A cable-stayed bridge damage identification method and system based on multi-wavelet packet energy and IHPO-SVM fusion

Abstract

The present invention discloses a cable-stayed bridge damage identification method and system integrating multi-wavelet packet energy and IHPO-SVM, and relates to the field of damage identification. An IHPO-SVM damage identification model is constructed by optimizing SVM parameters through improved IHPO, which is used for damage location and quantitative analysis of the main beam of a cable-stayed bridge. IHPO improves the global search capability and late search strength of the HPO algorithm by introducing Circle chaos mapping, Cauchy mutation formula and nonlinear convergence factor. It has been verified that the performance of IHPO on 10 test functions is better than that of HPO, HHO and WOA. IHPO-SVM exhibits fast and stable characteristics when optimizing SVM parameters. Compared with various models such as SSA-SVM, it has faster optimization speed and higher damage identification accuracy. It can accurately identify the location and degree of damage to the main beam under different noise levels, and shows good noise robustness.

Description

Technical Field

[0001] The present invention belongs to the field of damage identification of bridge structure health monitoring, and specifically, relates to a cable-stayed bridge damage identification method and system integrating multi-wavelet packet energy and improved hunter-prey optimizer (IHPO)-support vector machine (SVM). Background Art

[0002] In order to build an efficient wavelet neural network, domestic and foreign scholars have conducted extensive research and achieved a series of results. For example, Zhang X et al. used the relative wavelet energy of different frequency bands as input vectors to build a back propagation neural network and a probabilistic neural network, and successfully identified the structural damage of helicopter rotor blades. He Haoxiang et al. used wavelet packet filtering and reconstruction of the original structural response signal of the vehicle-bridge coupled vibration, and used the damage feature image generated by recursive analysis to input into the convolutional neural network, realizing accurate identification of the damage location and degree. Hamidian D et al. used a multilayer perceptron neural network combined with wavelet transform to effectively locate structural damage.

[0003] Although the above technologies have made some research progress, there are still some challenges when using wavelet neural networks to identify damage in cable-stayed bridge main beams. First, a single wavelet feature is often difficult to fully extract damage information, resulting in insufficient feature characterization capabilities. Second, the initial weights and thresholds of the neural network are usually randomly selected within a certain range. If the initial values ​​are significantly different from the ideal values, it may lead to poor network stability and low recognition accuracy.

[0004] In view of this, the present invention is proposed. Summary of the invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a cable-stayed bridge damage identification method and system integrating multi-wavelet packet energy and IHPO-SVM, which solves the problems raised in the above background technology.

[0006] In order to solve the above technical problems, the basic concept of the technical solution adopted by the present invention is:

[0007] A cable-stayed bridge damage identification method and system based on multi-wavelet packet energy and IHPO-SVM fusion, comprising the following steps:

[0008] S1: Establish a benchmark finite element model of a cable-stayed bridge and extract the vertical acceleration signal of the main beam cable;

[0009] S2: Calculate the wavelet packet energy change rate, wavelet packet coefficient fuzzy entropy and wavelet packet coefficient kurtosis value characteristics of the acceleration signal, use the Relief algorithm and forward search strategy to calculate the optimal feature subset, connect the optimal feature subsets in series to obtain the wavelet packet fusion feature, and divide the optimal feature subsets into training set and test set, and input the training set into the BP neural network for training;

[0010] It should be noted that in the serial fusion method, assuming that α and β are two different feature vectors, the number of which is m and n respectively, the serial fusion feature obtained is γ = [m×α, n×β]. It can be seen that the fusion method through serial connection is relatively simple and has low computational complexity. Compared with parallel fusion, the dimension of the features in serial fusion has increased significantly, which may increase unfavorable factors such as information conflict. The method of selecting feature subsets can simplify the features while retaining most of the useful information, thereby improving the representation ability of the features.

[0011] S3: Set the structure of the BP neural network, determine the number of nodes in the input layer, hidden layer and output layer, and the layers of the multi-layer BP neural network are fully connected, and the neurons in the same layer are not connected;

[0012] It should be noted that the close integration of wavelet packet analysis and data mining algorithms is based on the basic idea of ​​replacing the functions in conventional data mining algorithms with wavelet functions, and using the time-frequency processing capabilities of wavelet functions to improve the recognition ability of the model, thereby constructing a damage identification model for structural damage identification.

[0013] Wavelet neural network replaces the activation function of the hidden layer nodes of conventional neural network with wavelet function, and gradually updates the connection weights between neurons, the scaling factor and translation factor of wavelet function during network training. This fusion method can combine the time-frequency processing ability of wavelet function and the learning ability of neural network to improve the accuracy of damage identification. The structure diagram of wavelet neural network is shown in the figure below. Figure 3 Shown

[0014] S4: Using Circle chaos mapping, Cauchy mutation and nonlinear convergence factor to improve HPO, IHPO is obtained;

[0015] S5: Obtain a convergence factor C, determine the search agent by comparing the convergence factor C, update the position of the search agent by a corresponding position formula, and calculate the fitness value of each search agent;

[0016] S6: Determine whether the fitness value of each search agent is less than the average fitness value. If so, perform Cauchy mutation on the search agent. If the fitness value after mutation is better than the old fitness value, replace the old fitness value.

[0017] S7: Determine whether the fitness value of the search agent meets the search termination condition. When the fitness value meets the termination condition, output the initial weight and threshold represented by the current optimal fitness value, and construct a multi-feature wavelet neural network;

[0018] S8: input the damage location test set of the simulation model into the damage location multi-feature wavelet neural network, and determine the damage position of the main beam through the damage condition output by the multi-feature wavelet neural network;

[0019] S9: After the damage location is determined, the damage quantification test set of the damage location is input into the damage quantification multi-feature wavelet neural network, and the damage quantification of the main beam is performed according to the damage degree output by the multi-feature wavelet neural network;

[0020] S10: Extract the acceleration data of the actual bridge when it is completed and calculate the wavelet packet features, which are used as the data of the undamaged working condition to input the damage location and damage quantification multi-feature wavelet neural network for training;

[0021] S11: Extract the acceleration data of the actual bridge during operation and calculate the wavelet packet features, input them into the damage location multi-feature wavelet neural network, judge the damage position of the actual bridge through the damage condition output by the multi-feature wavelet neural network, input them into the damage quantification multi-feature wavelet neural network, and judge the damage degree of the actual bridge through the damage degree output by the multi-feature wavelet neural network.

[0022] Optionally, the step of calculating the wavelet packet energy change rate of the acceleration signal in S2 is:

[0023] S2.1.1: The vertical acceleration signal of the cable is extracted as the dynamic response signal, and the dynamic response signal is subjected to i-time wavelet transform to decompose the signal into i layers of wavelet packet coefficients of different frequencies and scales. The transformation calculation formula is:

[0024]

[0025] Where x(t) is the dynamic response signal;

[0026] S2.1.2: Using wavelet packet functions The linear combination of represents the obtained dynamic response signal, and its calculation formula is:

[0027]

[0028] In the formula, It is represented as the wavelet packet coefficient signal obtained after the i-th layer decomposition of the dynamic response signal. Expressed as wavelet packet coefficients;

[0029] S2.1.3: According to the wavelet packet coefficients of different frequencies and scales of layer i, the total energy Ei of the wavelet signal in the time domain of the dynamic response signal is calculated.

[0030]

[0031] S2.1.4: Substituting the wavelet packet coefficient signal Ei into formula (2), the calculation formula obtained is:

[0032]

[0033] In the formula, is the energy of each frequency band;

[0034] S2.1.5: Calculate the total energy of the continuous-time signal based on the wavelet packet coefficient signal Ei obtained from formula (4). The calculation formula is:

[0035]

[0036] In the formula, x i (t) is the time function calculation formula of signal i, is the instantaneous power of the signal;

[0037] S2.1.6: Normalize the energy of each frequency band to form the wavelet packet energy spectrum, which is calculated as follows:

[0038]

[0039] Where E1, E2 and Ei represent the energy of each frequency band, and E represents the total energy.

