Modern engineering design requires the exploration of complex nonlinear design spaces that relate large numbers of design variables and performance criteria. Effective exploration and decision making requires the availability of efficient representations of high dimensional design spaces. Techniques from the field of metamodeling, which builds models of models, are often used to represent complex design relationships. We have developed an alternative, spline-based metamodeling technique that is amenable to adaptive representation of high dimensional spaces and facilitates optimization-based exploration of such spaces. This paper describes our technique for fitting Non-Uniform Rational B-splines (NURBs) to points in a design space generated from simulations or experiments. The algorithm is illustrated with examples from metamodeling and nonlinear optimization literature. The results indicate that our method achieves an average global correlation of more than 99% and an average maximum local RMS error of less than 3% of full scale.

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