A New Sequential Robust Approach for MDO Problems Under Mixed Interval and Probabilistic Uncertainties

In the design process of complex multidisciplinary systems, uncertainties in parameters or variables cannot be ignored. Robust multidisciplinary design optimization methods (RMDOs) can treat uncertainties as specified probabilistic distributions when enough statistical information is available. RMDOs need to assign intervals for nondeterministic variables since some design quantities may not have enough information to obtain statistical distributions, especially in the early stage of a design optimization process. Both types of uncertainties are very likely to appear simultaneously. In order to obtain robust solutions for multidisciplinary design optimization problems under mixed interval and probabilistic uncertainties, this work proposed a new sequential robust MDO approach, mixed SR-MDO. First, the robust optimization problem in a single discipline under mixed uncertainties is formulated and solved. Then, following the SR-MDO framework in our early work, MDO problems under mixed uncertainties are solved by handling probabilistic and interval uncertainties sequentially in decomposed subsystem problems. Interval uncertainties are handled by using the worst-case sensitivity analysis and fixing probabilistic uncertainties at their mean first, and then the influence of probabilistic uncertainties in objectives, constraints as well as in discipline analysis models is characterized by corresponding mean and variance. The applied SR-MDO framework allows subsystems in its full autonomy robust optimization and sequential robust optimization stages to run independently in parallel. This makes mixed SR-MDO be efficient for independent disciplines to work simultaneously and be more time-saving. Computational complexity of the proposed approach mainly relates to the double-loop optimization process in the worst-case interval uncertainties analysis. Examples are presented to demonstrate the applicability and efficiency of the mixed SR-MDO approach.