm to fit the dataset Θ with the elastic modulus and Poisson's ratio as the abscissa and the modal frequency as the ordinate, and match with the experimental modal results to obtain the structural elastic modulus and Poisson's ratio; Step S601: Use the random forest to fit the response surface, and the specific process is as follows: (1) Encode the μ groups of modal simulation result data Θ calculated by the finite element software Patran as the input of the random forest algorithm; (2) Use the Bootstrap method to randomly and with replacement extract the training set and the test set from the dataset Θ; and use the training set as the root node to split and train multiple regression trees; (3) Split the nodes in the regression tree according to the principle of minimizing the mean squared error until no further splitting is possible. Repeat this operation to generate multiple regression trees and form a forest with these trees. Among them, is a random quantity; ρ is the sample; T is the number of regression trees; (4) Construct a series of independent and identically distributed decision trees and vote to determine the final category of the sample, and the obtained prediction result is as follows: Where: ν(ρ) is the prediction result of the random forest combined classification; is the decision tree classification model; Y T is the output variable of the random forest; I(·) is the indicator function; is the value of Y when the variable reaches the maximum value T value; (5) Based on the random forest model, fit the response surface with the structural elastic modulus and Poisson's ratio as the abscissa and the modal frequency as the ordinate; Step S602: Based on the modal frequency obtained in Step S5, the response surface fitted in Step S601, and the experimental modal results, obtain the structural elastic modulus and Poisson's ratio.

2. The method for solving structural parameters based on complete modal decomposition and random forest response surface fitting according to claim 1, characterized in that, The said Step S1 includes: Step S101: Obtain the estimated value of the structural main frequency number and the estimated value of the natural vibration frequency by using the autoregressive power spectrum (AR) model in combination with the automatic peak picking algorithm and the estimated value of the natural vibration frequency The autoregressive power spectrum P AR (e jω ) is calculated by the following formula: where p R is the order of the AR model; n = 1, 2, …, N represents the nth data point; N is the signal data length; is the variance of y(n); is the corresponding model parameter; r R (k R ) is the autocorrelation function; Step S102: Estimate the frequency division range according to the spectrogram and the minimum frequency difference between adjacent frequencies respectively satisfy: wherein, and are the estimated values of the i-th and j-th order frequencies respectively; min{·} represents taking the minimum value.

3. The method for solving structural parameters based on complete modal decomposition and random forest response surface fitting according to claim 1, characterized in that, The said Step S2 includes: Step S201: The VMD decomposition process is as follows: Under the constraint that the sum of each intrinsic mode function is equal to the original input signal y(t), k intrinsic mode functions u k (t) are sought such that the sum of the estimated bandwidths of each intrinsic mode function is minimized; decompose the original input signal: where, y(t) is the multi-component signal to be decomposed; u k (t) is the single-component signal obtained after VMD decomposition; A k (t) is the instantaneous amplitude of u k (t); is the instantaneous phase of u k (t); The constrained variational model expression of VMD decomposition is as follows: where {u k} = {u1,..., u K} and {ω k} = {ω1,..., ω K} are all modal sequences and their center frequencies respectively; δ(t) is the Dirac distribution; is the derivative with respect to time; * is the convolution operation; is the L 2 norm of the vector; is the instantaneous frequency; the last term of the VMD decomposition is the residual term, satisfying: In the formula, ru(t) is the residual term; K is the number of VMD decomposition modes; Step S202: Based on the minimum frequency difference between adjacent frequencies obtained in Step S1 Construct a frequency overlap criterion and its threshold. The frequency overlap criterion is constructed as follows: where ω l represents the center frequency of the l-th component obtained by VMD decomposition; r represents the center frequency overlap ratio; a threshold for setting the frequency overlap criterion is set. If the change in r is greater than the threshold, modal cleavage is considered to occur; otherwise, the VMD decomposition meets the requirements. The maximum value among all the component numbers K that meet the threshold requirements is selected as the optimal number of VMD decomposition components; Step S203: Based on Step S202, the main frequency number is determined as: n * = K + 1 (8).

