An Improved Stochastic Upscaling Method for Multiscale Engineering Systems

A stochastic multiscale modeling technique is proposed to construct coarse scale representation of a fine scale model for use in engineering design problems. The complexity of the fine scale heterogeneity under uncertainty is replaced with the homogenized coarse scale parameters by seeking agreement between the responses at both scales. Generalized polynomial chaos expansion is implemented to reduce the dimensionality of propagating uncertainty through scales and the computational costs of the upscaling method. It is integrated into a hybrid optimization procedure with the genetic algorithm and sequential quadratic programming. Two structural engineering problems that involve uncertainties in elastic material properties and geometric properties at fine scales are presented to demonstrate the applicability and merit of the proposed technique.