Robust optimization of NURBs metamodels for engineering design

Abstract

Engineering design is generally characterized as an activity where a designer compares alternative solutions to an engineering challenge in order to meet some required level of performance. Almost invariably this involves the selection of values for design variables such that the design meets performance requirements. Unfortunately, in many modern engineered products and systems the number of these design variables exceeds what an engineer may comfortably contemplate using traditional tools. Optimization tools which allow engineers to quantify and maximize performance in high-dimensional design spaces will become increasingly indispensable to the engineer if they can perform two tasks. These tools obviously must be able to search the design space for design variable values that maximize performance. Simultaneously, they must locate and quantify designs that provide robustness, or insensitivity in performance with respect to uncertainty or variation in design parameters. The considerations of modern manufacturing and control systems force this second requirement, as no machine component can be produced without variation, nor can any system be controlled with arbitrary accuracy. When optimizing a design, a common difficulty is encountered. Many, if not most, engineering challenges are represented by system models of great complexity. Adequate analysis and optimization of the model is subsequently impossible due to time and computation limitations. As a result, surrogate models termed "metamodels" are used in place of the actual system model. These metamodels are far more computationally efficient and allow the optimization of otherwise intractable problems. Non-Uniform Rational B-Splines (NURBs) have emerged as a powerful metamodeling technique capable of addressing the twin challenges posed above. Previous research has resulted in the development of algorithms capable of fitting NURBs metamodels to design spaces of many input variables and performance indicies, and performing various discreet optimizations upon these metamodels. In the present research we expand upon this basis by illustrating the development of robust optimization algorithms that leverages the unique properties of NURBs metamodels. This optimization is conducted in a general fashion by considering both optimality and various robustness metrics as global or local model properties, and illustrates the tradeoffs between them using a novel graphical approach.