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Research Papers

Saddlepoint Approximation for Sequential Optimization and Reliability Analysis

[+] Author and Article Information
Xiaoping Du

Department of Mechanical and Aerospace Engineering, University of Missouri—Rolla, Rolla, MO 65409-4494dux@umr.edu

J. Mech. Des 130(1), 011011 (Dec 07, 2007) (11 pages) doi:10.1115/1.2717225 History: Received January 11, 2006; Revised September 15, 2006; Published December 07, 2007

A good balance between accuracy and efficiency is essential for reliability-based design (RBD). For this reason, sequential-loops formulations combined with the first-order reliability method (FORM) are usually used. FORM requires a nonlinear non-normal-to-normal transformation, which may increase the nonlinearity of a probabilistic constraint function significantly. The increased nonlinearity may lead to an increased error in reliability estimation. In order to improve accuracy and maintain high efficiency, the proposed method uses the accurate saddlepoint approximation for reliability analysis. The overall RBD is conducted in a sequence of cycles of deterministic optimization and reliability analysis. The reliability analysis is performed in the original random space without any nonlinear transformation. As a result, the proposed method provides an alternative approach to RBD with higher accuracy when the non-normal-to-normal transformation increases the nonlinearity of probabilistic constraint functions.

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Figures

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Sequential loops procedure

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Outline of the SORA-SPA process

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Reliability analysis

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Shifting constraint boundary

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Constraint function in y space

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Constraint function in u space

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Constraint function in y space

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Constraint function in u space

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Cantilever beam

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Figure 11

Two-bar bracket

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