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Reliability analysis using adaptive Polynomial-Chaos Kriging and probability density evolution method

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  • Zhou, Tong
  • Peng, Yongbo

Abstract

An efficient reliability method that combines adaptive Polynomial-Chaos Kriging (PC-Kriging) and probability density evolution method (PDEM) is developed, which is abbreviated as the APCK-PDEM. First, according to the relative contributions of different representative points to the failure probability calculated by the PDEM, the notation of region of interest (ROI) is proposed, in which the representative points make critical contributions to the resultant failure probability. Then, three key aspects involved in the proposed APCK-PDEM are addressed: (a) A new learning function called PDEM-oriented expected improvement function (PEIF) is devised to cater for the demand of PDEM on the PC-Kriging accuracy; (b) A pertinent convergence criterion is defined in terms of the bound of failure probability estimated by the APCK-PDEM; (c) Since the true value of the boundary of ROI is unknown in the PEIF, an iterative determination scheme of this metric is performed at each iteration during the adaptive sampling process. Three examples are studied to showcase the performance of APCK-PDEM, and comparisons are made against other existing reliability methods. Numerical analyses and results show that the APCK-PDEM gains satisfactory estimation accuracy and high computational efficiency.

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  • Zhou, Tong & Peng, Yongbo, 2022. "Reliability analysis using adaptive Polynomial-Chaos Kriging and probability density evolution method," Reliability Engineering and System Safety, Elsevier, vol. 220(C).
    • Handle: RePEc:eee:reensy:v:220:y:2022:i:c:s0951832021007559
    DOI: 10.1016/j.ress.2021.108283
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    References listed on IDEAS

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    7. Pepper, Nick & Crespo, Luis & Montomoli, Francesco, 2022. "Adaptive learning for reliability analysis using Support Vector Machines," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    8. Dhulipala, Somayajulu L.N. & Shields, Michael D. & Chakroborty, Promit & Jiang, Wen & Spencer, Benjamin W. & Hales, Jason D. & Labouré, Vincent M. & Prince, Zachary M. & Bolisetti, Chandrakanth & Che, 2022. "Reliability estimation of an advanced nuclear fuel using coupled active learning, multifidelity modeling, and subset simulation," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    9. Zheng, Xiaohu & Yao, Wen & Zhang, Yunyang & Zhang, Xiaoya, 2022. "Consistency regularization-based deep polynomial chaos neural network method for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    10. Kröker, Ilja & Oladyshkin, Sergey, 2022. "Arbitrary multi-resolution multi-wavelet-based polynomial chaos expansion for data-driven uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    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).

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