Reliability Analysis using Second-Order Saddlepoint Approximation and Mixture Distributions

[+] Author and Article Information
Dimitrios Papadimitriou

Mechanical Engineering Department, Oakland University, Rochester MI 48309

Zissimos P. Mourelatos

Mechanical Engineering Department, Oakland University, Rochester MI 48309

Zhen Hu

Department of Industrial and Manufacturing Systems Engineering University of Michigan-Dearborn, Dearborn, MI 48128

1Corresponding author.

ASME doi:10.1115/1.4041370 History: Received March 09, 2018; Revised June 18, 2018


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 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.

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