Estimation of Failure Probabilities via Local Subset Approximations

Kenan Šehić*, Mirza Karamehmedović

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

We here consider the subset simulation method which approaches a failure event using a decreasing sequence of nested intermediate failure events. The method resembles importance sampling, which actively explores a probability space by conditioning the next evaluation on the previous evaluations using a Markov chain Monte Carlo (MCMC) algorithm. A Markov chain typically requires many steps to estimate the target distribution, which is impractical with expensive numerical models. Therefore, we propose to approximate each step of a Markov chain locally with Gaussian process (GP) regression. Benchmark examples of reliability analysis show that local approximations significantly improve overall efficiency of subset simulation. They reduce the number of expensive limit-state evaluations by over 80%. However, GP regression becomes computationally impractical with increasing dimension. Therefore, to make our use of a GP feasible, we employ the partial least squares (PLS) regression, a gradient-free reduction method, locally to explore and utilize a low-dimensional subspace within a Markov chain. Numerical experiments illustrate a significant computational gain with maintained sufficient accuracy. 
Original languageEnglish
JournalJournal of Engineering Mathematics
Number of pages21
ISSN0022-0833
Publication statusAccepted/In press - 2025

Keywords

  • Subset simulation
  • Markov chain Monte Carlo
  • Local approximation ·
  • Partial least squares regression ·
  • Rare events

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