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We here consider the subset simulation method which approaches a failureevent using a decreasing sequence of nested intermediate failure events. Themethod resembles importance sampling, which actively explores a probabilityspace by conditioning the next evaluation on the previous evaluations using aMarkov chain Monte Carlo (MCMC) algorithm. A Markov chain typically requiresmany steps to estimate the target distribution, which is impractical withexpensive numerical models. Therefore, we propose to approximate each step of aMarkov chain locally with Gaussian process (GP) regression. Benchmark examplesof reliability analysis show that local approximations significantly improveoverall efficiency of subset simulation. They reduce the number of expensivelimit-state evaluations by over $80\%$. However, GP regression becomescomputationally impractical with increasing dimension. Therefore, to make ouruse of a GP feasible, we employ the partial least squares (PLS) regression, agradient-free reduction method, locally to explore and utilize alow-dimensional subspace within a Markov chain. Numerical experimentsillustrate a significant computational gain with maintained sufficientaccuracy.

Estimation of Failure Probabilities via Local Subset Approximations