Multilevel Monte Carlo applied to a structural engineering model with random material parameters

Practical structural engineering problems often exhibit a significant degree of uncertainty in the properties of the materials being used, in the dimensions of the modeled structures, in the magnitude of loading forces, etc. In this paper, a cantilever/doubly clamped beam with uncertainty in the Young's modulus under a static and a dynamic load is considered. The uncertainty is modeled by means of a random variable and by means of a random field. In order to compute the statistical quantities of the static deflection and frequency response function, Multilevel Monte Carlo is combined with a Finite Element solver. This recent sampling method is based on the idea of variance reduction, and employs a hierarchy of finite element discretizations of the structural engineering model. The computational cost of the method is compared to the cost of standard Monte Carlo, demonstrating a significant speedup of up to several orders of magnitude.