  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).
