UC Berkeley

This paper presents an uncertainty quantification problem involving high-dimensional uncertainty inputs and a nonlinear structural analysis model. The uncertainty quantification problem can be considered a high-dimensional numerical integration with a nonlinear integrand. The crude Monte Carlo, multi-fidelity Monte Carlo, and randomized quasi-Monte Carlo methods are applied to solve the numerical integration problem, and numerical experiments are conducted to compare the efficiency of the Monte Carlo methods. It is shown that both multi-fidelity Monte Carlo and randomized quasi-Monte Carlo may significantly improve the efficiency of the studied problem. The randomized quasi-Monte Carlo method is easier to implement, but a carefully selected quasi-random sample and more sophisticated variance estimation are needed to successfully apply the randomized quasi-Monte Carlo method.