Time-dependent reliability-based design optimization considering aleatory and epistemic uncertainties
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RESEARCH PAPER
Time-dependent reliability-based design optimization considering aleatory and epistemic uncertainties Yan Shi 1,2 & Zhenzhou Lu 1
&
Jiayan Zhou 2,3 & Enrico Zio 2,4,5
Received: 28 March 2020 / Revised: 3 July 2020 / Accepted: 15 July 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Directly solving time-dependent reliability-based design optimization (TRBDO) with aleatory and epistemic uncertainties is time-demanding, which limits its engineering application. By treating aleatory and epistemic uncertainties with probability and evidence variables respectively, an advanced decoupling method named sequential optimization and unified time-dependent reliability analysis (SOUTRA) is proposed in this work. By the SOUTRA, the original nested optimization process is solved by a sequence of unified time-dependent reliability analysis, updated reliability index target estimation and deterministic optimization. Only few numbers of the unified time-dependent reliability analysis are required to derive the optimum by the SOUTRA; thus, it is highly efficient. Furthermore, in order to construct the deterministic optimization, a new probability transformation method named focal element midpoint (FEM) is established to convert the evidence variable into a random one. FEM can avoid the issues of uniformity approach and equal areas method, and both are used in the existing probability transformation. Several numerical and engineering applications are introduced to illustrate the effectiveness of the proposed SOUTRA. Keywords Time-dependent reliability-based design optimization . Hybrid uncertainties . Sequential optimization . Probability transformation method . Unified time-dependent reliability analysis
Highlights • A new method named SOUTRA is proposed to solve TRBDO with mixed uncertainties. • A new probability transformation method called FEM is established. • Original nested optimization is solved by a sequence of optimization process. • Only few numbers of unified time-dependent reliability analysis are required. Responsible Editor: Yoojeong Noh Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02691-4) contains supplementary material, which is available to authorized users. * Zhenzhou Lu [email protected] 1
School of Aeronautics, Northwestern Polytechnical University, Xi’an, China
2
Energy Department, Politecnico di Milano, Milan, Italy
3
College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, China
4
MINES Pairs Tech, PSL Research University, CRC, Sophia Antipolis, France
5
Department of Nuclear Engineering, College of Engineering, Kyung Hee University, Seoul, South Korea
Nomenclature RBDO TRBDO SOUTRA FEM SORA SLA KKT MPTP AMV AAMV MMV HDMV TIEM T-SORA T-SLA FARM DNOM
Reliability-based design optimization Time-dependent reliability-based design optimization Sequential optimization and unified time-dependent reliability analysis Focal element midpoint Sequential optimization and re
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