14 Surrogate Modeling with Non-Uniform Rational B-splines

Computer-aided engineering (CAE) analysis often necessitates the merger of information from multiple data sources, some of which may be the result of physical experiments or computer simulations, and others that are the result of empirical relationships. Through surrogate (or approximation) modeling techniques this disparate data can be combined into a single unified representation, sometimes termed a “metamodel” in the design engineering community. The expense of data acquisition and traditional modeling methods such as finite element analysis (FEA) can be mitigated through efficient surrogate modeling approaches, such as a class of geometric surrogate models defined using a non-uniform rational B-spline (NURBs) basis. NURBs-based surrogate models exhibit many desirable and useful properties in an engineering context. Their underlying structure supports adaptive data collection methods that can rapidly lead to accurate representations of high-dimensional (>3-D) nonlinear data sets. Furthermore, NURBsbasedsurrogates present interesting properties in terms of analysis and optimization capabilities. Many design optimization problems of interest exhibit nonlinear behaviors; are composed of combinations of continuous and discrete variables; and the desired solutions are not uniquely defined by a single design, but by a robust set of designs that perform despite manufacturing variations. While advances in computer simulation and analysis have made it feasible to analyze ever more complex engineering designs at increasing levels of fidelity, design optimization often demands solutions from these simulations to thousands and thousands of perturbations in the search for a solution.