This paper proposes a new second-order saddlepoint approximation (SOSA) method for reliability analysis of nonlinear systems with correlated non-Gaussian and multimodal random variables. The proposed method overcomes the limitation of current available SOSA methods, which are applicable to problems with only Gaussian random variables, by employing a Gaussian mixture model (GMM). The latter is first constructed using the expectation maximization (EM) method to approximate the joint probability density function (PDF) of the input variables. Expressions of the statistical moments of the response variables are then derived using a second-order Taylor expansion of the limit-state function and the GMM. The standard SOSA method is finally integrated with the GMM to effectively analyze the reliability of systems with correlated non-Gaussian random variables. The accuracy of the proposed method is compared with existing methods including a SOSA based on Nataf transformation. Numerical examples demonstrate the effectiveness of the proposed approach.
Reliability Analysis Using Second-Order Saddlepoint Approximation and Mixture Distributions
Rochester, MI 48309
University of Michigan-Dearborn,
Dearborn, MI 48128
Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 9, 2018; final manuscript received June 18, 2018; published online December 20, 2018. Assoc. Editor: Xiaoping Du.
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Papadimitriou, D. I., Mourelatos, Z. P., and Hu, Z. (December 20, 2018). "Reliability Analysis Using Second-Order Saddlepoint Approximation and Mixture Distributions." ASME. J. Mech. Des. February 2019; 141(2): 021401. https://doi.org/10.1115/1.4041370
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