Bridge Reliability Prediction Method Based on Dynamic Characteristics and Intelligent Algorithm Response Surface Method

Abstract

The present invention discloses a bridge reliability prediction method based on dynamic characteristics and response surface method, which includes the following steps: collecting and preprocessing the vibration characteristic information of existing bridges; establishing a structural analysis model in combination with bridge design data and operation conditions, and using sensitivity analysis method to screen out the design parameters to be corrected in the structural analysis model; obtaining output samples, forming training samples with input samples, and correcting the initial structural analysis model; based on the corrected structural analysis model, output samples, constructing training samples again, and normalizing the sample points to construct a response surface model; standard normalizing random variables, transforming the constrained optimization problem into an unconstrained optimization problem by using penalty function, and obtaining the optimal weights of random variables by using optimization algorithms; establishing a mathematical model for solving the structural reliability index through the prediction results of the constructed response surface model. The beneficial effects of the present invention are: high calculation accuracy and fast estimation speed.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge engineering, and particularly relates to a bridge reliability prediction method based on dynamic characteristics and response surface method. Background Art

[0002] The reliability problem of existing bridges is one of the research hotspots in the current civil engineering field. However, the analysis models for bridge reliability research are mainly established based on bridge design data, which has a large deviation from the actual situation of the long-term service material performance degradation of existing bridges and cannot truly and accurately reflect the reliable performance of existing bridge structures during the use process. In addition, in the reliability analysis of complex bridge projects, its performance function is generally implicit, which makes it difficult to directly use algorithms such as the first-order second-moment method (FORM), second-order second-moment method (SORM), and direct integration method. However, the direct Monte Carlo simulation method (MCS) is suitable for solving the reliability problem of implicit performance functions and has high calculation accuracy. However, to ensure the calculation accuracy, the MCS method requires a large number of sampling times. Especially when the performance function values need to be obtained by means of finite elements, the huge calculation amount leads to extremely long time consumption, resulting in great limitations of the MCS method in engineering applications. Therefore, using a small number of sampling points, using regression tools such as classical response surface (RSM), artificial neural network (ANN), Kriging surrogate model, and support vector machine (SVM) to construct the response surface of the implicit performance function, and then combining conventional methods such as FORM, SORM, and MCS for reliability analysis can effectively reduce the number of structural re-analyses and significantly improve the calculation efficiency. Currently, it has become an important approach for the reliability analysis of complex structures.

[0003] Aiming at the problem that the results in the current reliability analysis process of existing bridges have a large deviation and cannot truly reflect the reliability of the actual bridge during the use process, and in the reliability calculation process, the traditional response surface method has low fitting accuracy and the accuracy is difficult to meet the requirements when solving bridge reliability. Using the finite element model correction method, combining the characteristics of dynamic Bayesian network (DBN) and PSOSA optimization algorithm, a response surface method for bridge structure reliability prediction based on finite element model correction is proposed. This method first corrects the finite element model to make the corrected structural analysis model coincide with the performance parameters of the actual existing bridge; secondly, in the reliability calculation of the existing bridge structure, the proposed method not only utilizes the advantages of DBN in dealing with uncertainty problems and probabilistic inference problems, but also utilizes the characteristics of the PSOSA algorithm that can better update the particle swarm coordinates to search for the optimal solution faster, effectively improving the accuracy and efficiency of the reliability calculation of complex structures, overcoming the limitations of the classical response surface method in the reliability problems of highly nonlinear structures, and solving the problems such as the low calculation efficiency of the MCS method and the excessive dependence of the existing response surface method on the scale and distribution of preset samples. Summary of the Invention

[0004] In view of the large deviation between the analysis model and the actual bridge structure performance in the reliability analysis process of existing bridge structures, when using the traditional response surface method to solve the reliability problem, due to the highly nonlinear implicit functional function, the fitting accuracy is not high and the precision is difficult to meet the requirements.

[0005] To solve the above problems, the present invention proposes a bridge reliability prediction method based on dynamic characteristics and the response surface method, which is characterized by including the following steps:

[0006] S1 Collect and preprocess the vibration characteristic information of the existing bridge.

[0007] S2 Combine the bridge design data and operation conditions to establish a structural analysis model, and use the sensitivity analysis method to screen out the design parameters to be corrected in the structural analysis model.

[0008] S3 Calculate the target variables corresponding to each input sample to obtain the output samples, and then form the training samples with the input samples. Combine the intelligent algorithm and use the dynamic characteristic data in step S1 to realize the correction of the initial structural analysis model.

[0009] S4 Based on the corrected structural analysis model, calculate the target variables corresponding to each input sample again to obtain the output samples, construct the training samples again, and perform normalization processing on the sample points. Based on the intelligent algorithm, construct a response surface model.

