Research On Adaptive Analysis Method For Structural Reliability And Global Sensitivity Based On Kriging Model

Reliability is the core index to evaluate the quality of machinery products,and the development of reliability-centered structural reliability analysis and design has become an inevitable way to improve structural reliability and safety.With the rapid development of engineering structural technology systems,modern engineering structures are becoming more and more sophisticated and complex.There are more and more uncertainties that affect their reliability and safety.The calculation of performance functions characterizing the performance of structures is also becoming more and more complex.Traditional deterministic structural analysis has been difficult to meet the growing demand for high reliability,while the efficiency and accuracy of existing structural reliability and sensitivity analysis methods need to be improved.In this thesis,based on the theory of uncertainty analysis,the structural reliability and global sensitivity analysis methods based on the Kriging model are studied in depth.The research work includes the following main components:(1)A fast convergence strategy for adaptive structural reliability analysis is proposed by considering the effect of Kriging model cognitive uncertainty on the accuracy of failure probability estimation.For the problem of cognitive uncertainty in the Kriging model constructed based on a small number of discrete samples,the posterior expectation of the relative error in the failure probability estimation is derived.Further,an upper limit of expectation is obtained and a global convergence condition applicable to structural reliability analysis is given by restricting this upper limit;From the perspective of quickly satisfying the global convergence condition,the fast convergence strategy of adaptive structural reliability analysis is proposed based on the Kriging believer criterion and the importance sampling theory.Sequence and parallel adaptive structural reliability analysis by measuring the contribution of candidate samples to the accuracy of failure probability estimation through the Kriging believer criterion.And based on the importance sampling theory,a theoretical optimal importance sampling function characterizing the global convergence condition is derived,with the help of which a small number of candidate samples are generated and the analysis efficiency is improved.(2)A sequential and parallel adaptive structural reliability analysis method under rare failure probability conditions is proposed.To address the drawback that the above proposed fast convergence strategy requires huge computing resources in both the process of global convergence condition evaluation and failure probability estimation when dealing with rare failure probability problems,the quasi-optimal importance sampling function for estimating the failure probability is coupled with the normalization factor as failure probability with the help of this function,and based on the importance sampling theory and MCMC method,the efficient evaluation of global convergence condition is achieved.Based on the importance sampling principle,it is further demonstrated that the fast convergence strategy proposed in this thesis can disregard the magnitude of failure probability and achieve efficient sequence and parallel adaptive sampling even under rare failure probability conditions.Further,a Kriging model satisfying the global convergence condition is established,and based on the importance sampling and multidimensional kernel density estimation theory,the "Importance sampling-probability density estimation-Importance sampling(I2I)" method is proposed to achieve an efficient estimation of rare failure probability.(3)The sequence and parallel adaptive structural system reliability analysis method under multiple failure modes is proposed.The fast convergence strategy proposed above cannot be applied to structural system reliability analysis with multiple failure modes.The influence of the cognitive uncertainty of the Kriging model on the accuracy of structural system failure probability estimation is considered concerning the global convergence condition.The global convergence condition of the system applicable to the structural system reliability analysis is derived and proved,and the fast convergence strategy of the system is given.For the different cases of structural system reliability analysis,two variations of the fast convergence strategy of the system applicable to output-independent structural systems and multiple output structural systems,respectively,are proposed to further extend the applicability of the proposed fast convergence strategy of the system.(4)The sequence and parallel adaptive sampling strategy is proposed and a global accuracy surrogate model is constructed to achieve global sensitivity analysis.The global error of the Kriging model in the space of variables is defined,and the analytic or semi-analytic solutions of the posterior expectation and posterior variance of the global error are derived.The convergence condition applicable to the global accuracy surrogate model is given and proved by restricting the upper limit of the global error posterior expectation.Considering the fast satisfaction of the convergence condition and the relevance of the candidate samples,the sequence and parallel adaptive sampling strategies applicable to the global accuracy surrogate model are proposed in combination with the clustering algorithm.A global accuracy surrogate model is constructed to establish the basis for global sensitivity analysis.Finally,a novel moment-independent global sensitivity index is proposed by combining the information gain of the output conditional probability density,and a single-layer MCS method is used to further enhance the efficiency of global sensitivity analysis.