[0040] S2.1.7: The wavelet packet energy change rate is calculated based on the change in energy of each frequency band before and after damage. The calculation formula is:

[0041]

[0042] In the formula, is the energy of the ith node after damage, is the energy of the ith node when it is undamaged.

[0043] Optionally, the step of obtaining the fuzzy entropy of the wavelet packet coefficients in S2 is:

[0044] S2.2.1: For a time series of N points, an m-dimensional vector is constructed in sequence, and its calculation formula is:

[0045]

[0046] In the formula, the value of i is from 1 to N-m+1, and x0(i) is the mean of the m consecutive x values ​​starting from the i-th point of the time series;

[0047] S2.2.2: The calculation formula for obtaining the time moving average x0(i) is:

[0048]

[0049] In the formula, It is to accumulate the data values ​​from i to i+m-1;

[0050] S2.2.3: Calculate vector and Chebyshev distance between The calculation formula is:

[0051]

[0052] Wherein, the values ​​of i and j range from 1 to N-m+1, and i≠j;

[0053] S2.2.4: By vector and The Chebyshev distance between them gives the fuzzy function Defining Vectors and The similarity is calculated as follows:

[0054]

[0055] In the formula, Represented as a vector and The similarity of n is the gradient of the boundary, and r is the similarity tolerance;

[0056] S2.2.5: Based on vector and Similarity, defining the relationship dimension under the m dimension The calculation formula is:

[0057]

[0058] In the formula, It is expressed as the relational dimension under the m dimension. Represented as a vector and similarity;

[0059] S2.2.6: When the dimension increases to m+1, repeat the above steps S2.2.1 to S2.2.6 to calculate the relationship dimension:

[0060]

[0061] S2.2.7: Fuzzy entropy is defined according to the relationship dimension between m and m+1 dimensions. The fuzzy entropy calculation formula is:

[0062]

[0063] S2.2.8: If N is a finite value, the fuzzy entropy calculation formula is:

[0064]

[0065] Wherein, the values ​​of fuzzy entropy parameters are m=2, n=2 and r=0.15×std respectively.

[0066] Optionally, the step of acquiring the wavelet packet coefficient kurtosis value feature in S2 is:

[0067] S2.3.1: Perform wavelet packet decomposition on the signal to decompose it into wavelet packet coefficients of different scales and frequencies;

[0068] S2.3.2: Calculate the kurtosis value of each wavelet packet coefficient, and obtain the kurtosis value characteristics of the wavelet packet coefficient according to the kurtosis value of each wavelet packet coefficient. The calculation formula is:

[0069]

[0070] In the formula, x j It is expressed as the value of the wavelet packet coefficient, N is the number of wavelet packet coefficients, and σ is the standard deviation of the wavelet packet coefficients.

[0071] Optionally, the steps of calculating the optimal feature subset using the Relief algorithm and the forward search strategy described in S2 are:

[0072] S2.4.1: The ReliefF algorithm can estimate the importance of each feature by taking advantage of its ability to distinguish different damage categories. The calculation formula is:

[0073]

[0074] In the formula, A represents a certain characteristic parameter, W(A) represents the weight of the characteristic parameter A, and its initial value is 0, m is the number of cycles, k is the number of samples extracted, and diff(A,R,H j ) is expressed as the difference between two samples of the same damage category in the characteristic parameter A, diff(A,R,M j (C)) represents the difference in feature parameter A between two samples of different damage categories, class(R) represents the category of sample R, and P(C) is the proportion of category C;

[0075] It should be noted that the importance of each feature is obtained according to the ReliefF algorithm and then sorted. In order to avoid errors caused by artificially set thresholds, features are added by using a forward search strategy after feature sorting. The core of this strategy is to search forward step by step according to the rules of the problem until the target state is reached. This process usually involves a systematic exploration of the state space, which refers to the set of all possible states of the problem. When it is applied to feature selection, the effectiveness of the feature is judged based on the recognition accuracy. If the recognition accuracy is not improved, it means that the feature does not contribute to the target. The feature is filtered out. After filtering all irrelevant features, the optimal feature subset is obtained.

[0076] S2.4.2: Sort the importance of the features obtained, add features to the sorted damage features through a forward search strategy, and determine whether the features are effective based on the recognition accuracy. If the recognition accuracy is not improved, it means that the feature does not contribute to the target, and the feature is filtered out;

[0077] S2.4.3: After traversing all damage features, filter all irrelevant features to obtain the optimal feature subset;

[0078] S2.4.4: After obtaining the optimal feature subset, it is combined into a fusion feature. The calculation formula of the fusion feature is:

[0079] F=[F1 F2 … F n ] (18)

[0080] Where F is the fusion feature, and F1, F2 and Fn are the optimal feature subsets.

[0081] Optionally, the steps for setting the structure of the BP neural network in S3 are:

[0082] S3.1: A set of small non-zero values ​​are randomly assigned to the connection weights w between the input layer and the hidden layer ij and the connection weights wj between the hidden layer and the output layer i ;

[0083] S3.2: Assume that the number of training samples selected by the network is n, then the training sample set is X = [X1, X2, ..., X n ], the kth vector of the sample input layer is X k =[x k1 ,x k2 ,…,x km ], k = 1, 2, ..., n, the actual output of the BP neural network after the nth iteration is Y k (n) = [y k1 (n),y k2 (n),…,y kn (n)];

[0084] S3.3: Input the training sample set X and calculate the output of each neuron in the hidden layer. The calculation formula is:

[0085]

[0086] Where H is the hidden layer output, i is the number of hidden layer nodes, where i = 1, 2, …, q, α is the hidden layer threshold, and f is the hidden layer activation function;

[0087] S3.4: Calculate the output of each neuron in the output layer. The calculation formula is:

[0088]

[0089] In the formula, O is the output of the output layer, and b is the output layer threshold;

[0090] S3.5: Calculate the output error signal of the network, and the calculation formula is:

[0091] e k =d k -O k (twenty one)

[0092] Where K represents the data point, and k = 1, 2, ... L:

[0093] S3.5: According to the output error signal e, adjust the connection weight of the network, and its calculation formula is:

[0094]

[0095] ω ki =ω ki +ηH i e k i=1,2,…,q;k=1,2,…,L (23)

[0096] S3.6: adjusting the connection threshold of the network according to the output error signal e;

[0097]

[0098] b k =b k +e k k=1,2,…,L (25)

[0099] S3.6: Compare the error accuracy with the preset threshold. If the error accuracy is greater than the preset threshold, the training ends. If the error accuracy is less than the preset threshold, return to step 5 to continue weight adjustment until the error accuracy meets the requirement.

[0100] Optionally, in S4, the optimal solution is sought by simulating the process of predators preying on prey through HPO, and the steps are as follows:

[0101] S4.1.1: Randomize the initial population and generate a certain number of individuals, each of which represents a potential solution to the problem.

[0102] S4.1.2: Calculate the fitness values ​​of these initial individuals. The higher the fitness value, the more suitable the individual is for the environment, and take the highest fitness value among the individuals as the global optimal fitness value.

[0103] S4.1.3: Update the adaptive parameter Z and the balance parameter C to adjust the search behavior of the algorithm to adapt to different search spaces and the current optimization stage.

[0104] S4.1.4: Select different iteration methods to iterate the positions of individuals in the population in order to explore possible optimal solution positions in a larger space and find the optimal value.

[0105] S4.1.5: Determine whether the termination condition is met. If not, repeat steps S4.1.3 and S4.1.5 until the optimal solution is obtained.

