CN-121980829-A - Bridge structure reliability analysis method, device, equipment, medium and product

CN121980829ACN 121980829 ACN121980829 ACN 121980829ACN-121980829-A

Abstract

The application discloses a bridge structure reliability analysis method, a device, equipment, a medium and a product, and relates to the technical field of bridge engineering, wherein the method comprises the steps of determining structural parameters and corresponding structural responses of a bridge; the structural parameters at least comprise geometric design parameters, material properties and loads of the bridge, global sensitivity analysis is carried out according to the structural parameters and corresponding structural responses of the bridge to determine an improved secondary response surface model, monte Carlo simulation is carried out on probability distribution of the structural parameters of the bridge, and reliability analysis is carried out on the bridge structure based on the improved secondary response surface model. According to the application, the structural random parameters and function items which have important influences on the output response are screened through global variance sensitivity analysis, and a simple and accurate secondary response surface model is constructed, so that the synchronous improvement of bridge reliability analysis efficiency and accuracy is realized.

Inventors

XU ZHIFENG
LI ZHUOFENG
CHEN XUYONG
WU QIAOYUN

Assignees

武汉工程大学

Dates

Publication Date: 20260505
Application Date: 20260408

Claims (10)

1. The bridge structure reliability analysis method is characterized by comprising the following steps of: determining structural parameters of the bridge and corresponding structural response, wherein the structural parameters at least comprise geometric design parameters, material properties and loads of the bridge; according to the structural parameters and the corresponding structural responses of the bridge, performing global sensitivity analysis to determine an improved secondary response surface model; Performing Monte Carlo simulation on probability distribution of structural parameters of the bridge, and performing reliability analysis on the bridge structure based on the improved secondary response surface model; the method for determining the improved secondary response surface model according to the structural parameters and the corresponding structural response of the bridge specifically comprises the following steps: performing quasi-random sampling on the structural parameters of the bridge and obtaining structural responses corresponding to the structural parameters obtained by sampling; Taking the sampled structural parameters as input variables, and calculating the total global sensitivity of each input variable by combining structural responses corresponding to the input variables; Comparing the total global sensitivity of each input variable with a total global sensitivity threshold, and eliminating insensitive input variables to obtain important variables; calculating the global sensitivity of each function item in the important variable based on the important variable and the structural response corresponding to the important variable, wherein the function item comprises a linear item, a square item and a cross item; Comparing the item global sensitivity of each function item with an item global sensitivity threshold, and removing insensitive function items to obtain important items in each function item; determining a final functional form of the improved secondary response surface model based on the significant variables and significant terms; Fitting the fitting parameters in the final function form of the secondary response surface model to obtain the improved secondary response surface model.
2. The bridge structure reliability analysis method according to claim 1, wherein the calculating the total global sensitivity of each input variable by using the sampled structural parameter as the input variable and combining the structural response corresponding to the input variable specifically comprises: Mapping the sampled structural parameters serving as input variables to a unit hypercube space to obtain standardized variables; Generating an input set with the total sample size of N by using a quasi-random sampling method to normalize variables in the unit hypercube space; calculating a structural response of each sample point in the input set, thereby forming a response set; based on the input set and the response set, a total global sensitivity for each input variable is calculated.
3. The bridge structure reliability analysis method according to claim 2, wherein the calculating the total global sensitivity of each input variable based on the input set and the response set specifically comprises: dividing an input set into two equal-sized matrixes, namely a matrix U and a matrix V; Let the total number of variables in the input set be k, represent the input set as a one-dimensional vector set x= [ x 1 ,x 2 ,…,x k ], split the one-dimensional vector set x into vector subset x A and vector subset x B , wherein vector subset x A is the set of input vectors for which the total global sensitivity needs to be calculated, vector subset x B is the complement of x A in the one-dimensional vector set x, satisfying the following requirements , ; Dividing the matrix U and the matrix V into two matrices according to the vector subset x A and the vector subset x B respectively to obtain a matrix U A 、U B and a matrix V A 、V B which meet the requirements of 、、 And ; Constructing a hybrid input matrix for input variables And , wherein, , ; The total global sensitivity of the input variables is calculated by the following formula: ; wherein: For the total global sensitivity corresponding to the a-th input variable, Representing the selection matrix Structural response values when performing the analysis; Representing the selection matrix Structural response values when performing the analysis; Representative matrix Mean value of structural response values of (a) V represents a matrix And N is the total sample size.
4. A bridge construction reliability analysis method according to claim 3, wherein the term global sensitivity of each function term in the important variables is calculated by the following formula: ; wherein: Global sensitivity for the item of function item a, Representing the selection matrix Structural response values at the time of analysis.
5. The bridge structure reliability analysis method according to claim 3, wherein the final function form of the improved secondary response surface model is specifically: ; wherein: representing the predicted value of the function, >0 Means that it is in a safe state, And less than or equal to 0 is in a failure state, x i and x j respectively represent the ith variable and the jth variable, x i x j represents a function term formed by the ith variable and the jth variable, C 0 、C i 、C ij is a fitting parameter, if the input variable x i is eliminated through global sensitivity analysis, the corresponding fitting parameter C i = 0、C ij =0, and if the function term x i x j is eliminated through global sensitivity analysis, the corresponding fitting parameter C ij =0.
6. The bridge structure reliability analysis method according to claim 1 or 5, wherein the performing monte carlo simulation on the probability distribution of the structural parameters of the bridge and performing reliability analysis on the bridge structure based on the improved secondary response surface model specifically comprises: Generating random sample points through Monte Carlo simulation according to probability distribution of each structural parameter of the bridge, and inputting each sample point into an improved secondary response surface model to obtain a corresponding function predicted value; judging the safety state corresponding to each sample point according to the function predicted value, counting the number of samples in the safety state, and calculating the failure probability and reliability index of the bridge structure; and according to the failure probability or the reliability index, the reliability safety assessment of the bridge structure is completed by comparing with the design specification requirements.
7. The utility model provides a bridge structure reliability analysis device which characterized in that, bridge structure reliability analysis device includes: the parameter determining unit is used for determining structural parameters and corresponding structural responses of the bridge; The model building unit is used for carrying out global sensitivity analysis according to the structural parameters of the bridge and the corresponding structural response to determine an improved secondary response surface model; And the reliability analysis unit is used for performing Monte Carlo simulation on the probability distribution of the structural parameters of the bridge and performing reliability analysis on the bridge structure based on the improved secondary response surface model.
8. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor executes the computer program to implement the steps of the bridge structure reliability analysis method of any one of claims 1-6.
9. A computer readable storage medium having stored thereon a computer program, characterized in that the computer program when executed by a processor realizes the steps of the bridge construction reliability analysis method of any one of claims 1-6.
10. A computer program product comprising a computer program, characterized in that the computer program, when being executed by a processor, implements the steps of the bridge construction reliability analysis method of any one of claims 1-6.

