Management of Functional Data Variables in Decomposition-based Design Optimization.

Abstract

Design of complex systems such as electric vehicle (EV) powertrains often requires decomposition-based optimization strategies, such as Analytical Target Cascading (ATC). In these strategies, systems are represented as hierarchies of interacting subsystems. Coupling variables capture subsystem interactions and their proper determination ensures system consistency. When coupling variables consist of highly-discretized functional data, such as motor performance curves in EV powertrain design, the design optimization problem can become prohibitively large. Therefore, it becomes necessary to implement reduced dimension representations of functional data to enable efficient, practical design optimization while maintaining reasonable accuracy. However, reduced representation variables may have no physical meaning, making the determination of their applicability boundary beyond simple bound constraints very difficult. This dissertation presents proper orthogonal decomposition (POD) as a leading candidate for the reduced representation of coupled, functional data within decomposition-based design optimization. It demonstrates that high-fidelity POD representations possess good accuracy, reasonable dimensionality reduction, and enhance functional data consistency in ATC. However, ATC convergence is affected by the consistency measure used for the coupled, functional data. Therefore, the Accuracy and Validity Algorithm for SIMulation (AVASIM) is examined as an alternative to the standard root-mean-square error metric. A new, generalized formulation of AVASIM that emphasizes global functional data accuracy is found to be appropriate as a consistency measure, being relatively stable and affording more accurate design solutions using fewer function evaluations. Finally, as noted above, simple bound constraints for reduced representation variables can lead to ill-behaved analysis and optimization since they rarely capture the decision space accurately. A constraint management strategy is presented that augments the existing penalty value-based heuristic with support vector domain description (SVDD). The SVDD augmentation is effective as it forces function evaluations to remain in the feasible domain, and can lead to convergence using fewer function evaluations.