[0010] S5 Standardize the random variables to a standard normal distribution, use the penalty function to transform the constrained optimization problem into an unconstrained optimization problem, and use the optimization algorithm to obtain the optimal weights of the random variables.

[0011] S6 Establish a mathematical model for solving the structural reliability index through the prediction results of the constructed response surface model:

[0012] Compare the prediction results of the constructed response surface model with the results of the structural true limit state function. When the prediction results of the response surface model converge to the results of the structural true limit state function, directly use the response surface prediction results for structural reliability calculation. When the prediction results of the response surface model do not converge to the true limit state function, it is necessary to update and optimize the samples of the DBN prediction model so that the DBN prediction model can well approximate the sample points until the model constructs a response surface with sufficient accuracy to truly simulate the structural limit state function.

[0013] The limit state function of the structure should be determined according to various factors such as the specific form of the structure and the analysis object of the reliability.

[0014] Further, in step S1, the actual vibration characteristic information of the bridge structure is obtained by direct measurement method or indirect measurement method, and the collected vibration information is processed by signal processing methods.

[0015] Furthermore, the direct measurement method in step S1: The vibration pick-up is directly arranged at the bridge control section, the bridge vibration response signal is collected by the digital signal acquisition instrument, and the responses such as the bridge frequency are read from the peak value of the power spectrum diagram and the time-domain history curve actually measured and recorded by the acquisition system.

[0016] Indirect measurement method: The sensor is installed on the moving trolley. When the moving trolley passes over the bridge and the vehicle-bridge coupling effect occurs, the dynamic characteristics method of the bridge is extracted from the acceleration response of the vehicle body to obtain information such as the bridge frequency.

[0017] Signal processing method: By performing Fourier transform on the time-domain signal collected by the vibration pick-up, the frequency-domain result of the bridge frequency characteristics can be obtained. The Fourier transform formula is:

[0018]

[0019] In the formula: j is the imaginary unit, j^2 = -1, dimensionless; T is the period, unit is second; X is the original function of x; t is the time, unit is second; ω is the frequency, and x(t) is the continuous-time signal.

[0020] Preferably, step S1 adopts the direct measurement method to test the dynamic characteristic results of the bridge. The specific method is to arrange vibration pick-up devices at the typical sections of the existing bridge, such as the 1 / 2, 1 / 4, and fulcrum section positions. The bridge vibration response signal is collected by the digital signal acquisition instrument, and the responses such as the bridge frequency are read from the peak value of the power spectrum diagram and the time-domain history curve actually measured and recorded by the acquisition system. During signal processing, by performing Fourier transform on the time-domain signal collected by the vibration pick-up, the frequency-domain results (such as frequency, vibration mode, etc.) of the bridge frequency characteristics can be obtained. The Fourier transform formula is:

[0021]

[0022] In the formula: j is the imaginary unit, j^2 = -1, dimensionless; T is the period, unit is second; X is the original function of x; t is the time, unit is second; ω is the frequency, and x(t) is the continuous-time signal.

[0023] Further, in step S2, according to the design data of the existing bridge, the values of the bridge design parameters (such as material elastic modulus E, material unit weight γ, boundary conditions, load application, etc. parameters) are determined, an initial structural analysis model of the bridge is established, and a sensitivity analysis is performed on each design parameter to screen out the design parameters that have a greater impact on the bridge structure response.

[0024] Further, in step S2, according to the design data of the bridge, a numerical analysis model of the bridge structure is established using finite element software (such as ANSYS, ABAQUS, Midas, etc.). The Morris method is used to perform a sensitivity analysis on the design parameters, and the design parameters that have a greater impact on the bridge vibration response are selected as the design parameters to be corrected subsequently. The Morris method causes the change of the output response through the change amount of a single factor, and its calculation formula is:

[0025]

[0026] In the formula: d i (j) is the base effect of the j-th group of samples of the i-th parameter, j = 1, 2, 3, … R (R is the number of repeated samplings), n is the number of parameters; x i is the i-th parameter, Δ is the small change amount of a single parameter, and f(X) is the response output corresponding to the parameter group. Morris proposed two calculation indicators to judge the sensitivity of parameters, namely the mean value μ of the base effect and the standard deviation σ. Among them, μ characterizes the sensitivity of the parameter and determines the sorting of the parameters, and σ characterizes the non-linear degree between the parameters. The key design parameters that need to be corrected are selected through the Morris calculation results.

