Review of Metamodeling Techniques in Support of Engineering Design Optimization

Abstract

Computation-intensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximation or metamodeling techniques are often used. Metamodeling techniques have been developed from many different disciplines including statistics, mathematics, computer science, and various engineering disciplines. These metamodels are initially developed as “surrogates” of the expensive simulation process in order to improve the overall computation efficiency. They are then found to be a valuable tool to support a wide scope of activities in modern engineering design, especially design optimization. This work reviews the state-of-the-art metamodel-based techniques from a practitioner’s perspective according to the role of metamodeling in supporting design optimization, including model approximation, design space exploration, problem formulation, and solving various types of optimization problems. Challenges and future development of metamodeling in support of engineering design is also analyzed and discussed.

Statistical metamodeling of dynamic network loading

“…Metamodeling is first proposed for achieving better analytical insight and computational efficiency by providing a surrogate model of a complex process/simulation procedure/function/computer routine (Kleijnen, 2015;Wang and Shan, 2007). In the age of modern information, massive datasets have become available for interpreting complex systems, which inspire growing interests and research efforts to investigate problems with high dimensionality and nonlinearity.…”

“…In the age of modern information, massive datasets have become available for interpreting complex systems, which inspire growing interests and research efforts to investigate problems with high dimensionality and nonlinearity. In the past decade, new developments in metamodeling have been continuously coming forth, which have become powerful tools for approximating models, exploring design spaces, formulating problems, and supporting optimization, with good accuracy and performance at a reasonable cost (Wang and Shan, 2007).…”

“…Steps (2) and (3) are often coupled and considered in line with each other since learning/fitting techniques have evolved to be highly specific and dependent on the metamodel used. Examples of popular metamodels include polynomials (Montgomery, 2008), Kriging (Sacks et al, 1989), neural networks (Cheng and Titterington, 1994), radial basis functions (Fang and Horstemeyer, 2006;Regis and Shoemaker, 2013), multivariate adaptive regression splines (Friedman, 1991), and inductive learning (Wang and Shan, 2007).…”

“…Metamodeling is the process of building a "model of the model", i.e., a surrogate approximation of the exact models/processes in order to improve the computation efficiency or gain better analytical properties (Wang and Shan, 2007). Specifically, we treat the delay operator as a highly nonlinear mapping from the set of path departure rates to the set of path travel times, and interpret and approximate its inherent input-output mechanism using a statistical learning technique called Kriging (Matheron, 1963).…”

Performance study of multi-fidelity gradient enhanced kriging

“…The intention of surrogate modelling is to accurately imitate the behaviour of the computationintensive simulator over an entire input space with a minimal number of expensive simulations. Jin et al (2000), Simpson et al (2001) and Wang and Shan (2006) provided an overview of the most commonly used surrogate modelling techniques. Kriging, which was proposed by Sacks et al (1989b) for the design and analysis of computer experiments, is arguably popular to approximate deterministic data resulting from computer codes (Sacks et al 1989a;Kleijnen 2009).…”