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Probabilistic uncertainty analysis by mean-value first order Saddlepoint Approximation

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  • Huang, Beiqing
  • Du, Xiaoping

Abstract

Probabilistic uncertainty analysis quantifies the effect of input random variables on model outputs. It is an integral part of reliability-based design, robust design, and design for Six Sigma. The efficiency and accuracy of probabilistic uncertainty analysis is a trade-off issue in engineering applications. In this paper, an efficient and accurate mean-value first order Saddlepoint Approximation (MVFOSA) method is proposed. Similar to the mean-value first order Second Moment (MVFOSM) approach, a performance function is approximated with the first order Taylor expansion at the mean values of random input variables. Instead of simply using the first two moments of the random variables as in MVFOSM, MVFOSA estimates the probability density function and cumulative distribution function of the response by the accurate Saddlepoint Approximation. Because of the use of complete distribution information, MVFOSA is generally more accurate than MVFOSM with the same computational effort. Without the nonlinear transformation from non-normal variables to normal variables as required by the first order reliability method (FORM), MVFOSA is also more accurate than FORM in certain circumstances, especially when the transformation significantly increases the nonlinearity of a performance function. It is also more efficient than FORM because an iterative search process for the so-called Most Probable Point is not required. The features of the proposed method are demonstrated with four numerical examples.

Suggested Citation

  • Huang, Beiqing & Du, Xiaoping, 2008. "Probabilistic uncertainty analysis by mean-value first order Saddlepoint Approximation," Reliability Engineering and System Safety, Elsevier, vol. 93(2), pages 325-336.
  • Handle: RePEc:eee:reensy:v:93:y:2008:i:2:p:325-336
    DOI: 10.1016/j.ress.2006.10.021
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    References listed on IDEAS

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    1. Wang, Suojin, 1992. "General saddlepoint approximations in the bootstrap," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 61-66, January.
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    Cited by:

    1. Huang, Xianzhen & Jin, Sujun & He, Xuefeng & He, David, 2019. "Reliability analysis of coherent systems subject to internal failures and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 75-83.
    2. Xiao, Ning-Cong & Zuo, Ming J. & Zhou, Chengning, 2018. "A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 330-338.
    3. SakallI, Ümit Sami & Baykoç, Ömer Faruk, 2011. "An optimization approach for brass casting blending problem under aletory and epistemic uncertainties," International Journal of Production Economics, Elsevier, vol. 133(2), pages 708-718, October.
    4. Ning-Cong Xiao & Yan-Feng Li & Le Yu & Zhonglai Wang & Hong-Zhong Huang, 2014. "Saddlepoint approximation-based reliability analysis method for structural systems with parameter uncertainties," Journal of Risk and Reliability, , vol. 228(5), pages 529-540, October.
    5. Liu, Yu & Chen, Yiming & Jiang, Tao, 2018. "On sequence planning for selective maintenance of multi-state systems under stochastic maintenance durations," European Journal of Operational Research, Elsevier, vol. 268(1), pages 113-127.
    6. Hao Lu & Gang Shen & Zhencai Zhu, 2017. "An approach for reliability-based sensitivity analysis based on saddlepoint approximation," Journal of Risk and Reliability, , vol. 231(1), pages 3-10, February.
    7. Wang, Lei & Zhang, Xufang & Zhou, Yangjunjian, 2018. "An effective approach for kinematic reliability analysis of steering mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 62-76.
    8. Yuan, Xiukai & Lu, Zhenzhou, 2014. "Efficient approach for reliability-based optimization based on weighted importance sampling approach," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 107-114.
    9. Xianzhen Huang & Yimin Zhang, 2014. "A probability estimation method for reliability analysis using mapped Gegenbauer polynomials," Journal of Risk and Reliability, , vol. 228(1), pages 72-82, February.
    10. Rong Yuan & Debiao Meng & Haiqing Li, 2016. "Multidisciplinary reliability design optimization using an enhanced saddlepoint approximation in the framework of sequential optimization and reliability analysis," Journal of Risk and Reliability, , vol. 230(6), pages 570-578, December.
    11. Xu, Jun & Song, Jinheng & Yu, Quanfu & Kong, Fan, 2023. "Generalized distribution reconstruction based on the inversion of characteristic function curve for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    12. Yiwei Wang & Christian Gogu & Nicolas Binaud & Christian Bes & Raphael T Haftka & Nam-Ho Kim, 2018. "Predictive airframe maintenance strategies using model-based prognostics," Journal of Risk and Reliability, , vol. 232(6), pages 690-709, December.
    13. Ling, Chunyan & Lu, Zhenzhou & Zhang, Xiaobo, 2020. "An efficient method based on AK-MCS for estimating failure probability function," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    14. Zhou, Di & Pan, Ershun & Zhang, Xufang & Zhang, Yimin, 2020. "Dynamic Model-based Saddle-point Approximation for Reliability and Reliability-based Sensitivity Analysis," Reliability Engineering and System Safety, Elsevier, vol. 201(C).

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