Hamiltonian Monte Carlo Methods for Subset Simulation in Reliability Analysis

TL;DR

This paper introduces Hamiltonian Monte Carlo (HMC) algorithms tailored for Subset Simulation in structural reliability analysis, demonstrating improved efficiency and accuracy over traditional methods through theoretical explanation and practical examples.

Contribution

It develops two novel HMC algorithms for Subset Simulation, enhancing sampling efficiency in reliability analysis compared to existing techniques.

Findings

HMC algorithms outperform standard methods in efficiency

The proposed algorithms provide accurate reliability estimates

Source code and data are made publicly available

Abstract

This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic mechanism inspired by Hamiltonian dynamics to propose samples following a target probability distribution. The method alleviates the random walk behavior to achieve a more effective and consistent exploration of the probability space compared to standard Gibbs or Metropolis-Hastings techniques. After a brief review of the basic concepts of the HMC method and its computational details, two algorithms are proposed to facilitate the application of the HMC method to Subset Simulation in structural reliability analysis. Next, the behavior of the two HMC algorithms is illustrated using simple probability distribution models. Finally, the accuracy and efficiency of Subset Simulation employing the two HMC algorithms are tested using various reliability examples. The supporting source code and data are available for download at (the URL that will become available once the paper is accepted).