Design Optimization under Aleatory and Epistemic Uncertainties

This paper presents a design optimization methodology under three sources of uncertainty: physical variability (aleatory); data uncertainty (epistemic) due to sparse or imprecise data; and model uncertainty (epistemic) due to modeling errors/approximations. A likelihood-based method is use to fuse multiple formats of information, and a non-parametric probability density function (PDF) is constructed. Two types of model errors are considered: model form error and numerical solution error, each of which is a function of the design variables that are changing at each iteration of the optimization. Gaussian process (GP) surrogate models are constructed for efficient computation of model errors in the optimization. The treatment in this paper yields a distribution of the output that accounts for various sources of uncertainty. The use of a probabilistic approach to include both aleatory and epistemic uncertainties allows for their efficient integration into the optimization framework. The proposed methods are illustrated using a three-dimensional wing design problem involving fluid-structure interaction analysis.