First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis
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RESEARCH PAPER
First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis Changting Zhong1 · Mengfu Wang1 · Chao Dang1 · Wenhai Ke2 · Shengqi Guo1 Received: 6 December 2019 / Revised: 27 February 2020 / Accepted: 27 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The first-order reliability method (FORM) is a prevalent method in the structural reliability community. However, when solving the high-dimensional problem with a highly nonlinear limit state function, FORM usually encounters nonconvergence or divergence. In this study, an improved FORM combining Harris Hawks Optimization (HHO-FORM) is presented for high-dimensional reliability analysis. HHO is a meta-heuristic algorithm mimicking the predatory behavior of Harris hawks, and efficient in finding the global optimum of high-dimensional problems. In HHO-FORM, the reliability index is firstly formulated as the solution of a constrained optimization problem according to the FORM theory. Then, the constraints are handled with the exterior penalty function method. In addition, the optimal reliability index is determined by the Harris Hawks Optimization that accelerates the convergence by the population-based mechanism and the strategy of Levy Flight. The HHO-FORM does not require the derivatives of the limit state functions that reduce the computational burden for high-dimensional problems. So the simplicity of HHO-FORM greatly improves the efficiency in solving high-dimensional reliability problems. The HHO-FORM is firstly tested on three challenging numerical high-dimensional problems and then applied to two high-dimensional engineering problems to verify its performance. Four gradient-based FORM algorithms and four heuristic-based FORM algorithms are also compared with the proposed method. The experimental results demonstrate that HHO-FORM provides good accuracy and efficiency for high-dimensional reliability problems. Keywords First-order reliability method · Harris Hawks Optimization · High-dimensional reliability analysis · Meta-heuristics
1 Introduction In the design and risk analysis of structures, it is necessary to consider the effect of various uncertainties related to the dimension, load, material properties, etc. Reliability analysis is a very effective technique to consider these uncertainties, and its major task is to obtain the failure Responsible Editor: Xiaoping Du Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02587-3) contains supplementary material, which is available to authorized users. Mengfu Wang
[email protected] 1
College of Civil Engineering, Hunan University, Changsha, 410082, People’s Republic of China
2
School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, 330013, People’s Republic of China
probability of structures. When the dimension of random variables is low or medium, several approaches could be implemented to evaluate the failure probability w
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