An efficient algorithm for estimating time-dependent failure credibility by embedding double-loop adaptive Kriging in di
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RESEARCH PAPER
An efficient algorithm for estimating time-dependent failure credibility by embedding double-loop adaptive Kriging in dichotomy searching Ning Wei 1 & Zhenzhou Lu 1 & Kaixuan Feng 1 Received: 10 June 2019 / Revised: 17 February 2020 / Accepted: 27 February 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Time-dependent failure credibility (TDFC) in a given service time of interest can reasonably quantify the safety of the structure with fuzzy inputs. However, the estimation of TDFC requires high computational cost because it involves multi-layer optimization, especially for problems with the implicit performance functions in engineering. In order to improve the efficiency of estimating TDFC under satisfied precision, this paper proposes an efficient dichotomy searching algorithm (DSA) combined with double-loop adaptive Kriging (D-AK) model (shorten as D-AK-DSA). In the proposed D-AK-DSA, a double-loop adaptive Kriging model is constructed to provide the directions for the dichotomy searching TDFC. In the inner loop, the AK model is constructed to surrogate the relation of the performance function and time variable at the given fuzzy input realization so as to obtain the minimum performance function with respect to the time for the outer loop, and in the outer loop, the AK model is constructed to identify the sign of the upper/lower boundary of the minimum performance function with the fuzzy inputs at a given membership interval so as to provide the dichotomy searching direction for TDFC. By the proposed dichotomy searching strategy, accurately solving the values of the upper/lower boundaries in evaluating TDFC is innovatively replaced by identifying the signs of them, which greatly reduces the difficulty of constructing the outer AK model. At the same time, the proposed method enhances the convergence of the outer AK surrogate model by establishing a reasonably improved learning function. Three examples verify the accuracy and efficiency of the proposed D-AK-DSA method. Keywords Fuzzy uncertainty . Time-dependent . Failure credibility . Kriging surrogate model
1 Introduction The traditional reliability analysis of structure is based on the probabilistic theory framework, and the safety degree can be Responsible Editor: Mehmet Polat Saka Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02561-z) contains supplementary material, which is available to authorized users. * Zhenzhou Lu [email protected] Ning Wei [email protected] Kaixuan Feng [email protected] 1
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
measured by the failure probability (Choi 2007; Lu et al. 2009) which is estimated based on the known probability density functions (PDFs) or cumulative distribution functions (CDFs) of the input variables. Although many researches proved that the probabilistic framework is quite scientific practical and widely used in the safety analysis of structures (Cheng et al.
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