Optimal Design in the Presence of Modeling Uncertainties

The integration of modeling and simulation tools with robust and efficient methods of optimal design offers a rational approach to explore new concepts and designs. However, a widespread adaptation of these tools in the industry design environment will require that they incorporate a systematic analysis of uncertainty in all aspects of the design process. A lack of confidence in designs generated in a simulation-based approach is the result of uncertainties in the predictive capabilities of physics-based models used in the simulations, and poor representation of uncertainties and their propagation in a coupled systems engineering design problem. A data- and knowledge-lean environment, typical of a design process involving novel concepts, further exacerbates the situation; design engineers often make gross assumptions about distributional information of random variables and parameters, thereby adding to the uncertainty associated with the design results. The paper focuses on numerical and analytical tools by which to model uncertainty and risk in a simulation-based design environment, including cases where the uncertainty does not conform to standard probabilistic distributions. A specific focus of the modeling effort is an approach to establish confidence intervals for response predictions available from analytical and numerical models, as well as surrogate approximations used in the design process. Innovative adaptations of formal optimization methods in a nondeterministic design setting are discussed, including design problem formulations that examine the nondeterministic design problem in a multicriteria optimization framework. Simple design problems are used to illustrate the concepts and to underscore the deficiencies in a purely deterministic approach to the design problem.