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The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads

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  • Mattrand, C.
  • Bourinet, J.-M.

Abstract

The paper investigates the reliability of cracked components subjected to random amplitude loads modeled by discrete-time Markov processes. The proposed approach is able to capture interaction effects between cycles along the random loading sequence, which are of real interest in the damage tolerance design of aircraft structural components. Random fatigue loads are either modeled by discrete-time First-order Markov Chains or hidden Markov chains with continuous state space and their parameters are identified from in-flight data recorded on a fleet of fighter aircrafts. The uncertainties of the initial crack parameters and material properties are not accounted for in this work and some additional simplifying assumptions are made in order to define a tractable problem. The solution strategy for reliability assessment hinges on the cross-entropy method. The application of this method to Markov chains with discrete state space is first presented based on previous works of the literature and the paper then develops its extension to the selected Hidden Markov Model with continuous state space. Several damage tolerance applications are performed to illustrate the relevance and efficiency of the proposed methodology for which the strengths and limitations are finally highlighted.

Suggested Citation

  • Mattrand, C. & Bourinet, J.-M., 2014. "The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 171-182.
    • Handle: RePEc:eee:reensy:v:123:y:2014:i:c:p:171-182
    DOI: 10.1016/j.ress.2013.10.009
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    References listed on IDEAS

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    1. Liu, Yongming & Liu, Liming & Stratman, Brant & Mahadevan, Sankaran, 2008. "Multiaxial fatigue reliability analysis of railroad wheels," Reliability Engineering and System Safety, Elsevier, vol. 93(3), pages 456-467.
    2. Bickenbach, Frank & Bode, Eckhardt, 2001. "Markov or not Markov - this should be a question," Kiel Working Papers 1086, Kiel Institute for the World Economy (IfW Kiel).
    3. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
    4. Neddermeyer, Jan C., 2009. "Computationally Efficient Nonparametric Importance Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 788-802.
    5. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    6. Wang, Zequn & Wang, Pingfeng, 2013. "A new approach for reliability analysis with time-variant performance characteristics," Reliability Engineering and System Safety, Elsevier, vol. 115(C), pages 70-81.
    7. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    8. Ad Ridder, 2005. "Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy," Annals of Operations Research, Springer, vol. 134(1), pages 119-136, February.
    9. Morio, Jérôme, 2011. "Non-parametric adaptive importance sampling for the probability estimation of a launcher impact position," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 178-183.
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    Cited by:

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    2. El Masri, Maxime & Morio, Jérôme & Simatos, Florian, 2021. "Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. XiaoFei, Lu & Min, Liu, 2014. "Hazard rate function in dynamic environment," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 50-60.
    4. Santosh B. Rane & Prathamesh R. Potdar & Suraj Rane, 2019. "Accelerated life testing for reliability improvement: a case study on Moulded Case Circuit Breaker (MCCB) mechanism," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(6), pages 1668-1690, December.

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