[0106] Optionally, the steps of improving HPO by using Circle chaotic mapping, Cauchy mutation and nonlinear convergence factor to obtain IHPO in S4 are:

[0107] S4.2.1: The formula for Circle mapping is improved to initialize the position of the population. The calculation formula is:

[0108]

[0109] Where n is the dimension of the solution;

[0110] S4.2.2: Add the position iteration formula using Cauchy variation as the variable step length, where the calculation formula for obtaining Cauchy variation is:

[0111] r=tan[π×(R1-0.5)] (27)

[0112] Where R1 is a random number in the interval [0,1]

[0113] S4.2.3: Adjust the variable x based on the calculated r value i,j , the calculation formula is:

[0114]

[0115] In the formula, a scaling factor 1+r is applied to update the variable;

[0116] S4.2.4: Add a greedy strategy after Cauchy mutation. The calculation formula of the greedy strategy is as follows:

[0117]

[0118] In the formula, x' new represents the position of the individual in the population after greedy selection, f(x new ) represents the fitness of the position of the individual in the population before the change, and f(x') represents the fitness of the position of the individual in the population after the change;

[0119] S4.2.5: Improve the convergence mode of the convergence factor C using the sparrow search algorithm. The calculation formula is as follows:

[0120]

[0121] In the formula, when R2 < ST, it means there is no threat around, and food search can be carried out widely. The value of the latter part of the formula decreases adaptively;

[0122] S4.2.6: Modify the convergence factor C from linear to non - linear. The modified calculation formula is as follows:

[0123]

[0124] In the formula, it is the current iteration value, MaxIt is the maximum iteration value, C max is the maximum value of the parameter, C min is the minimum value of the parameter, and α is the adjustment factor;

[0125] S4.2.7: Obtain the IHPO formula according to the formula of Circle mapping, the position iteration formula of Cauchy mutation, and the modified convergence factor C of the formula.

[0126] Optionally, the steps for constructing the wavelet neural network in S7 are as follows:

[0127] S7.1: Use IHPO to optimize the initial weights and thresholds of the BP neural network, and perform loose - type fusion with the wavelet packet fusion features to form a loose - type wavelet neural network.

[0128] After adopting the above technical solutions, the present invention has the following beneficial effects compared with the prior art. Of course, any product implementing the present invention does not necessarily need to achieve all the advantages described below:

[0129] The present invention calculates the wavelet packet energy change rate, wavelet packet coefficient fuzzy entropy characteristics and wavelet packet coefficient kurtosis value of the cable dynamic response signal according to the wavelet packet energy and wavelet packet coefficient of the signal, combines the relief algorithm with the forward search strategy to perform feature selection, selects the optimal feature subset, and combines them in series to form a wavelet packet fusion feature; uses the proposed improved predator algorithm to optimize the initial weights and thresholds of the BP neural network, thereby improving the recognition accuracy of the neural network.

[0130] The specific implementation modes of the present invention are further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0131] The drawings described below are only some embodiments. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0132] In the figure:

[0133] Figure 1 Construct and apply a flowchart for the loose wavelet neural network application method;

[0134] Figure 2 It is the structure diagram of BP neural network;

[0135] Figure 3 This is the structure diagram of the wavelet neural network.

[0136] It should be noted that these drawings and textual descriptions are not intended to limit the conceptual scope of the present invention in any way, but are intended to illustrate the concept of the present invention for those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION

[0137] The present invention will now be described in further detail with reference to the accompanying drawings.

[0138] See also Figure 1-3 As shown, in this embodiment, a cable-stayed bridge damage identification method and system based on multi-wavelet packet energy and IHPO-SVM fusion are provided, including the following steps:

[0139] S1: Establish a benchmark finite element model of a cable-stayed bridge and extract the vertical acceleration signal of the main beam cable;

[0140] S2: Calculate the wavelet packet energy change rate, wavelet packet coefficient fuzzy entropy and wavelet packet coefficient kurtosis value characteristics of the acceleration signal, use the Relief algorithm and forward search strategy to calculate the optimal feature subset, connect the optimal feature subsets in series to obtain the wavelet packet fusion feature, and divide the optimal feature subsets into training set and test set, and input the training set into the BP neural network for training;

[0141] It should be noted that the Relief algorithm is a feature selection method used to select features from the data set that have important contributions to the classification task.

[0142] S3: Set the structure of the BP neural network, determine the number of nodes in the input layer, hidden layer and output layer, and the layers of the multi-layer BP neural network are fully connected, and the neurons in the same layer are not connected;

[0143] S4: Using Circle chaos mapping, Cauchy mutation and nonlinear convergence factor to improve HPO, IHPO is obtained;

[0144] It should be noted that Circle chaos mapping is a method of mapping dimensions to chaotic values.

[0145] It should be noted that the initial population of the predator algorithm is randomly generated, with strong randomness. The generated points may be concentrated in one area, which makes the individual similarity high, affecting the optimization time and speed of the algorithm. In addition, the algorithm lacks a perturbation update formula, and cannot explore more space during optimization, resulting in reduced population diversity. Therefore, based on the ordinary predator algorithm, the Circle chaos map is used to replace the original algorithm's random initial population generation mechanism to reduce randomness, and the Cauchy mutation formula is added to the algorithm to expand the algorithm's search space. The iteration method of the convergence factor is changed from linear to nonlinear, which enhances the algorithm's later search ability.

[0146] It is further explained that the chaotic mapping can effectively improve the problem of too much clustering of the initial population generation points in HPO. The principle is to map the variables to the value range of the chaotic variable space, so that the individuals are dispersed as evenly as possible, reduce the overlap of positions, and improve the optimization speed. The chaotic mappings commonly used for population initialization include Logistic mapping, Tent mapping, and Circle mapping. Among them, Logistic mapping has the problem of uneven distribution, Tent mapping has unstable cycles, and Circle mapping is better than the first two chaotic mappings, but it is still not very uniform and is concentrated between [0.20.5]. The formula of Circle mapping has been improved to make the distribution more uniform.

[0147] The expression of the original Circle mapping is:

[0148]

[0149] It should be noted that the Logistic map is a widely studied nonlinear dynamic system used to describe chaotic behavior; the Tent map is a simple discrete-time dynamic system with obvious chaotic characteristics; and the Circle map is a nonlinear dynamic system that describes angles.

[0150] S5: Obtain a convergence factor C, determine the search agent by comparing the convergence factor C, update the position of the search agent by a corresponding position formula, and calculate the fitness value of each search agent;

[0151] S6: Determine whether the fitness value of each search agent is less than the average fitness value. If so, perform Cauchy mutation on the search agent. If the fitness value after mutation is better than the old fitness value, replace the old fitness value.

[0152] S7: Determine whether the fitness value of the search agent meets the search termination condition. When the fitness value meets the termination condition, output the initial weight and threshold represented by the current optimal fitness value, and construct a multi-feature wavelet neural network;

[0153] S8: input the damage location test set of the simulation model into the damage location multi-feature wavelet neural network, and determine the damage position of the main beam through the damage condition output by the multi-feature wavelet neural network;

[0154] It should be noted that Figure 3 It can be seen that the structure of the wavelet neural network is generally divided into an input layer, a hidden layer, and an output layer, where the input layer has n neurons, the hidden layer has k neurons, and the output layer has m neurons. The number of neurons in the input layer and the output layer is determined according to actual requirements. vij represents the connection weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer, and wij represents the connection weight between the i-th neuron in the hidden layer and the j-th neuron in the output layer. The calculation formula for the hidden layer output is:

[0155]

[0156] Where h(j) is the output value of the jth node in the hidden layer, ψ(x) is the wavelet function, bj is the translation factor of the wavelet function, aj is the scaling factor of the wavelet function, vij is the weight of the input layer and the hidden layer, xi is the input layer parameter, and the activation function of the hidden layer neuron often uses Morlet wavelet:

[0157]

[0158] S9: After the damage location is determined, the damage quantification test set of the damage location is input into the damage quantification multi-feature wavelet neural network, and the damage quantification of the main beam is performed according to the damage degree output by the multi-feature wavelet neural network;

[0159] S10: Extract the acceleration data of the actual bridge when it is completed and calculate the wavelet packet features, which are used as the data of the undamaged working condition to input the damage location and damage quantification multi-feature wavelet neural network for training; the wavelet neural network is a loose wavelet neural network

[0160] It should be noted that the acceleration data of the cable is extracted, and the damage information in the acceleration data is extracted from the perspectives of wavelet packet energy change, wavelet packet coefficient complexity and wavelet packet coefficient distribution characteristics using wavelet packet fusion characteristics, which is then fused with the IHPO-BP neural network to establish a loose wavelet neural network to locate and quantify the damage of the main beam of the cable-stayed bridge.