4. A method for solving structural parameters based on complete modal decomposition and random forest response surface fitting according to claim 1, characterized in that, The said Step S3 includes: Step S301: Decompose the original modal signal based on the optimal number K of VMD decomposition components obtained in Step S2, and perform noise reduction processing on the K + 1 components including the K IMF components and the residual term obtained by the VMD decomposition respectively using SVD; Step S302: Select the order of the effective rank of SVD denoising to be twice the number of main frequencies in the source vibration signal, and reconstruct the K + 1 denoised signal components to obtain y f (t).

5. A method for solving structural parameters based on complete modal decomposition and random forest response surface fitting according to claim 1, characterized in that, The said Step S4 includes: Step S401: Completely partition the denoised reconstructed signal obtained in step S3 by using the variable-speed GWO algorithm in combination with an FIR band-pass filter; based on the structural main frequency number n obtained in step S2 * and the corresponding natural vibration frequency estimation values Establish the variable-speed GWO optimization parameters as where D i =[d i1 , d i2 is the left and right segmentation frequencies of the i-th mode, i = 1, 2,..., n * -1; d i2 -d i1 is the boundary frequency segmentation bandwidth of the i-th mode; the left and right cut-off frequencies of the FIR band-pass filter determined by the variable-speed GWO algorithm satisfy: Based on Equation (9), respectively according to the left and right cut-off frequencies of the first n * - 1 order, filtering is performed using a FIR band-pass filter, and the corresponding optimal left and right cut-off frequencies are determined according to the optimization objective function of the variable-speed GWO algorithm; After the left and right cut-off frequencies of the -1st order and their corresponding single-modal time-domain signals are determined, for the nth * order single-modal time-domain signal, the calculation formula is as follows: * ​ Step S402: Optimize the objective function using the variable-speed GWO algorithm, comprehensively consider the correlation coefficient, mutual approximate entropy, and envelope spectrum entropy, and use the entropy weight method to determine the weights of different factors and obtain the optimal segmentation frequency. The relevant calculation process is as follows: The update formulas for the velocity and position components are as follows: In the formula, is the moving speed of the gray wolf population; ζ is the inertia factor; c VSGWO1 , c VSGWO2 and c VSGWO3 are the learning factors respectively; r VSGWO1 = random(0, 1), r VSGWO2 = random(0, 1) and r VSGWO3 = random(0, 1) are random numbers respectively; is the current position of the gray wolf; t GWO is the number of iterations; and are intermediate auxiliary variables respectively; The optimization objective function is set by comprehensively considering the correlation coefficient, mutual approximate entropy, and envelope spectrum entropy, and the entropy weight method is used to determine the weights of different factors and obtain the optimal segmentation frequency for the denoised reconstructed signal y f (t) of the i-th single-frequency signal y i (t), and calculate its envelope spectrum entropy and its correlation coefficient and mutual approximate entropy with the signal y ri (t) = y f (t) - y i (t), where i = 1, 2, …, n * .

