Hyperdimensional Performance Maps for Engineering Design

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Design engineers are challenged with determining how to modify design variables in order to realize desired performance goals. For highly complex situations, the number of performance criteria that must be simultaneously considered far exceeds the number that a human engineer can comfortably contemplate. These performance criteria are typically highly non-linear functions of a large number of design variables, and few tools are available to assist engineers in managing such design spaces. The objective of this research is to provide a new method for representing complex high-dimension, highly non-linear design spaces. A hyperdimensional B-spline object (HyPerMap) is fit to data from design iterations (either simulations or experiments), resulting in a system that relates performance indices to variations in design variables. The system map is used to explore the design space, make optimal design decisions, and understand the impact of uncertainty on decisions. Furthermore, the B-spline based HyPerMap structure offers computational advantages over competing techniques during generation, evolution, evaluation, and optimization.The broad impact of this work will be an enhanced ability to design complex systems. Discussions with representatives from industry and research laboratories have convinced us that this research addresses a real need in the area of complex systems design. Our computational approach represents an opportunity to introduce a scientific foundation to a previously experiential process and to provide a basis for design optimization with knowledge of the associated system performance error and uncertainty. Thus, we expect the approach will also provide educational benefits for students of engineering design, particularly through the use of the resulting tools for complex systems design.