Description

Bridge structure reliability analysis method, device, equipment, medium and product Technical Field The application relates to the technical field of bridge engineering, in particular to a bridge structure reliability analysis method, a bridge structure reliability analysis device, bridge structure reliability analysis equipment, a bridge structure reliability analysis medium and a bridge structure reliability analysis product. Background In the structural reliability analysis of the current bridge engineering, the secondary response surface model (Response Surface Model, RSM) can replace complex implicit structural function functions by simple explicit functions, so that the calculation cost is obviously reduced, the analysis efficiency is improved, and the method is widely researched and applied. The traditional quadratic response surface model is mainly divided into two typical forms, namely a complete quadratic polynomial model containing all quadratic terms, cross terms and primary terms, and a simplified quadratic polynomial model omitting all cross terms. The complete quadratic polynomial model has higher fitting flexibility in theory, can better capture interaction effect and nonlinear characteristics among variables, but the number of parameters to be estimated increases sharply along with the increase of the variables, so that over-fitting can be caused, especially when sample points are limited, the stability of the model is reduced, extrapolation capability is weakened, and meanwhile, the complexity of model construction and subsequent reliability analysis is increased. In contrast, the method simplifies the quadratic model, remarkably reduces the number of parameters by eliminating the cross terms, reduces the complexity of the model and the requirement on samples, and is simpler, more convenient and more efficient in calculation. However, this simplification comes at the expense of model expressive power, and when there is significant variable interaction in the real structural response, the simplified model may not fully reflect its nonlinear characteristics, resulting in insufficient fitting accuracy, and thus affecting the accuracy of the reliability index calculation. Therefore, in the bridge engineering structure reliability analysis practice, how to balance the complexity and fitting precision of the secondary response surface model becomes a key challenge of the secondary response surface model in the bridge engineering structure reliability analysis application. Disclosure of Invention The application aims to provide a bridge structure reliability analysis method, device, equipment, medium and product, which are used for screening variables and function items which have important influence on output response through global variance sensitivity analysis and constructing a simple and accurate secondary response surface model so as to realize synchronous improvement of bridge reliability analysis efficiency and accuracy. In order to achieve the above object, the present application provides the following solutions: in a first aspect, the present application provides a method for analyzing reliability of a bridge structure, including: determining structural parameters of the bridge and corresponding structural response, wherein the structural parameters at least comprise geometric design parameters, material properties and loads of the bridge; according to the structural parameters and the corresponding structural responses of the bridge, performing global sensitivity analysis to determine an improved secondary response surface model; Performing Monte Carlo simulation on probability distribution of structural parameters of the bridge, and performing reliability analysis on the bridge structure based on the improved secondary response surface model; the method for determining the improved secondary response surface model according to the structural parameters and the corresponding structural response of the bridge specifically comprises the following steps: performing quasi-random sampling on the structural parameters of the bridge and obtaining structural responses corresponding to the structural parameters obtained by sampling; Taking the sampled structural parameters as input variables, and calculating the total global sensitivity of each input variable by combining structural responses corresponding to the input variables; Comparing the total global sensitivity of each input variable with a total global sensitivity threshold, and eliminating insensitive input variables to obtain important variables; calculating the global sensitivity of each function item in the important variable based on the important variable and the structural response corresponding to the important variable, wherein the function item comprises a linear item, a square item and a cross item; Comparing the item global sensitivity of each function item with an item global sensitivity threshold, and removing insensitive