Control Variate Approach for Efficient Stochastic Finite-Element Analysis of Geotechnical Problems

Abstract

Monte Carlo simulation is the most versatile solution method for problems in stochastic computational mechanics but suffers from a slow convergence rate. The number of simulations required to produce an acceptable accuracy is often impractical for complex and time-consuming numerical models. In this paper, an element-based control variate approach is developed to improve the efficiency of Monte Carlo simulation in stochastic finite-element analysis, with particular reference to high-dimensional and nonlinear geotechnical problems. The method uses a low-order element to form an inexpensive approximation to the output of an expensive, high-order model. By keeping the mesh constant, a high correlation between low-order and high-order models is ensured, enabling a large variance reduction to be achieved. The approach is demonstrated by application to the bearing capacity of a strip footing on a spatially variable soil. The problem requires 3 input random variables to represent the spatial variability by random fields, and would be difficult to solve by methods other than Monte Carlo simulation. Using an element-based control variate reduces the standard deviation of the mean bearing capacity by approximately half. In addition, two methods for estimating the cumulative distribution function as a complement to the improved mean estimator are presented.