A Basic Study on Adaptive Surrogate Model for Reliability Analysis and Bayesian Update

Abstract

Reducing computational cost in the reliability analysis or Bayesian updating process, especially for complex models, remains one of the key challenges. Adaptive surrogate models have attracted attention for the efficiency since active learning reliability method combining Kriging and MCS (AK-MCS) was proposed. The adaptive surrogate model approach can reduce the computation cost by appropriately replacing, possibly adaptively, the evaluation of the original computationally costly models with approximate ones that are much less costly. One of key points in this approach is how to construct the surrogated model based on the limited number of function calls such as estimation by finite element method, which needs large computation cost. AK-MCS uses Kriging for the construction of the surrogated model. This paper compares Gaussian Process Regression (GPR) with single random field and two random fields for the surrogated model. Single random field GPR is better in a simple reliability analysis benchmark example, though two random fields GPR is better in a Bayesian updating benchmark example. It seems the optimal number of the random field for the surrogated model depends on the complexity of the shape of limit state function or posterior probability density function. This paper also discusses the initial sampling placement for the surrogated model construction, and reliability analysis with ordinary random number, Latin Hypercube sampling, or low discrepancy sequence for the estimation of limit state probability.