[0027] Further, in step S3, the target variables corresponding to each input sample are calculated. Based on the uniform design theory, a training sample between the spatially full design parameters and the vibration response is constructed and substituted into the intelligent algorithm program for learning and training; the bridge vibration characteristic information obtained in step S1 is called as the input parameter and substituted into the response surface model to predict the actual values of each design parameter, and the predicted values of the design parameters are substituted into the initial structure analysis model established in step S2 to realize the correction of the bridge structure analysis model, and the corrected analysis model is consistent with the actual state of the existing bridge.

[0028] Further, in step S3, the Latin Hypercube Sampling (LHS) method is used to perform efficient sampling from the distribution interval of the design parameters. For K variables x1, x2,..., x k , N samples are drawn from them. The cumulative distribution of each variable is divided into the same N small intervals, and a value is randomly selected from each interval. The N values of each variable are randomly combined with the values of other variables. This method can ensure the full coverage of the range of each variable. Using each design parameter as the input data and the structural vibration response corresponding to each group of design parameters as the output data, training samples are generated. On the basis of the completion of the construction of the training samples, a Gaussian process response surface model is established. For the training sample set (x1, t1), (x2, t2)... (x N , t N ), t i is the target value corresponding to x i , predicting a new set of input quantities xN+1 The corresponding target value t can be obtained N+1 , and its training set is as follows:

[0029] R = {(X i , T i ), i = 1, 2, 3,..., i,..., N} (3);

[0030] The joint probability distribution of the training set follows a Gaussian distribution:

[0031] f(T N ) ~ GP(m(x), K(x, x')) (4);

[0032] Where:

[0033] m(x) = E[f(x)] (5);

[0034] K(x, x') = E[(f(x) - m(x))(f(x') - m(x'))] (6);

[0035] Among them, m(x) is the mean; f(x) is a function about the sample points; E is the symbol of the mean; K(x, x') is the covariance matrix;

[0036] By determining the mean m(x) and the covariance matrix K(x, x'), the corresponding Gaussian process response surface model can be determined;

[0037] After the Gaussian process response surface model is established, the bridge dynamic characteristic results obtained in step S1 are input into the Gaussian process response surface model to calculate the prediction results of the design parameters, and the prediction results are substituted into the initial structural analysis model in step S1 to complete the correction of the initial structural analysis model.

[0038] Furthermore, in step S4, based on the corrected structural analysis model, the target variables corresponding to each input sample are calculated again to obtain output samples, and training samples are constructed again. The sample points are normalized, and a basic DBN model is established based on the BN toolbox in MATLAB. Through the process of unsupervised training of the basic model with the input sample points and model parameter optimization, a DBN response surface model related to the structure is obtained.

[0039] Even further, in step S4, based on the corrected structural analysis model, the training samples are normalized using the normalization method so that the normalized results are between 0 and 1. The normalization formula:

[0040]

[0041] In the formula: x i is the sample point data, and y i is the result after normalization;

[0042] Substitute the normalized training samples into the DBN toolbox in MATLAB software to calculate the DBN corresponding surface model for the DBN random variables;

[0043] The construction of the response surface model is to use the built-in DBN toolbox in MATLAB software. Input the training sample data into the algorithm of the DBN toolbox to construct the response surface model;

[0044] Among them, DBN can be expressed as (B0, B → ), where B0 is the static BN, representing the probability distribution P(X0) of the nodes at the initial moment, and B → is a transition network containing two adjacent time slices, representing the state transition probability between the nodes of two adjacent time slices. The expression is:

[0045]

[0046] In the formula: is the i-th node on the t time slices; the parent node of can be within the same time slice or in its previous time slice. Through the process of unsupervised training of the basic model and optimization of model parameters with input sample points, a DBN response surface model related to the structure is obtained.

[0047] Furthermore, in step S5, the random variables are standardized to a standard normal distribution. The penalty function is used to transform the constrained optimization problem into an unconstrained optimization problem, construct a fitness equation suitable for solving by the PSOSA algorithm, and update the search particles and the optimal positions of the particle swarm through the PSOSA algorithm to iteratively obtain the optimal weights of the random variables to support the unsupervised learning process of the DBN model.

[0048] Even further, in step S5, the random variables are standardized to a standard normal distribution. In the standardization of random variables, it is assumed that each random variable follows a standard normal distribution, and this process is the standardization of random variables.

[0049] The penalty function method is used to transform the constrained optimization problem of random variables into an unconstrained optimization problem. By introducing the penalty function (9), the constrained optimization problem is transformed into an unconstrained optimization problem:

[0050]

[0051] In the formula, F(x, σ) is the penalty function, f(x) is the objective function, σ is the penalty factor, is the penalty term, and the parameter x in F(x, σ) has no restrictions and can take any value.

