TY - GEN
T1 - A direct hamiltonian MCMC approach for reliability estimation
AU - Nikbakht, Hamed
AU - Papakonstantinou, Konstantinos G.
PY - 2019
Y1 - 2019
N2 - Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often encountered in reliability analysis of complex engineering systems, by introducing a gradient-based Hamiltonian Markov Chain Monte Carlo (HMCMC) framework, termed Approximate Sampling Target with Post-processing Adjustment (ASTPA). The basic idea is to construct a relevant target distribution by weighting the high-dimensional random variable space through a one-dimensional likelihood model, using the limit-state function. To sample from this target distribution we utilize HMCMC algorithms that produce Markov chain samples based on Hamiltonian dynamics rather than random walks. We compare the performance of typical HMCMC scheme with our newly developed Quasi-Newton based mass preconditioned HMCMC algorithm that can sample very adeptly, particularly in difficult cases with high-dimensionality and very small failure probabilities. To eventually compute the probability of interest, an original post-sampling step is devised at this stage, using an inverse importance sampling procedure based on the samples. The involved user-defined parameters of ASTPA are then discussed and general default values are suggested. Finally, the performance of the proposed methodology is examined in detail and compared against Subset Simulation in a series of static and dynamic low-and high-dimensional benchmark problems.
AB - Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often encountered in reliability analysis of complex engineering systems, by introducing a gradient-based Hamiltonian Markov Chain Monte Carlo (HMCMC) framework, termed Approximate Sampling Target with Post-processing Adjustment (ASTPA). The basic idea is to construct a relevant target distribution by weighting the high-dimensional random variable space through a one-dimensional likelihood model, using the limit-state function. To sample from this target distribution we utilize HMCMC algorithms that produce Markov chain samples based on Hamiltonian dynamics rather than random walks. We compare the performance of typical HMCMC scheme with our newly developed Quasi-Newton based mass preconditioned HMCMC algorithm that can sample very adeptly, particularly in difficult cases with high-dimensionality and very small failure probabilities. To eventually compute the probability of interest, an original post-sampling step is devised at this stage, using an inverse importance sampling procedure based on the samples. The involved user-defined parameters of ASTPA are then discussed and general default values are suggested. Finally, the performance of the proposed methodology is examined in detail and compared against Subset Simulation in a series of static and dynamic low-and high-dimensional benchmark problems.
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U2 - 10.7712/120219.6375.18838
DO - 10.7712/120219.6375.18838
M3 - Conference contribution
AN - SCOPUS:85074016078
SN - 9786188284494
T3 - Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
SP - 735
EP - 747
BT - Proceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
A2 - Papadrakakis, M.
A2 - Papadopoulos, V.
A2 - Stefanou, G.
PB - National Technical University of Athens
T2 - 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
Y2 - 24 June 2019 through 26 June 2019
ER -