Efficient computational methods for uncertainty quantification of large systems.

Abstract

The quest to design environment-friendly and sustainable engineering systems has witnessed more and more fervent efforts in recent years. With the growth of affordable large-capacity computing resources, predictive, science-based computational models have become instrumental in this pursuit. The present work develops efficient computational methods for the uncertainty analysis of large dynamical and mechanical systems with local nonlinearities and uncertainties. Two approaches have been utilized: (i) reduction of the size of the system, and (ii) use of parallel computing resources. The first approach utilizes the response of a nominal system to efficiently compute the response of related systems; three types of analysis methods have been developed. The first method can be utilized for efficient modal analysis of undamped linear systems with local stiffness uncertainties. The second method can perform efficient frequency domain analysis of linear systems with local damping and stiffness uncertainties. The third method can be utilized for efficient time domain analysis of systems with local nonlinearities and uncertainties. These methods provide gains in computational efficiency approaching three orders of magnitude for moderately-sized computational models compared to the corresponding conventional methods. The gains in computational efficiency are expected to be more pronounced as the dimensionality of the system is increased. The second approach to increase computational efficiency utilizes modern parallel computing devices, specifically, graphics processing units (GPUs) to perform uncertainty analysis of computational models. A variety of uncertainty quantification methods have been implemented on a GPU. The gains in computational efficiency compared to corresponding CPU-based implementations range from one to three orders of magnitude. These GPU implementations are expected to serve as initial bases for further developments in the use of GPUs in this field.