[0052] The optimal weight of the random variable is solved by the Particle Swarm Optimization Algorithm (PSOSA), and its principle is as follows:

[0053]

[0054] In the formula: i is the particle serial number, d is the particle dimension serial number, k is the iteration number, w is the inertia weight, c1 is the individual learning factor, c2 is the swarm learning factor, r1 and r2 are random numbers within the interval [0 - 1], which increases the search randomness. is the velocity vector of particle i in the d-th dimension at the k-th iteration. is the position vector of particle i in the d-th dimension at the k-th iteration. is the historical optimal position of particle i in the d-th dimension at the k-th iteration. is the historical optimal position in the d-th dimension at the k-th iteration.

[0055] Through the gradual iteration of the above formula, the optimal weight of the random variable can be obtained.

[0056] Furthermore, in step S6, a mathematical model for solving the structural reliability index is established based on the prediction results of the DBN model. In this process, it is necessary to update and optimize the samples of the DBN prediction model each time, so that the DBN prediction model can approximate the sample points well until the model constructs a response surface with sufficient accuracy to truly simulate the structural limit state function.

[0057] Even further, in step S6, the prediction results of the constructed response surface model are compared with the results of the structural true limit state function. When the prediction results of the response surface model converge to the results of the structural true limit state function, the response surface prediction results are directly used for structural reliability calculation. When the prediction results of the response surface model do not converge to the true limit state function, it is necessary to update and optimize the samples of the DBN prediction model so that the DBN prediction model can approximate the sample points well until the model constructs a response surface with sufficient accuracy to truly simulate the structural limit state function.

[0058] The limit state function of the structure should be determined according to multiple factors such as the specific form of the structure and the analysis object of the reliability.

[0059] The beneficial effects of the present invention are as follows:

[0060] (1) A bridge reliability prediction method based on bridge dynamic characteristics and the response surface method is proposed. This method is based on the finite element model updating technology, making the analysis model more consistent with the actual structure of the existing bridge and the calculation results more accurate.

[0061] (2) A hybrid fast response surface method combining the dynamic Bayesian network (DBN) with the particle swarm optimization algorithm based on the idea of simulated annealing algorithm (PSOSA) is proposed for bridge reliability analysis. This method not only utilizes the advantages of DBN in dealing with uncertainty problems and probabilistic inference problems, but also takes advantage of the characteristics of the PSOSA algorithm that can better update the coordinates of the particle swarm to search for the optimal solution faster, effectively improving the accuracy and efficiency of the reliability calculation of complex structures.

[0062] (3) The proposed method overcomes the limitations of the classical response surface method in the reliability problems of highly nonlinear structures, and solves the problems such as the low calculation efficiency of the MCS method and the excessive dependence of the calculation accuracy of the existing response surface method on the scale and distribution of the preset samples.

[0063] (4) Compared with the traditional bridge reliability analysis methods, the DBN-PSOSA hybrid response surface method has the advantages of high calculation accuracy, fast estimation speed, and easy combination with the existing finite element analysis software, which is convenient for engineering applications, especially suitable for reliability problems with high structural analysis costs and highly nonlinear implicit functional functions. Brief Description of the Drawings

[0064] Figure 1a is the flow chart of the present invention.

[0065] Figure 1b is the acquisition frequency spectrum diagram of the dynamic characteristics of an actual bridge structure;

[0066] Figure 2 is the flow chart for modifying the finite element model of the bridge;

[0067] Figure 3 is the flow chart for predicting the reliability of the bridge based on dynamic characteristics and the response surface method;

[0068] Figure 4 is the PSOSA parameter optimization diagram for calculating the reliability of an actual bridge;

[0069] Figure 5 is the DBN prediction result diagram for calculating the reliability of an actual bridge. Detailed Embodiments

[0070] The following will describe in detail the specific embodiments of the embodiments of the present invention with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate and explain the embodiments of the present invention, and are not used to limit the embodiments of the present invention.

[0071] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0072] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with exemplary embodiments.

[0073] The present invention proposes a bridge reliability prediction method based on dynamic characteristics and response surface method, including the following steps:

[0074] S1 Collect and preprocess the vibration characteristic information of the existing bridge:

[0075] Measure the dynamic characteristics of the bridge by contact or non-contact, direct or indirect methods (such as machine vision, field test, etc.); among them, the dynamic characteristic parameters include the frequency, vibration mode, damping, impact coefficient, etc. of the bridge; Figure 1b For the field dynamic load test results of a bridge using the ambient excitation method in the direct measurement method, the test results will be used as the input parameters of the subsequent established machine learning intelligent algorithm prediction model to further predict the parameters to be corrected;

