꼬리 모형을 이용한 신뢰성 기반 최적설계를 위한 효율적인 비모수적 접근법

Abstract

In terms of the reliability-based design optimization (RBDO), many designers are interested in an approach to accurately estimate in the tail region because they want to guarantee high target reliability located in tail region of the distribution. The generalized Pareto distribution (GPD) is widely known as one of the tail focusing approach. However, conventional GPD approach is inefficient because the GPD performs the random sampling in the body region meaningless and unnecessary for RBDO. In this study, therefore, we propose the efficient approach which only uses the sample points in tail region without considering the overall region. The proposed approach priorly performs the random sampling in the Taylor expansion surface. Because Tayler expansion gives the direction to violate the constraints, we can extract some sample points in the tail region out of the generated random sampling. By analyzing only extracted sample points, a tail-model based on GPD is performed. In the RBDO process, the GPD can give system reliability and sensitivity to optimizer at the higher reliability over the threshold of the tail-model. However, since it is sometimes out of the boundary where the tail-model is defined, information of the body region is needed. The approach approximates the information of the body region from censored data of the sample points in the tail region, which is possible to obtain the reliability through the tail-model considering the number of sample points for the tail region. The approach may be inaccurate in body region. The target reliability always is higher than threshold but the sensitivity in body region is enough to provide the direction toward the target reliability. In conclusion, we can perform an efficient nonparametric RBDO considering the number of sample points in tail region. The efficiency of proposed approach is demonstrated through the mathematical examples.