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First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis

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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 non-convergence 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.

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Acknowledgments

The first author thanks Dr. Huiling Chen for opening the HHO optimizer code in website. The authors are grateful to the comments from the editor and four reviewers. These comments improve the original manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (No. 51578225)

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Authors and Affiliations

  1. College of Civil Engineering, Hunan University, Changsha, 410082, People’s Republic of China

    Changting Zhong, Mengfu Wang, Chao Dang & Shengqi Guo

  2. School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, 330013, People’s Republic of China

    Wenhai Ke

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  1. Changting Zhong
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Correspondence to Mengfu Wang.

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Responsible Editor: Xiaoping Du

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Replication of results

The algorithm of the HHO-FORM approach is coded in MATLAB, and the source code of one example is included in the Supplementary Material.

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Zhong, C., Wang, M., Dang, C. et al. First-order reliability method based on Harris Hawks Optimization for high-dimensional reliability analysis. Struct Multidisc Optim 62, 1951–1968 (2020). https://doi.org/10.1007/s00158-020-02587-3

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