Non-parametric stochastic subset optimization for design problems with reliability constraints

Abstract

The Non-Parametric Stochastic Subset Optimization (NP-SSO) is a recently developed algorithm appropriate for optimization problems that use the system reliability as objective function and involve computationally expensive numerical models. This paper discusses its extension to reliability-based design optimization (RBDO) applications involving the system reliability as a design constraint. The foundation of NP-SSO is the formulation of an augmented problem where the design variables are artificially considered as uncertain. In this context, the system reliability is proportional to an auxiliary probability density function related to the design variables. NP-SSO is based on simulation of samples from this density and approximates the system reliability through kernel density estimation (KDE) using these samples. The RBDO problem is then solved using this approximation for evaluating the reliability constraints. Thus, through a single analysis NP-SSO provides information for the system reliability over the entire design domain. To improve computational efficiency, an iterative approach is proposed; at the end of each iteration, a new reduced search domain is identified, until the algorithm converges to the feasible design domain satisfying the reliability constraints. Through this approach the samples for the design variables gradually move from regions with higher values of the system failure probability to regions with lower values (satisfying the required constraints). A nonparametric characterization of the search domain using a framework based on multivariate boundary KDE and support vector machine is established whereas to further improve the efficiency of the stochastic sampling stage, an adaptive kernel sampling density approach is proposed.

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