A nested single-loop Kriging model-based method for time-dependent failure credibility
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RESEARCH PAPER
A nested single-loop Kriging model-based method for time-dependent failure credibility Ning Wei 1
&
Zhenzhou Lu 1 & Kaixuan Feng 1 & Yingshi Hu 1
Received: 6 April 2020 / Revised: 12 June 2020 / Accepted: 15 July 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Most of the existing methods for estimating time-dependent failure credibility (TDFC) are based on optimization algorithms, which may result in a heavy burden on the computational cost and accuracy issue related to the local optimization. In order to achieve the best compromise between computational accuracy and cost, an efficient method is proposed in this work by embedding a single-loop adaptive Kriging model (S-AK) into the dichotomy searching algorithm (S-AK-DSA). The proposed S-AK-DSA can be regarded as a double-loop procedure. In the inner loop, the Kriging model of the real time-dependent performance function (TD-PF) is updated iteratively to accurately predict the signs of the upper/lower boundary of the TD-PF minimum with respect to the time variable at the given membership level. Based on the inner loop, the outer loop searches TDFC by continuously dichotomizing the searching interval of the TDFC. The advantages of S-AK-DSA are mainly manifested in two aspects. Firstly, S-AK-DSA converts the problem of optimizing the exact value of the upper/lower boundary into the problem of accurately identifying their signs, which can avoid the use of optimization algorithms. Secondly, at different membership levels, the S-AK-DSA method chooses the candidate sample pool and continuously updates the current Kriging model of TD-PF, and the adaptive learning function as well as appropriate stopping criterion can effectively reduce the cost of predicting the signs of the upper/lower boundary and improve the computational accuracy. Four case studies are introduced to demonstrate the feasibility and superiority of the proposed S-AK-DSA approach. Keywords Fuzzy . Time-dependent . Failure credibility . Kriging model
1 Introduction In recent decades, with the rapid development of modern science and technology and the deep understanding of Responsible Editor: Pingfeng Wang Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02694-1) contains supplementary material, which is available to authorized users. * Zhenzhou Lu [email protected] Ning Wei [email protected] Kaixuan Feng [email protected] Yingshi Hu [email protected] 1
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
uncertainty, reliability analysis and design methods have been paid more and more attention in theoretical research and engineering practice (Piscopo and Scamardella 2019; Qian et al. 2019; Vishwanathan and Vio 2019; Wei et al. 2016; Xu et al. 2018). The traditional reliability analysis is mostly based on the probability density function (PDF) to describe random uncertainties of the input variables, and it takes the failure probability as the index for me
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