[0161] S11: Extract the acceleration data of the actual bridge during operation and calculate the wavelet packet features, input them into the damage location multi-feature wavelet neural network, judge the damage position of the actual bridge through the damage condition output by the multi-feature wavelet neural network, input them into the damage quantification multi-feature wavelet neural network, and judge the damage degree of the actual bridge through the damage degree output by the multi-feature wavelet neural network.

[0162] In this embodiment, the step of calculating the wavelet packet energy change rate of the acceleration signal in S2 is:

[0163] S2.1.1: The vertical acceleration signal of the cable is extracted as the dynamic response signal, and the dynamic response signal is subjected to i-time wavelet transform to decompose the signal into i layers of wavelet packet coefficients of different frequencies and scales. The transformation calculation formula is:

[0164]

[0165] Where x(t) is the dynamic response signal;

[0166] It should be noted that each wavelet packet component contains the information of the signal in a specific time-frequency domain, and different wavelet packet components have different energy values. By combining all wavelet packet components, the complete characteristics of the signal in the time-frequency domain can be obtained, so the wavelet packet energy can be used as a feature to extract signal damage information.

[0167] S2.1.2: Using wavelet packet functions The linear combination of represents the obtained dynamic response signal, and its calculation formula is:

[0168]

[0169] In the formula, It is represented as the wavelet packet coefficient signal obtained after the i-th layer decomposition of the dynamic response signal. Expressed as wavelet packet coefficients;

[0170] S2.1.3: According to the wavelet packet coefficients of different frequencies and scales of layer i, the total energy Ei of the wavelet signal in the time domain of the dynamic response signal is calculated.

[0171]

[0172] S2.1.4: Substituting the wavelet packet coefficient signal Ei into formula (2), the calculation formula obtained is:

[0173]

[0174] In the formula, is the energy of each frequency band;

[0175] S2.1.5: Calculate the total energy of the continuous-time signal based on the wavelet packet coefficient signal Ei obtained from formula (4). The calculation formula is:

[0176]

[0177] In the formula, x i (t) is the time function calculation formula of signal i, is the instantaneous power of the signal;

[0178] S2.1.6: Normalize the energy of each frequency band to form the wavelet packet energy spectrum, which is calculated as follows:

[0179]

[0180] Where E1, E2 and Ei represent the energy of each frequency band, and E represents the total energy.

[0181] S2.1.7: The wavelet packet energy change rate is calculated based on the change in energy of each frequency band before and after damage. The calculation formula is:

[0182]

[0183] In the formula, is the energy of the ith node after damage, is the energy of the ith node when it is undamaged.

[0184] In this embodiment, the step of obtaining the fuzzy entropy of the wavelet packet coefficients in S2 is:

[0185] S2.2.1: For a time series of N points, an m-dimensional vector is constructed in sequence, and its calculation formula is:

[0186]

[0187] In the formula, the value of i is from 1 to N-m+1, and x0(i) is the mean of the m consecutive x values ​​starting from the i-th point of the time series;

[0188] S2.2.2: The calculation formula for obtaining the time moving average x0(i) is:

[0189]

[0190] In the formula, It is to accumulate the data values ​​from i to i+m-1;

[0191] S2.2.3: Calculate vector and Chebyshev distance between The calculation formula is:

[0192]

[0193] Wherein, the values ​​of i and j range from 1 to N-m+1, and i≠j;

[0194] S2.2.4: By vector and The Chebyshev distance between them gives the fuzzy function Defining Vectors and The similarity is calculated as follows:

[0195]

[0196] In the formula, Represented as a vector and The similarity of n is the gradient of the boundary, and r is the similarity tolerance;

[0197] S2.2.5: Based on vector and Similarity, defining the relationship dimension under the m dimension The calculation formula is:

[0198]

[0199] In the formula, It is expressed as the relational dimension under the m dimension. Represented as a vector and similarity;

[0200] S2.2.6: When the dimension increases to m+1, repeat the above steps S2.2.1 to S2.2.6 to calculate the relationship dimension:

[0201]

[0202] S2.2.7: Fuzzy entropy is defined according to the relationship dimension between m and m+1 dimensions. The fuzzy entropy calculation formula is:

[0203]

[0204] S2.2.8: If N is a finite value, the fuzzy entropy calculation formula is:

[0205]

[0206] Wherein, the values ​​of fuzzy entropy parameters are m=2, n=2 and r=0.15×std respectively.

[0207] In this embodiment, the step of acquiring the wavelet packet coefficient kurtosis value feature in S2 is:

[0208] S2.3.1: Perform wavelet packet decomposition on the signal to decompose it into wavelet packet coefficients of different scales and frequencies;

[0209] S2.3.2: Calculate the kurtosis value of each wavelet packet coefficient, and obtain the kurtosis value characteristics of the wavelet packet coefficient according to the kurtosis value of each wavelet packet coefficient. The calculation formula is:

[0210]

[0211] In the formula, x j It is expressed as the value of the wavelet packet coefficient, N is the number of wavelet packet coefficients, and σ is the standard deviation of the wavelet packet coefficients.

[0212] It should be noted that the kurtosis value is the normalized fourth-order central moment, which reflects the distribution characteristics of the signal and can be used to measure the outlier degree of the data.

[0213] In this embodiment, the step of calculating the optimal feature subset using the Relief algorithm and the forward search strategy in S2 is:

[0214] S2.4.1: Use the Relief algorithm to evaluate the importance of each damage feature. The calculation formula is:

[0215]

[0216] In the formula, A represents a certain characteristic parameter, W(A) represents the weight of the characteristic parameter A, and its initial value is 0, m is the number of cycles, k is the number of samples extracted, and diff(A,R,H j ) is expressed as the difference between two samples of the same damage category in the characteristic parameter A, diff(A,R,M j (C)) represents the difference in feature parameter A between two samples of different damage categories, class(R) represents the category of sample R, and P(C) is the proportion of category C;

[0217] S2.4.2: Sort the importance of the features obtained, add features to the sorted damage features through a forward search strategy, and determine whether the features are effective based on the recognition accuracy. If the recognition accuracy is not improved, it means that the feature does not contribute to the target, and the feature is filtered out;

[0218] S2.4.3: After traversing all damage features, filter all irrelevant features to obtain the optimal feature subset;

[0219] S2.4.4: After obtaining the optimal feature subset, it is combined into a fusion feature. The calculation formula of the fusion feature is:

[0220] F=[F1 F2 … F n ] (18)

[0221] Where F is the fusion feature, and F1, F2 and Fn are the optimal feature subsets.

[0222] In this embodiment, the BP neural network is generally multi-layered, and its structure includes: an input layer, a hidden layer, and an output layer. Figure 2 shown.

[0223] The layers of the multi-layer BP neural network are fully connected, and there is no connection between neurons in the same layer. The typical design of the BP neural network is that the hidden layer uses the Sigmoid function as the transfer function, while the output layer uses the linear function as the transfer function.

[0224] After determining the number of layers of the BP network and the number of neurons in each layer, it is also necessary to determine the weight coefficients between the layers in order to give the correct output value based on the input. The learning of the BP network is supervised learning, which requires a set of learning samples with known target outputs. During training, random values ​​are first used as weights, and the learning samples are input to obtain the output of the network. Then the error is calculated based on the output value and the target output. The error is then used to modify the weights layer by layer according to a certain criterion to reduce the error. This process is repeated until the error no longer decreases, and the network training is completed. The standard BP network uses the steepest descent method to modulate the weights of each layer, which is mainly divided into three parts: variable definition, forward propagation of working signals, and back propagation of errors. Taking a three-layer BP network as an example, the learning algorithm of the standard BP network is as follows:

[0225] S3.1: Randomly assign a set of small non-zero values ​​to the connection weights w between the input layer and the hidden layer i j and the connection weight wj between the hidden layer and the output layer i ;

[0226] S3.2: Assume that the number of training samples selected by the network is n, then the training sample set is X = [X1, X2, ..., X n ], the kth vector of the sample input layer is X k =[xk1 ,x k2 ,…,x km ], k = 1, 2, ..., n, the actual output of the BP neural network after the nth iteration is Y k (n) = [y k1 (n),y k2 (n),…,y kn (n)];

[0227] S3.3: Input the training sample set X and calculate the output of each neuron in the hidden layer. The calculation formula is:

[0228]

[0229] Where H is the hidden layer output, i is the number of hidden layer nodes, where i = 1, 2, …, q, α is the hidden layer threshold, and f is the hidden layer activation function;

[0230] It should be noted that the input layer has n neurons, the hidden layer has k neurons, and the output layer has m neurons. The number of neurons in the input layer and the output layer is determined according to actual requirements.