[0076] In this embodiment, the dynamic characteristics of the bridge are measured by the direct measurement method in step S1. The specific method is to arrange vibration pick-up devices at the typical sections of the existing bridge, such as the 1 / 2, 1 / 4 and support section positions. The digital signal acquisition instrument is used to collect the bridge vibration response signal, and the response of the bridge frequency, etc. is read through the peak value of the power spectrum diagram and the time-domain history curve measured and recorded by the acquisition system. When processing the signal, the time-domain signal collected by the vibration pick-up is Fourier-transformed to obtain the frequency-domain results (such as frequency, vibration mode, etc.) of the bridge frequency characteristics. The Fourier transform formula is:

[0077]

[0078] In the formula: j is the imaginary unit, j^2 = -1, dimensionless; T is the period, unit is second; X is the original function of x; t is the time, unit is second; ω is the frequency, and x(t) is the continuous time signal.

[0079] Figure 1b For the field dynamic load test results of a bridge using the ambient excitation method in the direct measurement method, the abscissa is the sampling time and the ordinate is the amplitude.

[0080] S2 Establish a structural analysis model in combination with the bridge design data and operation status, and use the sensitivity analysis method to screen out the design parameters to be corrected in the structural analysis model:

[0081] According to the design data of the existing bridge, clarify the geometric shapes, specific dimensions and material property values of each component of the bridge and the form of boundary conditions, establish the initial structural analysis model of the bridge structure using structural analysis software, use the global sensitivity analysis method to analyze the influence degree of different design parameters on the bridge structure, and finally screen out the key design parameters of the bridge structure.

[0082] Specifically, according to the design data of the bridge, a numerical analysis model of the bridge structure is established using finite element software (such as ANSYS, ABAQUS, Midas, etc.). The sensitivity analysis method is adopted to screen the sensitivity design parameters of the bridge. The sensitivity analysis method uses the Morris method. The Morris method calculates the change in the output response caused by the change in a single factor, and its calculation formula is:

[0083]

[0084] In the formula: d i (j) is the base effect of the j-th sample of the i-th parameter, j = 1, 2, 3, … R (R is the number of repeated samplings), n is the number of parameters; x i is the i-th parameter, Δ is the small change in a single parameter, and f(X) is the response output corresponding to the parameter group. Morris proposed two calculation indicators to judge the sensitivity of parameters, namely the mean value μ of the base effect and the standard deviation σ. Among them, μ characterizes the sensitivity of the parameter and determines the ranking of the parameters, and σ characterizes the non-linear degree between the parameters. The key design parameters that need to be corrected are screened out through the Morris calculation results.

[0085] S3 calculates the target variables corresponding to each design parameter sample to obtain the output samples, and then forms the training samples with the input samples. The dynamic characteristic data of the bridge obtained in step 1 is input, and the optimal values of a group of parameters to be corrected are predicted through the machine learning intelligent algorithm. The predicted values of this group are substituted into the initial structural analysis model to realize the correction of the structural analysis model. Figure 2 is the flowchart for the finite element model correction of the existing bridge; the machine learning intelligent algorithm includes the Kriging model algorithm, Gaussian process algorithm, Bayesian algorithm, random forest algorithm, cloud theory algorithm, and various surrogate models, etc. In this embodiment, the Gaussian process response surface model algorithm is adopted.

[0086] In this embodiment, the Latin Hypercube Sampling (LHS) method is used to perform efficient sampling from the distribution intervals of the design parameters. For K variables x1, x2,..., x k , N samples are drawn from them. The cumulative distribution of each variable is divided into the same N small intervals, and a value is randomly selected from each interval. The N values of each variable are randomly combined with the values of other variables. This method can ensure full coverage of the range of each variable. Using each design parameter as the input data and the structural vibration response corresponding to each group of design parameters as the output data, training samples are generated. On the basis of the completion of the construction of the training samples, a Gaussian process response surface model is established. The Gaussian process response surface model for the training sample set (x1, t1), (x2, t2)... (x N , t N ), t i is x iFor the corresponding target value, predict a new set of input quantities x N+1 The corresponding target value t can be obtained N+1 , and its training set is:

[0087] R = {(X i , T i ), i = 1, 2, 3,..., i,..., N} (3);

[0088] The joint probability distribution of the training set follows a Gaussian distribution:

[0089] f(T N ) ~ GP(m(x), K(x, x')) (4);

[0090] Where:

[0091] m(x) = E[f(x)] (5);

[0092] K(x, x') = E[(f(x) - m(x))(f(x') - m(x'))] (6);

[0093] Among them, m(x) is the mean; f(x) is a function about the sample points; E is the symbol of the mean; K(x, x') is the covariance matrix;

[0094] By determining the mean m(x) and the covariance matrix K(x, x'), the corresponding Gaussian process response surface model can be determined. After the Gaussian process response surface model is established, the bridge dynamic characteristic results obtained in step S1 are input into the Gaussian process response surface model, the prediction results of the design parameters are calculated, and the prediction results are substituted into the initial structural analysis model in step S1 to complete the correction of the initial structural analysis model.

