Research On Improved Method Of Structural Reliability Calculation Based On Adaptive Surrogate Model

Structural reliability is an important basis of civil engineering structural design at the present stage.In recent years,driven by the actual engineering needs,civil engineering structures have started to grow larger and more complex,so the cost of calculating structural response for reliability analysis has increased dramatically.The surrogate model with cheaper computational cost can largely reduce the computational cost of the real structural response,and it has been used in many fields that require repeated invocation of the structural response,such as structural reliability calculation.However,analysis shows that the existing surrogate model reliability calculation methods still have some shortcomings,such as excessive computation for low failure probability problems and low efficiency of sampling candidate sample,which restrict their application scope.Therefore,based on the basic computational framework of adaptive surrogate model,this paper focuses on the optimization of the sampling methods of training sample points and candidate sample points,and improves the existing most used AK-MCS algorithm,which achieves better results.The main research contents and results of the paper are as follows:(1)A detailed introduction of the structural reliability analysis method based on adaptive surrogate model and its basic principles,an in-depth analysis of each component of the classical active learning surrogate model reliability calculation method AK-MCS calculation method,and a summary of the limitations of the AK-MCS method,i.e.,the method suffers from high computational cost of the low failure probability problem,low sampling efficiency of the candidate sampling pool and un-normalized learning function variables.(2)For address the high computational cost of the low failure probability problem,the importance sampling method based on the existing method is improved by using radial uniform sampling,which improves the sampling efficiency of the most likely failure point and can construct the probability density function of the importance sampling in a more efficient and accurate way.Finally,the validity of the proposed method is verified by classical numerical cases by using the system reliability problem with strong nonlinearity and the reliability problem with low probability of failure,respectively.The results show that the method has good computational accuracy and stability for the low failure probability problem and the strongly nonlinear function problem.(3)For the problem of low sampling efficiency of the candidate sampling pool of AK-MCS method,the same radial uniform sampling method as above is used to improve the sampling range and sampling efficiency of the training sample points.In order to solve the problem that the variables of the learning function are not normalized,we propose to improve the learning function by using the method of ranking normalization,and the new learning function is formed by weighting and summing the normalized variables to solve the influence caused by the extreme distribution of variables,and using the convergence criterion judged by the results,which reduces the number of calls of the original function compared with the overly conservative learning function U.(4)The complete procedure of the reliability analysis method for the adaptive surrogate model is constructed by combining the above methods.Numerical examples are used to compute the proposed method for classical strong nonlinear problems,high-dimensional problems,low failure probability problems,and axial compressive strength problems of the arch ribs of a largespan steel and concrete arch bridge in an actual project.The results of the numerical examples show that the proposed method effectively solves the problems of low sampling efficiency of the normal distribution sampling method,poor adaptability of the learning function and poor calculation accuracy of the strong nonlinear function in the reliability calculation method.