[0231] S3.4: Calculate the output of each neuron in the output layer. The calculation formula is:

[0232]

[0233] In the formula, O is the output of the output layer, and b is the output layer threshold;

[0234] S3.5: Calculate the output error signal of the network, and the calculation formula is:

[0235] e k =d k -O k (twenty one)

[0236] Where K represents the data point, and k = 1, 2, ... L:

[0237] S3.5: According to the output error signal e, adjust the connection weight of the network, and its calculation formula is:

[0238]

[0239] ω ki =ω ki +ηH i e k i=1,2,…,q;k=1,2,…,L (23)

[0240] S3.6: adjusting the connection threshold of the network according to the output error signal e;

[0241]

[0242] b k =b k +e k k=1,2,…,L (25)

[0243] S3.6: Compare the error accuracy with the preset threshold. If the error accuracy is greater than the preset threshold, the training ends. If the error accuracy is less than the preset threshold, return to step 5 to continue weight adjustment until the error accuracy meets the requirement.

[0244] It should be noted that when establishing the BP neural network model, the initial weights and thresholds are mostly randomly generated, which have great randomness and have a great impact on the final recognition results. IHPO is used to optimize the initial weights and thresholds of the BP neural network and construct the IHPO-BP neural network.

[0245] In this embodiment, in S4, the optimal solution is sought by simulating the process of a predator preying on prey through HPO, and the steps are as follows:

[0246] S4.1.1: Randomize the initial population and generate a certain number of individuals, each of which represents a potential solution to the problem.

[0247] S4.1.2: Calculate the fitness values ​​of these initial individuals. The higher the fitness value, the more suitable the individual is for the environment, and take the highest fitness value among the individuals as the global optimal fitness value.

[0248] S4.1.3: Update the adaptive parameter Z and the balance parameter C to adjust the search behavior of the algorithm to adapt to different search spaces and the current optimization stage.

[0249] S4.1.4: Select different iteration methods to iterate the positions of individuals in the population in order to explore possible optimal solution positions in a larger space and find the optimal value.

[0250] S4.1.5: Determine whether the termination condition is met. If not, repeat steps S4.1.3 and S4.1.5 until the optimal solution is obtained.

[0251] In this embodiment, the steps of improving HPO by using Circle chaotic mapping, Cauchy mutation and nonlinear convergence factor to obtain IHPO in S4 are as follows:

[0252] S4.2.1: The formula for Circle mapping is improved to initialize the position of the population. The calculation formula is:

[0253]

[0254] Where n is the dimension of the solution, the initial solution dimension distribution graph and the initial solution dimension distribution histogram of the two;

[0255] S4.2.2: Add the position iteration formula using Cauchy variation as the variable step length, where the calculation formula for obtaining Cauchy variation is:

[0256] r=tan[π×(R1-0.5)] (27)

[0257] Where R1 is a random number in the interval [0,1]

[0258] S4.2.3: Adjust the variable x based on the calculated r value i, j, the calculation formula is

[0259] x i,j (t+1)=x i,j (t)×(1+r) (28)

[0260] In the formula, a scaling factor 1+r is applied to update the variable;

[0261] S4.2.4: It should be noted that in the later stage of HPO, the algorithm will enter the local development stage, convergence will slow down, and it is not conducive to global search. Cauchy mutation originates from Cauchy distribution, which is characterized by a shorter peak and a wider distribution range, which makes the individuals after Cauchy mutation less constrained by local extreme points and easier to jump out of local extreme points. Therefore, Cauchy mutation can make individuals have a greater probability of jumping to a better position and enhance the global search ability of the algorithm. The calculation formula is shown in formula (27). Therefore, the position iteration formula with Cauchy mutation as the variable step length is added to the algorithm, as shown in formula, to perform perturbation updates on the search agents whose fitness values ​​are lower than the average value in the algorithm.

[0262] Further explanation: using disturbance update to mutate the position does not guarantee that each updated position is better than the previous position, so a greedy strategy needs to be added after the disturbance update. The greedy strategy means that when solving a problem, it always makes the best choice at the moment. The specific approach in the algorithm is to judge the next action by comparing the fitness values ​​represented by the positions before and after the change. When the fitness value after the change is better than the fitness value before the change, the fitness value after the change is used to replace the fitness value before the change. If the fitness value after the change is not as good as the fitness value before the change, no update is performed, and the position before the change is continued to be iterated. The calculation formula of the greedy strategy is:

[0263]

[0264] In the formula, x' new represents the position of individuals in the population after greedy selection, f(x new) represents the fitness of the population individual position before the change, and f(x') represents the fitness of the population individual position after the change;

[0265] S4.2.5: The sparrow search algorithm is used to improve the convergence mode of the convergence factor C, and its calculation formula is:

[0266]

[0267] In the formula, when R2 < ST, it indicates that there is no threat around, and food search can be widely carried out, and the value of the latter part of the formula decreases adaptively;

[0268] S4.2.6: Modify the convergence factor C from linear to non - linear, and its modified calculation formula is:

[0269]

[0270] In the formula, it is the current iteration value, MaxIt is the maximum iteration value, C max is the maximum value of the parameter, C min is the minimum value of the parameter, and α is the adjustment factor;

[0271] It should be noted that: It can be seen from Equation 31 that the parameter C is similar to a linear change in the early stage of iteration, which can better perform global search, and is similar to an exponential decline in the later stage, which is beneficial to local development. The non - linear adjustment parameter can better balance global and local search and improve the algorithm performance.

[0272] S4.2.7: Obtain the IHPO formula according to the formula of Circle mapping, the position iteration formula of Cauchy mutation, and the modified convergence factor C of the formula.

[0273] In this embodiment, the steps of updating the position of the search agent in S5 are as follows:

[0274] S5.1: Obtain the search route of the predator, and the calculation formula of the search route of the predator is:

[0275] x i,j (t + 1) = x i,j (t)+0.5[(2CZP pos(j) -x i,j (t))+(2(1 - C)Zu (j) -x i,j (t)] (32)

[0276] In the formula, x i,j (t) is the current position of the predator, x i,j (t + 1) is the next position of the predator, Ppos is the position of the prey, and u is the average value of all positions;

[0277] S5.2: Get the average value of all positions. The calculation formula of the average value is:

[0278]

[0279] S5.3: Obtain the adaptive parameter Z, the calculation formula is:

[0280]

[0281] IDX=(P==0)

[0282]

[0283] In the formula, and is a random vector in the range [0,1], R2 is a random number in the range [0,1], and IDX is the number of indices that meet the condition;

[0284] S5.4: C is the balance parameter between the exploration and development phases. The value of C decays from 1 to 0.02. The calculation formula is:

[0285]

[0286] Where MaxIt is the maximum number of iterations, it is the current iteration value;

[0287] S5.5: Calculate the Euclidean distance of all search agents from the average position, and then consider the search agent farthest from the average position as prey, which is calculated as:

[0288]

[0289] S5.6: To solve the setting of convergence in the later stage of the algorithm, the expression is:

[0290] kbest = round(C × N) (37)

[0291] In the formula, kbest represents the number of optimal results determined after calculation, and N is the number of search agents;

[0292] S5.7: Combining equation (38) and equation (39) together, we get the position calculation formula of the prey:

[0293]

[0294] S5.8: When a predator is chasing its prey, and the prey escapes to the best position, the predator needs to change its prey. The calculation formula is:

[0295] x i,j (t+1)=Tpos(j) +czcos(2πR4)×(T pos(j) -x i,j (t)) (39)

[0296] In the formula, x i,j (t) is the current position of the prey, x i,j (t+1) is the next position of the prey, Tpos(j) is the global optimal position, and R4 is a random number in [0,1];

[0297] S5.9: According to S5.1-S5.8, the calculation formula for the search proxy is:

[0298] x i,j (t+1)=x i,j (t)+0.5[(2CZP pos(j) -x i,j (t))+2(1-C)Zu (j) -x i,j (t)] (a)

[0299] x i,j (t+1)=T pos(j) +CZcos(2πR4)×(T pos(j) -x i,j (t))(b) (40)

[0300] In the formula, a random number R5 with a value between 0 and 1 is set, and a tuning parameter b with a value of 0.1 is set. When the value of R5 is less than b, the search agent is selected as a predator, and when the value of R5 is greater than b, the search agent becomes a prey.