[0095] S4 Based on the corrected structural analysis model, calculate the target variables corresponding to each input sample again to obtain output samples, construct training samples again, perform normalization processing on the sample points, and establish a basic DBN model based on the BN toolbox in MATLAB;

[0096] Based on the corrected structural analysis model, use the normalization processing method to normalize the training samples so that the normalized results are between 0 and 1. The normalization formula:

[0097]

[0098] In the formula: x i is the sample point data, and y i is the result after normalization. Substitute the normalized training samples into the DBN toolbox in MATLAB software to calculate the DBN response surface model for the DBN random variables.

[0099] The construction of the response surface model is to use the DBN toolbox built in MATLAB software. By inputting the training sample data into the algorithm of the DBN toolbox, the response surface model can be constructed.

[0100] DBN can be expressed as (B0, B → ), where B0 is the static BN, representing the probability distribution P(X0) of the nodes at the initial moment, and B → is a transition network containing two adjacent time slices, representing the state transition probability between the nodes of two adjacent time slices. The expression is:

[0101]

[0102] In the formula: is the i-th node at t time slices; The parent node of can be within the same time slice as or in its previous time slice. Through the process of unsupervised training of the basic model with input sample points and optimization of model parameters, a DBN response surface model related to the structure is obtained; Figure 3 is the flow chart of bridge reliability prediction based on dynamic characteristics and response surface method.

[0103] Standardize the S5 random variable. Use the penalty function to transform the constrained optimization problem into an unconstrained optimization problem, construct the fitness equation suitable for solving by the PSOSA algorithm, and update the search particles and the optimal positions of the particle swarm through the PSOSA algorithm, and iteratively obtain the optimal weights of the random variables to support the unsupervised learning process of the DBN model.

[0104] Standardize the random variable. In the standardization of the random variable, it is assumed that each random variable follows the standard normal distribution, and this process is the standardization of the random variable.

[0105] Use the penalty function method to transform the random variable constrained optimization problem into an unconstrained optimization problem. By introducing the penalty function (9), the constrained optimization problem is transformed into an unconstrained optimization problem:

[0106]

[0107] In the formula, F(x,σ) is the penalty function, f(x) is the objective function, σ is the penalty factor, is the penalty term, and the parameter x in F(x,σ) has no limit and can take any value.

[0108] The optimal weights of the random variables are solved by the particle swarm optimization algorithm (PSOSA), and its principle is:

[0109]

[0110] where: i is the particle serial number, d is the particle dimension serial number, k is the iteration number, w is the inertia weight, c1 is the individual learning factor, c2 is the swarm learning factor, r1 and r2 are random numbers within the interval [0 - 1] to increase the search randomness, is the velocity vector of particle i in the d-th dimension at the k-th iteration, is the position vector of particle i in the d-th dimension at the k-th iteration, is the historical optimal position of particle i in the d-th dimension at the k-th iteration, is the historical optimal position in the d-th dimension at the k-th iteration. Through the gradual iteration of the above formula, the optimal weight of the random variable can be obtained. Figure 4 In the embodiment, w1 - w 17 For 17 random variables, after 100 iterations, the root mean square error reaches the minimum value of 0.1107%. At this time, the optimal weights of each random variable are as Figure 4 shown. Figure 4 is a state equation containing 17 random variables. The sample input points and sample output points are jointly used to form the training samples. The sample points are normalized and then input into the basic DBN model for training, and the PSOSA algorithm is used for parameter optimization to obtain the optimal weight parameters w1 - w 17 The optimization process of Figure 4 is as

[0111] S6 establishes a mathematical model for solving the structural reliability index through the prediction results of the DBN model. In this process, it is necessary to update and optimize the samples of the DBN prediction model each time, so that the DBN prediction model can well approximate the sample points until the model constructs a response surface with sufficient accuracy to truly simulate the structural limit state function, Figure 5 is the DBN prediction result constructed from 50 groups of training samples generated by the random variables using the uniform design.

[0112] In this embodiment, by comparing the prediction results of the constructed response surface model with the results of the structural true limit state function, when the prediction results of the response surface model converge to the results of the structural true limit state function, the structural reliability is directly calculated using the response surface prediction results. When the prediction results of the response surface model do not converge to the true limit state function, it is necessary to update and optimize the samples of the DBN prediction model so that the DBN prediction model can well approximate the sample points until the model constructs a response surface with sufficient accuracy to truly simulate the structural limit state function. Figure 5 From the embodiment of

[0113] In addition, the limit state function of the structure should be determined based on multiple factors such as the specific form of the structure and the analysis object of reliability.

