Unified uncertainty analysis by the mean value first order saddlepoint approximation

Unified uncertainty analysis by the mean value first order saddlepoint approximation

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Article ID: iaor20126920
Volume: 46
Issue: 6
Start Page Number: 803
End Page Number: 812
Publication Date: Dec 2012
Journal: Structural and Multidisciplinary Optimization
Authors: , , , ,
Keywords: simulation: applications
Abstract:

Uncertainties exist in products or systems widely. In general, uncertainties are classified as epistemic uncertainty or aleatory uncertainty. This paper proposes a unified uncertainty analysis (UUA) method based on the mean value first order saddlepoint approximation (MVFOSPA), denoted as MVFOSPA‐UUA, to estimate the systems probabilities of failure considering both epistemic and aleatory uncertainties simultaneously. In this method, the input parameters with epistemic uncertainty are modeled using interval variables while input parameters with aleatory uncertainty are modeled using probability distribution or random variables. In order to calculate the lower and upper bounds of system probabilities of failure, both the best case and the worst case scenarios of the system performance function need to be considered, and the proposed MVFOSPA‐UUA method can handle these two cases easily. The proposed method is demonstrated to be more efficient, robust and in some situations more accurate than the existing methods such as uncertainty analysis based on the first order reliability method. The proposed method is demonstrated using several examples.

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