[0301] In this embodiment, the steps of constructing the wavelet neural network in S7 are:

[0302] S7.1, IHPO is used to optimize the initial weights and thresholds of the BP neural network, and loosely fuses with the wavelet packet fusion features to form a loose wavelet neural network. The performance of IHPO on 10 test functions is better than that of the predator algorithm HPO, Harris Hawk algorithm HHO and whale algorithm WOA. IHPO-SVM shows fast and stable characteristics when optimizing SVM parameters. Compared with models such as SSA-SVM, it has faster optimization speed and higher damage identification accuracy. It can accurately identify the location and degree of main beam damage under different noise levels, showing good noise robustness.

[0303] SSA is defined as the Sparrow Algorithm.

[0304] Example 1: Damage Identification of Cable-Stayed Bridge

[0305] In order to verify the effectiveness of the proposed method in the damage location of the main beam of the cable-stayed bridge, the wavelet packet fusion feature and the IHPO-BP neural network are used to form a fusion feature loose wavelet neural network, the wavelet packet fusion feature and the compact wavelet neural network are used to form a fusion feature compact wavelet neural network, the wavelet packet energy change rate and the IHPO-BP neural network are used to form a single feature loose wavelet neural network, and the wavelet packet energy change rate and the compact wavelet neural network are used to form a single feature compact wavelet neural network. The above four wavelet neural networks are used to identify the damage position of the main beam of the cable-stayed bridge. The recognition results of the fusion feature loose wavelet neural network and the fusion feature compact wavelet neural network in the damage location of the cable-stayed bridge.

[0306] The steps of building and applying a compact wavelet neural network are as follows:

[0307] (1) Set the parameters of IHPO and the structure of compact wavelet neural network.

[0308] (2) Input the test set of wavelet packet energy change rate into the compact wavelet neural network.

[0309] (3) Use Circle mapping to initialize the position of the population, calculate the C value and Z value of IHPO, and perform position iteration according to the corresponding position iteration formula.

[0310] (4) Determine whether the fitness value is less than the average fitness value. If so, perform Cauchy mutation on the search agent. If the fitness value after mutation is better than the old fitness value, replace the old fitness value.

[0311] (5) Determine whether the search agent meets the termination conditions.

[0312] (6) When the search agent meets the termination condition, it outputs the initial weight, translation factor and shrinkage factor represented by the current optimal fitness value, and constructs an optimized compact wavelet neural network model.

[0313] (7) Input the wavelet packet energy change rate into the compact wavelet neural network model to identify the damage location and damage degree of the cable-stayed bridge

[0314] The loose wavelet neural network performs well in damage location. The recognition accuracy of the loose wavelet neural network in working conditions 1, working conditions 2 and working conditions 5 is 100%, and the recognition accuracy of the other two working conditions is as low as 88.9%, indicating that the loose wavelet neural network can effectively locate the damage of the main beam of the cable-stayed bridge. The recognition accuracy of the compact wavelet neural network is 100% only in working condition 1, and the recognition accuracy of other working conditions is as high as 94.4% and as low as 77.8%. By comparison, it can be found that the loose wavelet neural network can effectively realize the damage location of the main beam, and the recognition effect is better than that of the compact wavelet neural network.

[0315] Example 2: Project Overview and Benchmark Finite Element Model

[0316] Take a single-tower single-span cable-stayed bridge as an example. The bridge width is 37.5m, and the span is 130m+130m. The main beam of the bridge adopts a prestressed concrete inverted trapezoidal single-box four-chamber section. The cable tower is an H-shaped tower with a total height of 93.2m. The cable-stayed cable adopts parallel steel wire cables, and the shape layout adopts a fan-shaped layout. The cable distance on the beam is 6m, and there are 18 pairs of cable-stayed cables on each side.

[0317] The finite element software ANSYS is used to establish a benchmark finite element model of the cable-stayed bridge. The bean188 unit is used for the bridge and the cable tower, the link10 unit is used for the cable, consolidation is used at the bottom of the cable tower, and vertical and lateral constraints are applied at both ends of the cable-stayed bridge. The prestressing of the main beam and the bridge tower crossbeam is applied using the equivalent load method. The influence matrix method and optimization method are used to establish the benchmark finite element model.

[0318] Example 3: Damage localization of a baseline finite element model

[0319] When calculating the rate of change of wavelet packet energy, the appropriateness of the choice of wavelet basis has a very important impact on the final result. The dbN wavelet basis has the advantages of orthogonality, compact support and regularity, so the dbN wavelet basis function is used as the basis function for wavelet packet analysis. To determine the optimal order of the dbN wavelet basis, the ratio of wavelet packet energy to information entropy is used for selection. The calculation formula is as follows:

[0320]

[0321]

[0322] Where Pi is the ratio of each energy spectrum to all energy, H is the information entropy, and Ex is the wavelet packet energy.

[0323] Example 4: Damage Quantification of a Benchmark Finite Element Model

[0324] In order to identify the damage degree of the cable-stayed bridge, twenty groups of accelerations with a mean of 0 and a variance of 0.055-0.15 m / s2 are applied at the location, and the difference is 0.005 m / s2. The acceleration data of working conditions 2, 3, 4 and 5 under three damage degrees are extracted to identify the damage degree, and the identification error is calculated to verify the effectiveness of this method in damage quantification. The calculation formula is as follows:

[0325]

[0326] Where Dai is the actual damage degree, Dpi is the predicted damage degree, and n is the number of test samples.

[0327] Example 5: Noise robustness analysis

[0328] In order to further verify the noise robustness of the proposed method, Gaussian white noise with a degree of 5%, 10% and 15% was added to the extracted main beam acceleration data. The calculation formula is as follows:

[0329] S k =S k,u +S k,u σχ (54)

[0330] Where Sk is the acceleration response signal with noise added, Sk,u is the acceleration response signal without noise, σ represents a normal distribution with a mean of 0 and a variance of 1, and χ is the intensity of the Gaussian white noise level.

[0331] The dynamic response signal after adding noise is decomposed and reconstructed by wavelet packets, and the damage information of the signal is extracted by calculating the wavelet packet energy change rate. IHPO is used to optimize the parameters of SVM, and the kernel function and penalty factor are obtained according to the optimal fitness value to construct IHPO-SVM. The wavelet packet energy change rate under 5% intensity noise, 10% intensity noise and 15% intensity noise interference is input into IHPO-SVM respectively to identify the damage location and damage degree of the main beam of the cable-stayed bridge.

[0332] Example 6: Establishment and application steps of IHPO-SVM cable-stayed bridge damage identification model

[0333] When building a cable-stayed bridge damage identification model based on support vector machine, the selection of penalty factor and kernel function will have a great impact on the identification effect. Inappropriate parameter selection will affect the final identification result. In order to reduce the impact of parameters on the results, IHPO is used to optimize the kernel function and penalty factor of SVM to build the IHPO-SVM model. The specific steps are as follows:

[0334] (1) Establish a benchmark finite element model of the cable-stayed bridge and extract the acceleration data of the main beam.

[0335] (2) Calculate the rate of change of the wavelet packet energy of the acceleration signal and use it as the feature vector to input into the SVM.

[0336] (3) Set the parameters of IHPO, the maximum number of iterations, the population size, the number of parameters to be optimized, and the upper and lower limits of the parameters, and use Circle mapping to initialize the position of the population.

[0337] (4) Input the position vector of the initial population into SVM to obtain the initial fitness value.