[0114] The 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 according to the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by researchers in the technical field based on the concept of the present invention and through logical analysis, reasoning or limited experiments on the basis of the prior art are within the protection scope determined by the claims.

Claims

1. A bridge reliability prediction method based on the dynamic characteristics and intelligent algorithm response surface method, characterized in that, The following steps are involved: S1 collects and preprocesses the dynamic characteristic data of the existing bridge; obtains the dynamic characteristic data of the bridge structure by direct measurement or indirect measurement, and processes the collected vibration information by signal processing method; wherein: Direct measurement method: Place the vibration pickup directly on the bridge control section, collect the bridge vibration response signal through the digital signal acquisition instrument, and read the bridge frequency response through the power spectrum peak and time domain history curve measured and recorded by the acquisition system; Indirect measurement method: The sensor is installed on a mobile vehicle. When the mobile vehicle passes over the bridge, vehicle-bridge coupling occurs. The dynamic characteristic data of the bridge structure is extracted from the acceleration response of the vehicle body to obtain the bridge frequency information. Signal processing method: The time domain signal collected by the vibration pickup is transformed by Fourier transform to obtain the frequency domain result of the bridge frequency characteristics; the Fourier transform formula is: Where: j is an imaginary unit, j^2=-1, no unit; T is the period, in seconds; X(·) is the original function of x(·); t is time, in seconds; ω is the frequency, and x(t) is a continuous time signal; S2 combines the bridge design data and operation status to establish an initial structural analysis model, and uses sensitivity analysis methods to screen out the design parameters to be revised in the initial structural analysis model; S3 calculates the target variable corresponding to each input sample, obtains the output sample, and then forms a training sample with the input sample. Combined with the intelligent algorithm, the dynamic characteristic data of step S1 is used to realize the correction of the initial structural analysis model; the target variable corresponding to each input sample is calculated, and based on the uniform design theory, a training sample between the design parameters and the vibration response that are distributed in the space is constructed, and the training sample is substituted into the intelligent algorithm program for learning and training; the dynamic characteristic data obtained in step S1 is called as an input parameter, substituted into the response surface model, and the actual value of each design parameter is predicted. The predicted value of the design parameter is substituted into the initial structural analysis model established in step S2 to realize the correction of the initial structural analysis model, and the corrected analysis model is consistent with the actual state of the existing bridge; S4 recalculates the target variables corresponding to each input sample based on the modified structural analysis model, obtains the output sample, reconstructs the training sample, normalizes the sample points, and constructs the response surface model based on the intelligent algorithm; S5 random variables are normalized, a penalty function is used to transform the constrained optimization problem into an unconstrained optimization problem, and an optimization algorithm is used to obtain the optimal weights of random variables; S6 establishes a mathematical model for solving structural reliability indicators through the prediction results of the constructed response surface model.

2. The bridge reliability prediction method based on the dynamic characteristics and intelligent algorithm response surface method according to claim 1, characterized in that: Step S2 determines the values ​​of bridge design parameters based on the existing bridge design data, establishes an initial structural analysis model of the bridge, and performs sensitivity analysis on each design parameter to select design parameters with greater response to the bridge structure.

3. The bridge reliability prediction method based on the dynamic characteristics and the intelligent algorithm response surface method according to claim 2, wherein: In step S2, according to the design data of the existing bridge, a numerical analysis model of the bridge structure is established using finite element software; the sensitivity analysis method is adopted to screen the sensitive design parameters of the bridge; the sensitivity analysis method uses the Morris method. The Morris method calculates the change in the output response caused by the change in a single factor, and its calculation formula is: where: d i (j) is the base effect of the j-th group of samples of the i-th parameter, j = 1, 2, 3, … R, R is the number of repeated samplings, and n is the number of parameters; x i is the i-th parameter, Δ is the small change of a single parameter, and f(.) is the response output of the corresponding parameter group; The Morris method proposes two calculation indicators to judge the sensitivity of parameters, namely the elementary effect mean μ and the standard deviation σ; where μ characterizes the sensitivity of the parameter and determines the ranking of the parameters, and σ characterizes the non - linear degree between the parameters; the key design parameters that need to be corrected are screened out through the calculation results of the Morris method.

