基于凸集模型的多学科耦合系统不确定性分析

研究了用凸集模型描述不确定参数时，多学科系统的不确定性分析方法．为了减少计算量，采用一阶泰勒近似并结合全局敏度方程推导了系统状态变量变差范围的近似计算公式，可用于超椭球凸集与区间变量并存的情形．该方法只需借助各学科分析的敏度信息，易于与各种基于敏度的寻优算法融合，进行不确定环境下的多学科优化设计．实例计算表明，在不确定程度较小时，该方法可以给出状态变量变差范围，而计算量远远小于Monte Carlo仿真算法．

Uncertainty analysis for multidisciplinary systems based on convex models

The convex model theory is implemented to handle the uncertain parameters of multidisciplinary systems. Two types of convex models are considered simultaneously to account for the uncertainties: the ellipsoid convex model and the uniform bound convex model (or interval variables). In order to improve computing efficiency, the first-order Taylor approximation combined with global sensitivity equations (GSE) is used to estimate the intervals of the end performance of multidisciplinary systems. The sensitivity information needed in this method is often a byproduct for many gradient-based optimization algorithms, so this approach can be easily integrated with a non-deterministic optimization framework to perform the robust design for multidisciplinary systems. The method is validated using the Monte Carlo simulation in application to an electronic packaging problem. Results show that it can give a good approximation for the uncertainty intervals of the coupling variables with a small amount of calculation when the uncertainty level is low.