[0338] (5) Calculate the value of parameter C according to formula (3-15), update the position of the search agent through the corresponding position formula, and calculate the fitness value of each search agent.

[0339] (6) Determine whether the fitness value of each search agent is less than the average fitness value. If so, perform Cauchy mutation on the search agent. If the fitness value after mutation is better than the old fitness value, replace the old fitness value.

[0340] (7) Determine whether the fitness values ​​of all search agents meet the search termination conditions.

[0341] (8) When the fitness value meets the termination condition, the kernel function and penalty factor represented by the current optimal fitness value are output, and the IHPO-SVM cable-stayed bridge damage identification model is constructed.

[0342] The present invention is not limited to the above-mentioned embodiments. Anyone should be aware that any structural changes made under the enlightenment of the present invention, and any technical solutions that are the same or similar to the present invention, fall within the protection scope of the present invention. The technology, shape, and structural parts not described in detail in the present invention are all well-known technologies.

Claims

1. A cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion, characterized in that: The following steps are involved: S1: Establish a benchmark finite element model of a cable-stayed bridge and extract the vertical acceleration signal of the main beam cable; S2: Calculate the wavelet packet energy change rate, wavelet packet coefficient fuzzy entropy and wavelet packet coefficient kurtosis value characteristics of the acceleration signal, use the Relief algorithm and forward search strategy to calculate the optimal feature subset, connect the optimal feature subsets in series to obtain the wavelet packet fusion feature, and divide the optimal feature subsets into training set and test set, and input the training set into the BP neural network for training; S3: Set the structure of the BP neural network, determine the number of nodes in the input layer, hidden layer and output layer, and the layers of the multi-layer BP neural network are fully connected, and the neurons in the same layer are not connected; S4: Using Circle chaos mapping, Cauchy mutation and nonlinear convergence factor to improve HPO, IHPO is obtained; S5: Obtain a convergence factor C, determine the search agent by comparing the convergence factor C, update the position of the search agent by a corresponding position formula, and calculate the fitness value of each search agent; S6: Determine whether the fitness value of each search agent is less than the average fitness value. If so, perform Cauchy mutation on the search agent. If the fitness value after mutation is better than the old fitness value, replace the old fitness value. S7: Determine whether the fitness value of the search agent meets the search termination condition. When the fitness value meets the termination condition, output the initial weight and threshold represented by the current optimal fitness value, and construct a multi-feature wavelet neural network; S8: input the damage location test set of the simulation model into the damage location multi-feature wavelet neural network, and determine the damage position of the main beam through the damage condition output by the multi-feature wavelet neural network; S9: After the damage location is determined, the damage quantification test set of the damage location is input into the damage quantification multi-feature wavelet neural network, and the damage quantification of the main beam is performed according to the damage degree output by the multi-feature wavelet neural network; S10: Extract the acceleration data of the actual bridge when it is completed and calculate the wavelet packet features, which are used as the data of the undamaged working condition to input the damage location and damage quantification multi-feature wavelet neural network for training; S11: Extract the acceleration data of the actual bridge during operation and calculate the wavelet packet features, input them into the damage location multi-feature wavelet neural network, judge the damage position of the actual bridge through the damage condition output by the multi-feature wavelet neural network, input them into the damage quantification multi-feature wavelet neural network, and judge the damage degree of the actual bridge through the damage degree output by the multi-feature wavelet neural network.

2. The cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion according to claim 1 is characterized in that: The steps for calculating the rate of change of wavelet packet energy of the acceleration signal in S2 are: S2.1.1: The vertical acceleration signal of the cable is extracted as the dynamic response signal, and the dynamic response signal is subjected to i-time wavelet transform to decompose the signal into i layers of wavelet packet coefficients of different frequencies and scales. The transformation calculation formula is: Where x(t) is the dynamic response signal; S2.1.2: Using wavelet packet functions The linear combination of represents the obtained dynamic response signal, and its calculation formula is: In the formula, It is represented as the wavelet packet coefficient signal obtained after the i-th layer decomposition of the dynamic response signal. Expressed as wavelet packet coefficients; S2.1.3: According to the wavelet packet coefficients of different frequencies and scales of layer i, the total energy Ei of the wavelet signal in the time domain of the dynamic response signal is calculated. S2.1.4: Substituting the wavelet packet coefficient signal Ei into formula (2), the calculation formula obtained is: In the formula, is the energy of each frequency band; S2.1.5: Calculate the total energy of the continuous-time signal based on the wavelet packet coefficient signal Ei obtained from formula (4). The calculation formula is: In the formula, x i (t) is the time function calculation formula of signal i, is the instantaneous power of the signal; S2.1.6: Normalize the energy of each frequency band to form the wavelet packet energy spectrum, which is calculated as follows: In the formula, E1, E2 and Ei represent the energy of each frequency band, and E represents the total energy; S2.1.7: When there is damage to the structure, the dynamic response signal at the damaged part will be more chaotic, and the wavelet coefficient will change significantly, resulting in an increase in wavelet energy. The wavelet packet energy at the damaged part increases relative to the wavelet packet energy at the same part before damage, and the change is the largest; on the contrary, the total wavelet energy at the undamaged part changes less; therefore, the relative change of the total wavelet energy at the measuring point before and after damage can be used as a damage indicator to extract the damage information of the signal; the calculation formula for the wavelet packet energy change rate is as follows: In the formula, is the energy of the ith node after damage, is the energy of the ith node when it is undamaged.

3. The cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion according to claim 1 is characterized in that: The steps for obtaining the fuzzy entropy of the wavelet packet coefficients in S2 are: S2.2.1: For a time series of N points, an m-dimensional vector is constructed in sequence, and its calculation formula is: In the formula, the value of i is from 1 to N-m+1, and x0(i) is the mean of the m consecutive x values ​​starting from the i-th point of the time series; S2.2.2: The calculation formula for obtaining the time moving average x0(i) is: In the formula, It is to accumulate the data values ​​from i to i+m-1; S2.2.3: Calculate vector and Chebyshev distance between The calculation formula is: Wherein, the values ​​of i and j range from 1 to N-m+1, and i≠j; S2.2.4: By vector and The Chebyshev distance between them gives the fuzzy function Defining Vectors and The similarity is calculated as follows: In the formula, Represented as a vector and The similarity of n is the gradient of the boundary, and r is the similarity tolerance; S2.2.5: Based on vector and Similarity, defining the relationship dimension under the m dimension The calculation formula is: In the formula, It is expressed as the relational dimension under the m dimension. Represented as a vector and similarity; S2.2.6: When the dimension increases to m+1, repeat the above steps S2.2.1 to S2.2.6 to calculate the relationship dimension: S2.2.7: Fuzzy entropy is defined according to the relationship dimension between m and m+1 dimensions. The fuzzy entropy calculation formula is: S2.2.8: If N is a finite value, the fuzzy entropy calculation formula is: Wherein, the values ​​of fuzzy entropy parameters are m=2, n=2 and r=0.15×std respectively.

4. The cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion according to claim 1 is characterized in that: The steps for obtaining the kurtosis value feature of the wavelet packet coefficient in S2 are: S2.3.1: Perform wavelet packet decomposition on the signal to decompose it into wavelet packet coefficients of different scales and frequencies; S2.3.2: Calculate the kurtosis value of each wavelet packet coefficient, and obtain the kurtosis value characteristics of the wavelet packet coefficient according to the kurtosis value of each wavelet packet coefficient. The calculation formula is: In the formula, x j It is expressed as the value of the wavelet packet coefficient, N is the number of wavelet packet coefficients, and σ is the standard deviation of the wavelet packet coefficients.

