Design space covering for uncertainty

Abstract

Managing uncertainty in engineering design continues to challenge engineers. By combining the concept of regret from robust optimization with that of design space reduction from set-based design, a new complementary view on uncertainty referred to as Design Space Covering for Uncertainty (DSC-U) is introduced. This method develops a trade-space between reducing the design space and locking in sub-optimal performance while considering interval uncertainty that impacts the problem. A double-loop algorithm and a more efficient set covering algorithm are presented along with the structure of the method. These are demonstrated on three sample problems, a previously-studied cantilever tube optimization, the Rosenbrock function with different levels of coupling between the uncertain parameters, and a ship midship section design problem with thirty-six design variables and four uncertain terms. The DSC-U approach is shown to be practical in providing a complementary insight into the impact of uncertainty for a wide range of design techniques.

Keywords:

• Uncertainty
• robust optimization
• set-based design
• regret
• set covering

Disclosure statement

The authors report there are no competing interests to declare.

Data availability

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Funding

This work was supported in part by LIFT (operated by the American Lightweight Materials Manufacturing Innovation Institute—ALMMII), the Rackham Graduate School at the University of Michigan, and grants from Code 331 of the Office of Naval Research [N00014-11-1-0845 and N00014-16-1-2978], with Ms Kelly Cooper and Dr Paul Hess as program managers.