Explicit Design Space Decomposition with Adaptive Sampling for Design Optiimization and Uncertainty Quantification

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0800117PI: MissoumThe research objective of this award is to develop a method to aid designers and engineers in optimizing complex products under uncertainty. The design of complex systems such as a vehicle or an engine often requires very long computational times due to the presence of nonlinear behaviors. Because optimization requires repeated calls to a simulation code (e.g., crash analysis) to investigate a multi-dimensional design space, it is critical to use a sound methodology to select relevant design configurations in the search for the best solutions. The proposed approach, referred to as explicit design space decomposition, partitions the design space into regions whose boundaries, which are defined explicitly in terms of the variables, separate "acceptable" and "unacceptable" designs. These boundaries are constructed using a Support Vector Machine (SVM) which is able to define multi-dimensional, disjoint, and non-convex regions. This gives insight to the designer through a direct correspondence between regions of the design space and specific behaviors of a system. In addition, accurate SVM-based boundaries can be obtained by adaptively adding relevant samples corresponding to specific designs. This approach has the potential to limit trial-and-error steps and reduce the total computational time. Finally, explicit boundaries are useful for problems with discontinuous behaviors such as buckling and provide a straightforward calculation of probabilities of failure. All in all, this approach allows the designer to reach better and more reliable designs in fewer design iterations.If successful, the results of this research will provide a general framework for design optimization and design under uncertainty of nonlinear problems characterized by, but not limited to, discontinuous responses and long simulation times (e.g., design for crashworthiness). The generality of the proposed approach will make it applicable to traditional industries (e.g., automobile and aerospace) as well as fields such as the design of biomedical devices. The reduction of trial-and-error steps will, if successful, drastically reduce design cycle times and cost. The results of this research will be included in graduate coursework and disseminated through technical publications and presentations. In addition, this approach is expected to have a significant impact on industry, resulting in streamlined design processes and better products.