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Journal of Applied Mathematics
Volume 2013, Article ID 513261, 16 pages
Research Article

Time-Dependent Reliability-Based Design Optimization Utilizing Nonintrusive Polynomial Chaos

1School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
2Key Laboratory for Reliability & Environmental Engineering, Beijing 100191, China

Received 13 December 2012; Revised 16 April 2013; Accepted 26 May 2013

Academic Editor: Xiaojun Wang

Copyright © 2013 Yao Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Time-dependent reliability-based design optimization (RBDO) has been acknowledged as an advance optimization methodology since it accounts for time-varying stochastic nature of systems. This paper proposes a time-dependent RBDO method considering both of the time-dependent kinematic reliability and the time-dependent structural reliability as constrains. Polynomial chaos combined with the moving least squares (PCMLS) is presented as a nonintrusive time-dependent surrogate model to conduct uncertainty quantification. Wear is considered to be a critical failure that deteriorates the kinematic reliability and the structural reliability through the changing kinematics. According to Archard’s wear law, a multidiscipline reliability model including the kinematics model and the structural finite element (FE) model is constructed to generate the stochastic processes of system responses. These disciplines are closely coupled and uncertainty impacts are cross-propagated to account for the correlationship between the wear process and loads. The new method is applied to an airborne retractable mechanism. The optimization goal is to minimize the mean and the variance of the total weight under both of the time-dependent and the time-independent reliability constraints.