6. A method for solving structural parameters based on complete modal decomposition and random forest response surface fitting according to claim 5, characterized in that, For the noise-reduced reconstructed signal y f (t), calculate the envelope spectrum entropy of its i-th single-frequency signal y i (t) respectively, as well as its correlation coefficient with the signal y ri (t) = y f (t) - y i (t). The relevant calculation processes of the correlation coefficient and mutual approximate entropy are as follows: (1) The calculation process of the correlation coefficient is as follows: In the formula, Cov(·) represents the covariance of the variable; Var[·] is the variance of the signal; re(·) is the correlation coefficient of the signal; the larger the correlation coefficient, the greater the correlation between the two signals; (2) The calculation process of the mutual approximate entropy is as follows: Normalize the sequences yi(t) and yj(t) (i = 1, 2,..., n * ; j = 1, 2,..., n * ; i ≠ j) respectively, i.e.: In the formula, SD(·) represents the standard deviation of the variable; i n and i m represent the i n -th and i m -th data points respectively, and i n = 1, 2, ..., N; i m = 1, 2, ..., N; i n ≠ i m ; mean(·) represents taking the average of a variable; then take the similarity tolerance as ry = 0.2C ov (y i , y j ) to calculate the cross - approximate entropy of the new sequence {y i * (i n ) , y j * (i m )} as the cross - approximate entropy of the original sequence {y i (i n ) , y j (i m )}; For a time series containing N data points, first calculate the N×N binary distance matrix D t , D t The element in the i n -th row and the i m -th column of inim is denoted as d and its expression is as follows: Using the elements in matrix D t calculate the component correlation coefficients and Based on the results of equations (16) and (17), the sum of the results of each diagonal line summation is accumulated and then the average value is calculated, that is, and Furthermore, the mutual approximate entropy formula is obtained as follows: In the formula, CrossApEn(2,ry) is the mutual approximate entropy; (3) Calculate the component y i (t) envelope spectrum entropy; (4) Use the entropy weight method to determine the weights of different factors.

7. A method for solving structural parameters based on complete modal decomposition and random forest response surface fitting according to claim 6, characterized in that, The specific steps to determine the weights of different factors using the entropy weight method include: First, the evaluation indicators are homogenized and standardized to obtain the standardized matrix χ={X1,X2,...,X α } and weight vector ω τ ={W1,W2,...,W β }, where α and β are the dimension of the data to be evaluated and the number of evaluation indicators respectively; Secondly, the indicator attributes in the original data set are homogenized to obtain the matrix E, and the weighted normalized matrix Z is constructed. Z is the sum of E and ω τ After multiplication, we get: Wherein: is the weight of the j ω th attribute. The index weights are determined by the entropy weight method. The specific process of the entropy weight method is as follows: Calculate each element in the probability matrix P as follows: Calculate the entropy of each index respectively as follows: The calculation of each weight coefficient is as follows: Then, calculate the distances of each sample index from the positive and negative ideal solutions, that is, calculate the degree of closeness of each evaluation object to the optimal solution and the worst solution: The calculation formula for the positive ideal solution is as follows: The calculation formula for the negative ideal solution is as follows: The calculation formula for the distance of each sample index from the positive ideal solution is as follows: The calculation formula for the distance of each sample index from the negative ideal solution is as follows: Finally, calculate the closeness degree C of each evaluation object to the optimal solution iω , and rank them according to the value of C iω to give the evaluation results; Where: 0 ≤ C iω ≤ 1, and the closer C iω is to 1, the better the sample score is.

8. A method for solving structural parameters based on complete modal decomposition and random forest response surface fitting according to claim 1, characterized in that, The said step S5 includes: Step S501: Obtain the complete modal decay signal y i (t), where i = 1, 2, …, n * , and use the Hilbert transform to obtain the envelope spectrum. At the same time, the process of calculating the cross-correlation function based on the NExT method is as follows: When the external excitation f kd (t) acts on the scope system k d point, the cross-correlation function corresponding to the i p point and the j p point is calculated as follows: wherein, is the r-th p modal vibration mode of the i-th d measurement point of the structure; represents the constant term related to the excitation point k d and the modal order r d ; is the s-th p modal vibration mode of the j-th d measurement point of the structure; represents the constant term related to the excitation point k d and the modal order s d ; is the eigenvalue of the r-th d vibration mode; is the eigenvalue of the s-th d vibration mode; N d is the degree of freedom of the system; p d , q d and τ all represent the system time delay; E[·] represents the cross-correlation function of the variable; Step S502: Obtain the modal frequency and damping ratio by fitting the envelope of the cross-correlation function based on the least squares method.

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