Control Variate Approach for Efficient Stochastic Finite-Element Analysis of Geotechnical Problems
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4, Issue 3
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 300 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.
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Acknowledgments
The first author is funded by a studentship grant from the Engineering and Physical Sciences Research Council (EPSRC) and Atkins. This support is gratefully received and acknowledged.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 4 • Issue 3 • September 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Nov 10, 2017
Accepted: Apr 12, 2018
Published online: Jul 13, 2018
Published in print: Sep 1, 2018
Discussion open until: Dec 13, 2018
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