Decoupled Methods For Reliability-based Design Optimization Based On Quantiles And Boundary Penalty

There are a lot of uncertainties in practical engineering,such as external load,structural size,material properties,etc.Reliability-based design optimization(RBDO)considers the influence of uncertainties on structural performance,which can balance the relationship between structural performance and structural reliability properly.The problems of RBDO can generally be solved by double-loop methods,single-loop methods or decoupled methods.The sequence optimization and reliability assessment method(SORA)is a widely used decoupled method due to its good efficiency and stability.However most research on SORA is based on minimum performance target point(MPTP),which may cause the unavoidable error of the first order reliability methods(FORM).Moreover,SORA uses the failure surface to replace the true reliability boundary,and this approximation will reduce accuracy and stability of SORA.As a result,SORA has poor performance in solving RBDO with complex performance functions.To overcome the intrinsic shortcomings of MPTP based methods,this paper presents a new decoupled method based on quantiles instead of MPTP,which decouples RBDO in probability space using quantiles.Quantiles are obtained by Monte Carlo Method(MCS)without using MPTPs which can avoid the approximate error of FORM.In order to apply this method to practical engineer problems,the objective function and constraint functions are replaced by Kriging models.The efficient sample point updating strategies are adopted to make the sample points distribute in the region significant for solving RBDO problems,and the sample point utilization is high and Kriging model is accurate.The conventional SORA uses approximate boundaries to replace real reliability constraints,which may lead to convergence premature or oscillation of SORA when the approximate boundary error is large.This paper proposes a conjugate boundary penalty based SORA method to modified approximate boundaries.The approximate boundary may cause superfluous area or missing area of the feasible region.This paper adopts the whole reliability information technology and boundary penalty strategies to modify these two kinds of areas to improve the performance of SORA.For complex performance functions,MPTP has a poor relation with the mean values of random variables,which causes the MPTP-based methods have a bad robustness.In this paper,the conjugate boundary penalty based decoupled method using quantiles is proposed.The quantile,which is more stable and continuous than MPTP,is used to decouple RBDO.And the boundary penalty strategies are also used to modified the approximate boundaries.The modified decoupled method using quantiles can solve RBDO problems with multiple design points and complex performance functions efficiently and accurately.