Structural Reliability Analysis Method Based On The Approximation Model With Lower Dimension And Sparseness

In the field of engineering structure design and analysis,uncertain parameters are extremely important for structural reliability analysis.Reasonable handling of these uncertain parameters is the key to ensure the accuracy of structural reliability analysis.The traditional uncertainty model relies on sufficient samples to establish accurate probability distribution model,which is expensive and difficult in engineering practice.Non-probabilistic interval model only needs less sample information to determine the range of uncertain parameters,which has attracted more and more attention.This paper will study the reliability of probabilistic and interval uncertain structures.The functional function of actual engineering structure is complex,with strong nonlinearity and high dimension.If the real function is directly used for reliability analysis,the calculation is often complex,involving a large number of finite element analysis,and the calculation cost is high or even unacceptable.In order to improve the computational efficiency,it is an effective way to solve this problem by using the surrogate model to replace the real function for structural reliability analysis.The usual surrogate models include polynomial,Kriging,support vector machine,neural network,high dimensional representation model,Chebyshev model,etc.The existing research has certain limitations in dealing with high dimensional complex problems,and the computational cost tends to increase exponentially with the increase of dimension.Therefore,this paper will study the lowdimensional and sparse approximate surrogate model,and apply it to the reliability analysis of random and interval structures.The main work is as follows :Firstly,structural random-interval hybrid reliability analysis based on variable-center high-dimensional representation model.On the one hand,this method represents the complex high-dimensional function as the sum of approximate functions of multiple one-dimensional random variables or interval variables through the high-dimensional representation model,so as to separate random variables and interval variables.Then,the uncertain structural reliability analysis problems existing in random variables and interval variables are alternately considered,and the design checking points and extreme points of the two problems are calculated respectively as the expansion center of the high-dimensional representation model.The upper and lower bounds of the probability of the reliability problem of the original random-interval hybrid structure are obtained by the approximate high dimensional representation model established by finite iteration.Numerical and structural examples prove the effectiveness,accuracy and practicability of this method in engineering.Secondly,structural interval reliability analysis based on low power Chebyshev reduction model.Firstly,based on the relationship between the accuracy of Chebyshev expansion approximation model and the coefficients of each sub-item,a Chebyshev expansion reduction approximation model is established.Then,the Chebyshev expansion test design point is determined,and the coefficients of each sub-item of the Chebyshev approximation model are solved.The approximation model is used to replace the original high-dimensional and complex function.Combined with the central composite test design method and discrete optimization algorithm,the upper and lower limits of the Chebyshev expansion reduction approximation model and the reliability of the structure are calculated.Finally,through several numerical and structural examples,this method is compared and verified with the Chebyshev expansion and subinterval decomposition analysis method,which proves the accuracy and effectiveness of this method.Thirdly,structural interval reliability analysis based on sub-interval analysis and Chebyshev sparse approximation model.Firstly,the coefficients of the Chebyshev expansion model of the function are estimated based on the sub-interval decomposition analysis method,and the sparse approximation model of the Chebyshev expansion is established by screening the items with larger coefficients.The approximation model is used to replace the original high-dimensional and complex function.Then,combined with the central composite test design method and discrete optimization algorithm,the upper and lower limits of the sparse approximation model of the Chebyshev expansion and the reliability of the structure are calculated.Finally,through several numerical and structural examples,this method is compared with the first-order Taylor expansion method,and the accuracy and effectiveness of this method are proved.