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.

Riemannian Manifold Hamiltonian Monte Carlo Based Subset Simulation for Reliability Analysis in non-Gaussian Space / Chen, W.; Wang, Z.; Broccardo, M.; Song, J.. - In: STRUCTURAL SAFETY. - ISSN 0167-4730. - 94:102134(2022), pp. 1-13. [10.1016/j.strusafe.2021.102134]

Riemannian Manifold Hamiltonian Monte Carlo Based Subset Simulation for Reliability Analysis in non-Gaussian Space

Broccardo M.;
2022-01-01

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.
2022
102134
Chen, W.; Wang, Z.; Broccardo, M.; Song, J.
Riemannian Manifold Hamiltonian Monte Carlo Based Subset Simulation for Reliability Analysis in non-Gaussian Space / Chen, W.; Wang, Z.; Broccardo, M.; Song, J.. - In: STRUCTURAL SAFETY. - ISSN 0167-4730. - 94:102134(2022), pp. 1-13. [10.1016/j.strusafe.2021.102134]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/321400
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