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Unified uncertainty analysis by the mean value first order saddlepoint approximation

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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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Abbreviations

UUA:

Unified Uncertainty Analysis

FORM:

First Order Reliability Method

SORM:

Second Order Reliability Method

FOSPA:

First Order Saddlepoint Approximation

PDF:

Probability Density Functions

CDF:

Cumulative Distribution Functions

MLP:

Most Likelihood Point

MVFOSPA:

Mean Value First Order Saddlepoint Approximation

MPP:

Most Probable Point

FFT:

Fast Fourier Transforms

MVFOSPA-UUA:

Unified Uncertainty Analysis based on the MVFOSPA

MCS:

Monte Carlo Simulation

SPA:

Saddlepoint Approximation

CGF:

Cumulant Generating Function

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Acknowledgments

This research was partially supported by the National Natural Science Foundation of China under the contract number 51075061, and the National High Technology Research and Development Program of China (863 Program) under the contract number 2007AA04Z403.

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Authors and Affiliations

  1. School of Mechatronics Engineering, University of Electronic Science and Technology of China, No. 2006, Xiyuan Avenue, West Hi-Tech Zone, Chengdu, Sichuan, 611731, China

    Ning-Cong Xiao, Hong-Zhong Huang, Zhonglai Wang, Yu Liu & Xiao-Ling Zhang

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  1. Ning-Cong Xiao
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  2. Hong-Zhong Huang
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  3. Zhonglai Wang
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  4. Yu Liu
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  5. Xiao-Ling Zhang
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Correspondence to Hong-Zhong Huang.

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Xiao, NC., Huang, HZ., Wang, Z. et al. Unified uncertainty analysis by the mean value first order saddlepoint approximation. Struct Multidisc Optim 46, 803–812 (2012). https://doi.org/10.1007/s00158-012-0794-4

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  • DOI: https://doi.org/10.1007/s00158-012-0794-4

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