A direct hamiltonian MCMC approach for reliability estimation

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationProceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
EditorsM. Papadrakakis, V. Papadopoulos, G. Stefanou
PublisherNational Technical University of Athens
Pages735-747
Number of pages13
ISBN (Print)9786188284494
DOIs
StatePublished - 2019
Event3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019 - Crete, Greece
Duration: Jun 24 2019Jun 26 2019

Publication series

NameProceedings of the 3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019

Conference

Conference3rd International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2019
CountryGreece
CityCrete
Period6/24/196/26/19

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Theoretical Computer Science

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