Engineering Mechanics Institute Conference 2013

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Non-parametric stochastic subset optimization for reliability-based design optimization problems

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Gaofeng Jia
University of Notre Dame
United States

Alexandros Taflanidis
University of Notre Dame
United States

Abstract:
Stochastic Subset Optimization (SSO) is a recently developed algorithm appropriate for Reliability –based Optimization (RBO) problems that use the system reliability as objective function and involve computationally expensive numerical models. It is based on simulation of samples of the design variables from an auxiliary probability density function (treating them as uncertain) and uses the information contained in these samples to efficiently identify subsets for the optimal solution within some predefined class of admissible subsets. The latter identification requires an optimization, with respect to some parametric description of the admissible subset class, for the one that has the smallest volume density of samples. Even though SSO has been proven efficient for various challenging optimization problems, it does have two vulnerabilities ; the identification of the optimal subset involves a challenging non-smooth optimization problem, whereas the subset identified is the one that has the smallest average value for the objective function (among the admissible subsets) which does not always guarantee that it includes the minimum of the objective function.

This paper discusses an extension of SSO, termed Non-Parametric SSO (NP-SSO), that addresses these vulnerabilities. NP-SSO adopts Kernel Density Estimation (KDE) to approximate the objective function using the information from the available samples of the design variables, and then uses this approximation to identify candidate points (not subsets) for the global minimum. As such it avoids the parametric identification for the candidate class of optimal subsets, required in SSO, whereas it has the additional advantage to converge to the global minimum. An iterative approach is also established to reduce the computational effort; through this approach the samples for the design variable gradually move from regions with higher values of the objective function to regions with lower values, to ultimately establish a higher accuracy KDE in these regions of greater interest. Appropriate reflection approaches are introduced for the KDE and the impact of potential multiple local minima on the computational framework is also addressed. The approach is illustrated in an example considering the optimization of a base-isolation protective system for a three story structure.

 

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