Riemannian Manifold Hamiltonian Monte Carlo based subset simulation for reliability analysis in non-Gaussian space. (January 2022)

• Record Type: Journal Article
• Authors: Chen, Weiming; Wang, Ziqi; Broccardo, Marco; Song, Junho
• Is Part Of: Structural safety. Volume 94(2022)
• Publication Date: 2022-01
• Subjects: Riemannian manifold -- Hamiltonian Monte Carlo -- High-dimensional reliability -- Non-Gaussian space -- Subset simulation; Structural stability -- Periodicals; Safety factor in engineering -- Periodicals; Reliability (Engineering) -- Periodicals; Constructions -- Stabilité -- Périodiques; Coefficient de sécurité en ingénierie -- Périodiques; Fiabilité -- Périodiques; 620.86
• DOI: 10.1016/j.strusafe.2021.102134
• Languages: English
• ISSNs: 0167-4730

Abstract

Abstract: This paper proposes a Riemannian Manifold Hamiltonian Monte Carlo based subset simulation (RMHMC-SS) method to overcome limitations of existing Monte Carlo approaches in solving reliability problems defined in highly-curved non-Gaussian spaces. RMHMC is based on the second-order geometric information of a probability space. Specifically, it generates an optimized path for Markov chain evolutions in a Hamiltonian constructed on the Riemannian manifold. Compared with the recently proposed Hamiltonian Monte Carlo based subset simulation (HMC-SS) approach, the RMHMC-SS approach shows better performance in handling highly-curved probability distributions. After a brief review of HMC-SS, the theory and implementation details of RMHMC-SS are presented. Finally, various reliability examples are studied to test and verify the proposed RMHMC-SS method. Highlights: Riemannian Manifold Hamiltonian Monte Carlo based subset simulation is developed. Second order geometric information is used for efficient MCMC evolution. The method is designed for reliability problems in highly-curved non-Gaussian space. The method is successfully demonstrated by applications to non-Gaussian problems.