Shape-Preserving Response Prediction for Surrogate Modeling and Engineering Design Optimization

Abstract

Computer simulation models are fundamental tools of contemporary engineering design. The components, structures, and systems considered in most engineering disciplines are far too complex to be accurately described using simple theoretical models. Therefore, numerical simulation is often the only way to evaluate the performance of the design with sufficient reliability. However, accurate, high-fidelity simulations are computationally expensive. Consequently, their use for design automation, especially when exploiting conventional optimization algorithms is often prohibitive. Availability of faster computers and more efficient simulation software does not always translate into computational speedup due to growing demand for improved accuracy and the need to evaluate larger and larger systems. Surrogate-based optimization (SBO) techniques belong to the most promising approaches capable of alleviating these difficulties. SBO allows for reducing the number of expensive objective function evaluations in a simulation-driven design process. This is obtained by replacing the direct optimization of the expensive model by iterative updating and re-optimization of its cheap surrogate model. Among proven SBO techniques, the methods exploiting physics-based low-fidelity models are probably the most efficient. This is because the knowledge about the system of interest embedded in the low-fidelity model allows constructing the surrogate model that has good generalization capability at a cost of just a few evaluations of the original model. This chapter reviews one of the most recent SBO techniques, the so-called shape-preserving response prediction (SPRP). We discuss the formulation of SPRP, its limitations, and generalizations, and, most importantly, demonstrate its applications to solve design problems in various engineering areas, including microwave engineering, antenna design, and aerodynamic shape optimization. We also discuss the use of SPRP for creating fast surrogate models with illustrations from the microwave engineering area.