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Saddlepoint approximation-based reliability analysis method for structural systems with parameter uncertainties

Author

Listed:
  • Ning-Cong Xiao
  • Yan-Feng Li
  • Le Yu
  • Zhonglai Wang
  • Hong-Zhong Huang

Abstract

Due to epistemic uncertainty, precisely determining parameters of all distribution is impossible in engineering practice. In this article, a novel reliability analysis method based on the saddlepoint approximation is proposed for structural systems with parameter uncertainties. The proposed method includes four main steps: (1) sampling for random and probability-box variables, (2) approximating the cumulant generating functions for systems under the best and worst cases, (3) calculating saddlepoints for the best and worst cases, and (4) calculating the lower and upper bounds of the probability of failure. The proposed method is effective because it does not require a large sample size or solving complicated integrals. Furthermore, the proposed method provides results that have the same accuracy as the existing interval Monte Carlo simulation method, but with significantly reduced computational effort. The effectiveness of the proposed method is demonstrated with three examples that are compared against with the interval Monte Carlo simulation method.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:risrel:v:228:y:2014:i:5:p:529-540
    DOI: 10.1177/1748006X14537619
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    References listed on IDEAS

    as
    1. N-C Xiao & H-Z Huang & Z Wang & Y Li & Y Liu, 2012. "Reliability analysis of series systems with multiple failure modes under epistemic and aleatory uncertainties," Journal of Risk and Reliability, , vol. 226(3), pages 295-304, June.
    2. 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.
    3. Beiqing Huang & Xiaoping Du & Ramaprasad E. Lakshminarayana, 2006. "A saddlepoint approximation based simulation method for uncertainty analysis," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 1(1/2), pages 206-224.
    4. Ferson, Scott & Troy Tucker, W., 2006. "Sensitivity analysis using probability bounding," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1435-1442.
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