HyPerModels: hyperdimensional performance models for engineering design
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Engineering design is an iterative process where the designer determines an appropriate set of design variables and cycle parameters so as to achieve a set of performance index goals. The relationships between design variables, cycle parameters and performance indices define the design space, a hyperdimensional representation of possible designs. To represent the design space, engineers employ metamodels, a technique that builds approximate or surrogate models of other models. Metamodels may be constructed from a wide variety of mathematical basis functions but Hyperdimensional Performance Models (HyPerModels) derived from Non-Uniform Rational Bsplines (NURBs) offer many unique advantages when compared to other metamodeling approaches. NURBs are defined by a set of control points, knot vectors and the NURBs orders, resulting in a highly robust and flexible curve definition that has become the de facto computer graphics standard. The defining components of a NURBs HyPerModel can be used to define adaptive sequential sampling algorithms that allow the designer to efficiently survey the design space for interesting regions. The data collected from design space surveys can be represented with a HyPerModel by adapting NURBs fitting algorithms, originally developed for computer graphics, to address the unique challenges of representing a hyperdimensional design space. With a HyPerModel representation, visualization of the design space or design subspaces such as the Pareto subspace is possible. HyPerModels support design space analysis for adaptive sequential sampling algorithms, to detect robust design space regions or for fault detection by comparing multiple HyPerModels obtained from the same system. Significantly, HyPerModels uniquely allow multi-start optimization algorithms to locate the global metamodel optimum in finite time. Each of these capabilities is demonstrated with demonstration problems including brushless DC motor fault detection and composite material I-beam and gas turbine engine design problems with the HyPerMaps software package. HyPerMaps defines the necessary algorithms to adaptively sample a design space, construct a HyPerModel and to use a HyPerModel for visualization, analysis or optimization. With HyPerMaps, an engineering designer has a window into the hyperdimensional design space, allowing the designer to explore the design space for undiscovered design variable combinations with superior performance capabilities.