5. The cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion according to claim 1 is characterized in that: The steps for calculating the optimal feature subset using the Relief algorithm and forward search strategy described in S2 are: S2.4.1: Use the Relief algorithm to evaluate the importance of each damage feature. The calculation formula is: In the formula, A represents a certain characteristic parameter, W(A) represents the weight of the characteristic parameter A, and its initial value is 0, m is the number of cycles, k is the number of samples extracted, and diff(A,R,H j ) is expressed as the difference between two samples of the same damage category in the characteristic parameter A, diff(A,R,M j (C)) represents the difference in feature parameter A between two samples of different damage categories, class(R) represents the category of sample R, and P(C) is the proportion of category C; S2.4.2: Sort the importance of the features obtained, and add features to the sorted damage features through a forward search strategy. Determine whether the feature is effective based on the recognition accuracy. If the recognition accuracy is not improved, it means that the feature does not contribute to the target, and the feature is filtered out. S2.4.3: After traversing all damage features, filter all irrelevant features to obtain the optimal feature subset; S2.4.4: After obtaining the optimal feature subset, it is combined into a fusion feature. The calculation formula of the fusion feature is: F=[F1 F2 … F n ] (18) Where F is the fusion feature, and F1, F2 and Fn are the optimal feature subsets.

6. The cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion according to claim 1 is characterized in that: The structural steps of setting the BP neural network in S3 are: S3.1: A set of small non-zero values ​​are randomly assigned to the connection weights w between the input layer and the hidden layer ij and the connection weights wj between the hidden layer and the output layer i ; S3.2: Assume that the number of training samples selected by the network is n, then the training sample set is X = [X1, X2, ..., X n ], the kth vector of the sample input layer is X k =[x k1 ,x k2 ,…,x km ], k = 1, 2, ..., n, the actual output of the BP neural network after the nth iteration is Y k (n) = [y k1 (n),y k2 (n),…,y kn (n)]; S3.3: Input the training sample set X and calculate the output of each neuron in the hidden layer. The calculation formula is: Wherein, H is the output of the hidden layer, i is the number of hidden layer nodes, where i = 1, 2, …, q, α is the hidden layer threshold, and f is the hidden layer activation function; S3.4: Calculate the output of each neuron in the output layer, and its calculation formula is: Wherein, O is the output of the output layer, and b is the output layer threshold; S3.5: Calculate the output error signal of the network, and its calculation formula is: e k =d k -O k (21) Wherein, K represents the data point, and k = 1, 2, ... L: S3.5: According to the output error signal e, adjust the connection weights of the network, and its calculation formula is: oh ki =ω ki +ηH i e k i=1,2,…,q;k=1,2,…,L (23) S3.6: According to the output error signal e, adjust the connection thresholds of the network; b k =b k +e k k=1,2,…,L (25) S3.6: Compare the error accuracy with the preset threshold. If the error accuracy is greater than the preset threshold, the training ends. If the error accuracy is less than the preset threshold, return to step five to continue adjusting the weights until the error accuracy meets the requirements.

7. The cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion according to claim 1 is characterized in that: In S4, HPO seeks the optimal solution by simulating the process of a predator preying on prey, and its steps are as follows: S4.1.1: Randomize the initial population and generate a certain number of population individuals. Each individual represents a potential solution to the problem; S4.1.2: Calculate the fitness values of these initial individuals. The higher the fitness value, the more suitable the individual is for the environment, and take the highest fitness value in the individuals as the global optimal fitness value; S4.1.3: Update the adaptive parameter Z and the balance parameter C, and adjust the search behavior of the algorithm to adapt to different search spaces and the current optimization stage; S4.1.4: Select different iteration methods to perform position iteration on the population individuals to explore possible optimal solution positions in a larger space and find the optimal value; S4.1.5: Determine whether the termination condition is met. When it is not met, repeat steps S4.1.3 and S4.1.5 until the optimal solution to the problem is obtained.

8. The cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion according to claim 1 is characterized in that: The steps of improving HPO to obtain IHPO by using Circle chaotic mapping, Cauchy mutation, and non-linear convergence factor in S4 are as follows: S4.2.1: Improve the formula of the Circle mapping and initialize the position of the population. Its calculation formula is: Wherein, n is the dimension of the solution; S4.2.2: Add a position iteration formula with Cauchy mutation as the mutation step size. Among them, the calculation formula for obtaining Cauchy mutation is: r = tan[π×(R1 - 0.5)] (27) Wherein, R1 is a random number in the interval [0, 1] S4.2.3: Adjust the variable x based on the calculated r value i,j , the calculation formula is: x i,j (t+1)=x i,j (t)×(1+r) (28) Wherein, a scale factor 1 + r is applied to update the variable; S4.2.4: Add a greedy strategy after Cauchy mutation. The calculation formula of the greedy strategy: In the formula, x' new represents the position of individuals in the population after greedy selection, f(x new ) represents the fitness of the individual position of the population before the change, and f(x') represents the fitness of the individual position of the population after the change; S4.2.5: Improve the convergence mode of the convergence factor C by using the sparrow search algorithm. Its calculation formula is: Wherein, when R2 < ST, it means there is no threat around, and food search can be carried out widely. The value of the latter part of the formula is adaptively reduced; S4.2.6: Modify the convergence factor C from linear to non-linear, and its modified calculation formula is: In the formula, it is the current iteration value, MaxIt is the maximum iteration value, C max is the maximum value of the parameter, C min is the minimum value of the parameter, and α is the adjustment factor; S4.2.7: Obtain the IHPO formula according to the formula of the Circle mapping, the position iteration formula of Cauchy mutation, and the modified convergence factor C.

9. The cable-stayed bridge damage identification method based on multi-wavelet packet energy and IHPO-SVM fusion according to claim 1 is characterized in that: The steps of constructing the wavelet neural network in S7 are: S7.1, using IHPO to optimize the initial weights and thresholds of the BP neural network, and performing loose fusion with the wavelet packet fusion features to form a loose wavelet neural network.

10. A cable-stayed bridge damage identification system fused with multi-wavelet packet energy and IHPO-SVM, characterized in that: include Model building module, which is used to build a reference finite element model of a cable-stayed bridge and extract vertical acceleration signals of the main beam cables; The calculation module is used to calculate the wavelet packet energy change rate, wavelet packet coefficient fuzzy entropy and wavelet packet coefficient kurtosis value characteristics of the acceleration signal, calculate the optimal feature subset using the Relief algorithm and the forward search strategy, connect the optimal feature subsets in series to obtain the wavelet packet fusion feature, and divide the optimal feature subsets into a training set and a test set, and input the training set into the BP neural network for training; Setting module, the setting module is used to set the structure of BP neural network, determine the number of nodes in input layer, hidden layer and output layer, and the layers of BP neural network composed of multiple layers are fully connected, and the neurons in the same layer are not connected; Improvement module, which is used to improve HPO by using Circle chaos mapping, Cauchy mutation and nonlinear convergence factor to obtain IHPO; Search module, the search module is used to obtain the convergence factor C, determine the search agent by comparing the convergence factor C, update the position of the search agent through the corresponding position formula, and calculate the fitness value of each search agent; The fitness value judgment module is used to judge whether the fitness value of each search agent is less than the fitness average value. If so, the search agent is subjected to Cauchy mutation. If the fitness value after mutation is better than the old fitness value, the old fitness value is replaced. Wavelet neural network building module: The wavelet neural network building module is used to determine whether the fitness value of the search agent meets the search termination condition. When the fitness value meets the termination condition, the initial weight and threshold represented by the current optimal fitness value are output to build a multi-feature wavelet neural network; Position judgment module: The position judgment module is used to input the damage location test set of the simulation model into the damage location multi-feature wavelet neural network, and judge the damage location of the main beam through the damage working condition output by the multi-feature wavelet neural network; The quantitative judgment module, after determining the damage location, inputs the damage quantitative test set of the damage location into the damage quantitative multi-feature wavelet neural network, and performs damage quantification of the main beam according to the damage degree output by the multi-feature wavelet neural network; Training module, which is used to extract acceleration data of the actual bridge when it is completed and calculate wavelet packet features, which are used as data input for damage location and damage quantification multi-feature wavelet neural network training; The comparison module is used to extract the acceleration data of the actual bridge during operation and calculate the wavelet packet features, input them into the damage location multi-feature wavelet neural network, judge the damage location of the actual bridge through the damage working condition output by the multi-feature wavelet neural network, input them into the damage quantification multi-feature wavelet neural network, and judge the damage degree of the actual bridge through the damage degree output by the multi-feature wavelet neural network.

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