Improving accuracy of first-order reliability estimate by importance sampling simulations

Presented in this paper is a computational approach that uses Importance Sampling Simulations (ISS) to improve the accuracy of model reliability estimates obtained by the First-order Reliability Method (FORM). The approach considers uncertainties associated with boundary conditions, initial conditions, and material constitutive parameters of finite element groundwater flow and contaminant transport models. Each spatially correlated random field is represented by its own grid of random variables and direct data. Their values at Gaussian integration points are computed using an Optimal Linear Estimator (OLE). A high-order Gaussian quadrature rule is used in element matrix computations to account for material parameter variation within an element. To benefit from the accuracy of Monte Carlo simulations (MCS) and the efficiency of the FORM, we performed the reliability analysis by ISS at realization points in the vicinity of the FORM design point. In addition to providing point-wise probabilistic estimates, the data generated by ISS are used to estimate probability distributions in the vicinity of the FORM design points. To efficiently obtain a design point accurate enough for ISS, we applied the FORM using relatively coarse random variable meshes. The random variable meshes are refined to represent the local correlation structures in higher resolution in the subsequent ISS. OLE is used to estimate the design point for the refined meshes based on the design point corresponding to the coarse meshes. The results of numerical experiments demonstrated the accuracy and efficiency of this approach.