Development of Theoretical Framework for Uncertainty-Based Design Problems.

摘要

The research objectives of the project revolve around the development of a rigorous mathematical framework for uncertainty-based design optimization, with an emphasis on the construction and analysis of a set of efficient numerical methods applicable for complex systems. The objectives include the following major components: 1. Constructing a mathematical framework, using generalized polynomial chaos (gPC) theory, to facilitate the analysis of uncertainty-based design optimization. 2. Developing novel and efficient numerical algorithms. 3. Conducting rigorous analysis and error estimates for the new algorithms. The work is performed on two kinds of uncertainty-based design optimization: * Robust design optimization, where the objective is to optimize the system performance while minimizing its sensitivity to uncertainty. * Reliability-based design optimization, where the objective is to optimize the system performance while keeping its failure probability under control.