4. The bridge reliability prediction method based on the dynamic characteristics and the intelligent algorithm response surface method according to claim 1, wherein: Step S3 uses the Latin hypercube sampling method to perform efficient sampling from the distribution intervals of the design parameters. For k variables x1, x2,..., x k , N samples are drawn from them. The cumulative distribution of each variable is divided into the same N small intervals, and a value is randomly selected from each interval. The N values of each variable are randomly combined with the values of other variables. The Latin hypercube sampling method can ensure full coverage of each variable range; using each design parameter as input data and the corresponding structural vibration response of each design parameter as output data, training samples are generated; Based on the completion of the construction of the training samples, a Gaussian process response surface model is established; The Gaussian process response surface model for the training sample set (x1, t1), (x2, t2)... (x N , t N ), t i is the target value corresponding to x i . To predict the target value t N+1 corresponding to a new set of input quantities x N+1 , its training set is: R = {(x i , t i ), i = 1, 2, 3,..., N} (3); The joint probability distribution of the training set follows a Gaussian distribution: f(t N ) ~ GP(m(x), K(x, x')) (4); Where: m(x) = E[f(x)] (5); K(x,x') = E[f(x) - m(x)(f(x') - m(x'))] (6); Among them, m(x) is the mean value; f(x) is a function about the sample points; E is the symbol of the mean value; K(x,x') is the covariance matrix; By determining the mean value m(x) and the covariance matrix K(x,x'), the corresponding Gaussian process response surface model can be determined; After the Gaussian process response surface model is established, the dynamic characteristic data obtained in step S1 is input into the Gaussian process response surface model to calculate the prediction results of the design parameters, and the prediction results are substituted into the initial structural analysis model in step S2 to complete the correction of the initial structural analysis model.

5. The method for predicting the reliability of a bridge based on the dynamic characteristics and the intelligent algorithm response surface method according to claim 4, wherein: In step S4, based on the corrected structural analysis model, the normalization processing method is used to normalize the training samples so that the normalized results are between 0 and 1. The normalization formula: Where: x i is the sample point data, y i is the result after normalization; The normalized training samples are substituted into the DBN toolbox in MATLAB software to calculate the DBN response surface model about the DBN random variables; The construction of the response surface model is to use the DBN toolbox built in the MATLAB software. By inputting the training sample data into the algorithm of the DBN toolbox, the response surface model can be constructed. Among them, DBN is expressed as (B0, B → ), where B0 is the static BN, representing the probability distribution P(X0) of the nodes at the initial moment, and B → is a transition network containing two adjacent time slices, representing the state transition probability between the nodes of two adjacent time slices. The expression is: Wherein: is the i-th node on the t time slices; the parent node of and are within the same time slice or within the previous time slice thereof.

6. The bridge reliability prediction method based on the dynamic characteristics and intelligent algorithm response surface method according to claim 5, characterized in that: In step S5, the random variables are standardized to a standard normal distribution. The penalty function is used to transform the constrained optimization problem into an unconstrained optimization problem, and a fitness equation suitable for solving by the PSOSA algorithm is constructed. The search particles and the optimal positions of the particle swarm are updated through the PSOSA algorithm, and the optimal weights of the random variables are iteratively obtained to support the unsupervised learning process of the DBN model. In the standard normal distribution of random variables, it is assumed that each random variable follows a standard normal distribution, and this process is the standard normal distribution of random variables.

7. The bridge reliability prediction method based on dynamic characteristics and intelligent algorithm response surface method according to claim 6, characterized in that: The penalty function method is used to transform the constrained optimization problem of random variables into an unconstrained optimization problem. By introducing the penalty function (9), the constrained optimization problem is transformed into an unconstrained optimization problem: where \(F(x,\sigma)\) is the penalty function, \(\sigma\) is the penalty factor, is the penalty term, and there is no restriction on the parameter \(x\) in \(F(x,\sigma)\), which can take any value; The optimal weights of the random variables are solved by the particle swarm optimization algorithm, and its principle is: where: i is the particle serial number, d is the particle dimension serial number, k is the iteration number, w is the inertia weight, c1 is the individual learning factor, c2 is the swarm learning factor, r1 and r2 are random numbers within the range [0 - 1], increasing the search randomness, is the velocity vector of particle i in the d-th dimension at the k-th iteration, is the position vector of particle i in the d-th dimension at the k-th iteration, is the historical optimal position of particle i in the d-th dimension at the k-th iteration, is the historical optimal position in the d-th dimension at the k-th iteration; Through the gradual iteration of formula (10), the optimal weights of the random variables can be obtained.

8. The bridge reliability prediction method based on the dynamic characteristics and intelligent algorithm response surface method according to claim 7, characterized in that: Step S6 establishes a mathematical model for solving the structural reliability index based on the prediction results of the DBN model. In this process, it is necessary to update and optimize the samples of the DBN prediction model each time, so that the DBN prediction model can well approximate the sample points until the DBN prediction model constructs a response surface with sufficient accuracy to truly simulate the structural limit state function.

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