Extended radial basis functions: More flexible and effective metamodeling

Economic competitiveness is driving industry to new frontiers of engineering design. Robustness and reliability-based design, multidisciplinary-simulation-based design, increased complexity and sophistication of our design, and optimization-aided design are four such areas that are seriously challenging our ability to keep pace with the need to adequately model the systems we seek to design-in spite of the exponential growth of computing power. An emerging consensus within the community is that the effective development of computationally benign models (metamodels) will help us navigate the challenging road ahead. The process of constructing metamodels for computationally expensive models, such as finite element, aerodynamic, and heat-transfer models, is representative of the tasks we must address. Among the available metamodeling techniques, radial basis functions (RBFs) have recently generated much interest for their effectiveness and versatility. Radial basis functions offer numerous advantages over the traditional response surface methodology, including their ability to effectively generate multidimensional interpolative approximations. However, we show how the typical RBF approach lacks the critical flexibility required to handle the wide variety of complex models arising from the use of advanced techniques, such as uncertainty handling and multiobjective optimization, often encountered in modern design. Furthermore, in this paper we propose a novel approach-the extended radial basis function (E-RBF) approach-that provides the designer with significant flexibility and freedom in the metamodeling process, compared to conventional RBFs. Examples are provided that demonstrate the effectiveness of the new approach and explore its potential superiority to traditional RBF and response surface methodologies. Initial investigation indicates that the E-RBF possesses unique and novel properties not available in any other single method.