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An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization

Author

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  • Bolin Liu

    (School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
    Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang 110819, China)

  • Liyang Xie

    (School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
    Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang 110819, China)

Abstract

The Kriging-based reliability method with a sequential design of experiments (DoE) has been developed in recent years for implicit limit state functions. Such methods include the efficient global reliability analysis, the active learning reliability method combining Kriging and MCS Simulations. In this research, a novel local approximation method based on the most probable failure point (MPFP) is proposed to improve such methods. In this method, the MPFP calculated in the last iteration is the center of the next sampling region. The size of the local region depends on the reliability index obtained by the First Order Reliability Method (FORM) and the deviation distance of the standard deviation. The proposed algorithm, which approximates the limit state function accurately near MPFP rather than in the whole design space, can avoid selecting samples in regions that have negligible effects on the reliability analysis results. In addition, a multi-point enrichment technique is also introduced to select multiple sample points in each iteration. After the high-quality approximation of limit state function is obtained, the failure probability is calculated by the Monte Carlo method. Four numerical examples are used to validate the accuracy and efficiency of the proposed method. Results show that the proposed method is very effective for an accurate evaluation of the failure probability.

Suggested Citation

  • Bolin Liu & Liyang Xie, 2020. "An Improved Structural Reliability Analysis Method Based on Local Approximation and Parallelization," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:209-:d:317584
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    References listed on IDEAS

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    1. Sun, Zhili & Wang, Jian & Li, Rui & Tong, Cao, 2017. "LIF: A new Kriging based learning function and its application to structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 152-165.
    2. Zhang, Xufang & Wang, Lei & Sørensen, John Dalsgaard, 2019. "REIF: A novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 440-454.
    3. Echard, B. & Gayton, N. & Lemaire, M. & Relun, N., 2013. "A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 232-240.
    4. Gaspar, B. & Teixeira, A.P. & Guedes Soares, C., 2017. "Adaptive surrogate model with active refinement combining Kriging and a trust region method," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 277-291.
    5. Wen, Zhixun & Pei, Haiqing & Liu, Hai & Yue, Zhufeng, 2016. "A Sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 170-179.
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