Research On Decoupling Method For Reliability Optimization Based On Stochastic Simulation And Kriging Model

Structural reliability analysis and reliability-based optimization design are necessary research fields in modern structural engineering design.It can effectively consider the universal uncertainty in structural systems and quantify the impact of uncertainty in structural design and optimization,so it has been widely used.This article focuses on several problems existing in structural system reliability analysis and reliability optimization design,and explores and develops corresponding theories and methods.It has important theoretical value and engineering application significance.The main research contents are as follows:(1)For reliability analysis research,three contribution indexes have been proposed,which are the relative changes when a sample is included in reliability calculation or not.The indexes in four simulation-based methods are examined.These indexes are proposed to quantify the sample contribution to the failure probability estimate and its statistical characteristics,thus investigate the efficiency of widely used reliability analysis methods from the contribution of the sample aspect.(2)For the research on reliability-based optimization design(RBDO),An efficient approach has been presented to address the reliability-based optimization problem for nonlinear system with high-dimensional uncertainties,e.g.,random structure subject to stochastic dynamic excitation.The ’weighted approach’ proposed by the author previously is introduced to explicitly approximate the failure probability function(FPF)contained in the RBDO problem.The FPF can be obtained through a single Importance Sampling thereby repeated reliability analysis avoided.Meanwhile,it is incorporated with the decoupling approach and the sequential approximation optimization framework.That is,optimization loop are decoupled after reliability analysis,it is implemented sequentially until the optimization result is converged.(3)For the research on the structural reliability-based optimization,an efficient decoupling method for structural reliability optimization based on Gradient-enhanced Kriging is proposed.This method’s uniqueness is that the surrogate model of the failure probability function in the constraint is established by using the Gradient-enhanced Kriging method,and the surrogate model is gradually updated by the optimization candidate points of the optimization process.The failure probability function’s surrogate model is established by the failure probability calculated by the importance sampling method and the corresponding sensitivity information.After constructing the surrogate model that obtains the global failure probability function,the original reliability optimization problem is decoupled into a deterministic optimization problem.Finally,two calculation examples are given to verify the feasibility and efficiency of the proposed optimization method.