1 Copyright © 2012 by ASME Proceedings of the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2012 August 12-15, 2012, Chicago, Illinois, USA DETC2012-70715 Sampling-based RBDO using Probabilistic Sensitivity Analysis and Virtual Support Vector Machine Hyeongjin Song, K.K. Choi* Department of Mechanical & Industrial Engineering College of Engineering The University of Iowa, Iowa City, IA 52242, USA hyesong@engineering.uiowa.edu, kkchoi@engineering.uiowa.edu *Corresponding author Ikjin Lee Department of Mechanical Engineering The University of Connecticut, Storrs, CT 06269, USA ilee@engr.uconn.edu Liang Zhao Schlumberger 1310 Rankin Rd, Houston, TX 77073, USA lzhao01@slb.com David Lamb US Army RDECOM/TARDEC Warren, MI 48397-5000, USA david.lamb@us.army.mil ABSTRACT In this paper, a sampling-based RBDO method using a classification method is presented. The probabilistic sensitivity analysis is used to compute sensitivities of probabilistic constraints with respect to random variables. Since the probabilistic sensitivity analysis requires only the limit state function, and not the response surface or sensitivity of the response, an efficient classification method can be used for a sampling-based RBDO. The proposed virtual support vector machine (VSVM), which is a classification method, is a support vector machine (SVM) with virtual samples. By introducing virtual samples, VSVM overcomes the deficiency in existing SVM that uses only classification information as their input. In this paper, the universal Kriging method is used to obtain locations of virtual samples to improve the accuracy of the limit state function for highly nonlinear problems. A sequential sampling strategy effectively inserts new samples near the limit state function. In sampling-based RBDO, Monte Carlo simulation (MCS) is used for the reliability analysis and probabilistic sensitivity analysis. Since SVM is an explicit classification method, unlike implicit methods, computational cost for evaluating a large number of MCS samples can be significantly reduced. Several efficiency strategies, such as the hyper-spherical local window for generation of the limit state function and the Transformations/Gibbs sampling method to generate uniform samples in the hyper-sphere, are also applied. Examples show that the proposed sampling-based RBDO using VSVM yields better efficiency in terms of the number of required samples and the computational cost for evaluating MCS samples while maintaining accuracy similar to that of sampling-based RBDO using the implicit dynamic Kriging (D-Kriging) method. KEYWORDS Surrogate Model, Sampling-based RBDO, Probabilistic Sensitivity Analysis, Support Vector Machine (SVM), Sequential Sampling, Virtual Samples, Virtual Support Vector Machine (VSVM), Hyper-spherical Local Window 1. Introduction The reliability-based design optimization (RBDO) methods that use sensitivity have been widely applied to various engineering applications. Using sensitivities, the most probable point (MPP)-based reliability analysis can be carried out for approximating the reliability of the system [1-6]. However, the sensitivity often is not available or is difficult to obtain in complex multi-physics or multidisciplinary simulation-based engineering design applications. In this case, the surrogate- based method can provide approximations of otherwise expensive computer simulations for design optimization [7]. In RBDO, once accurate surrogate models are constructed, Monte Carlo simulation (MCS) [8-11] can be directly applied to the surrogate model for the reliability analysis and probabilistic