Efficient uncertainty analysis methods for multidisciplinary robust design

Robust design has been gaining wide attention, and its applications have been extended to making reliable decisions when designing complex engineering systems in a multidisciplinary design environment. Though the usefulness of robust design is widely acknowledged for multidisciplinary design systems, its implementation is rare. One of the reasons is the complexity and computational burden associated with the evaluation or performance variations caused by the randomness (uncertainty) of a system. A multidisciplinary robust design procedure that utilizes efficient methods for uncertainty analysis is developed here. Different from the existing uncertainty analysis techniques, our proposed techniques bring the features of a multidisciplinary design optimization (MDO) framework into consideration. The system uncertainty analysis method and the concurrent subsystem uncertainty analysis method are developed to estimate the mean and variance of system performance subject to uncertainties associated with both design parameters and design models. As shown both analytically and empirically, compared to the conventional Monte Carlo simulation approach, the proposed techniques used for uncertainty analysis will significantly reduce the number of design evaluations at the system level and, therefore, improve the efficiency or robust design in the domain of MDO. A mathematical example and an electronic packaging problem are used as examples to verify the effectiveness of these approaches.