Surrogate Modeling of Complex Systems Using Adaptive Hybrid Functions

Abstract

This paper explores the effectiveness of the recently developed surrogate modeling method, the Adaptive Hybrid Functions (AHF), through its application to complex engineered systems design. The AHF is a hybrid surrogate modeling method that seeks to exploit the advantages of each component surrogate. In this paper, the AHF integrates three component surrogate models: (i) the Radial Basis Functions (RBF), (ii) the Extended Radial Basis Functions (E-RBF), and (iii) the Kriging model, by characterizing and evaluating the local measure of accuracy of each model. The AHF is applied to model complex engineering systems and an economic system, namely: (i) wind farm design; (ii) product family design (for universal electric motors); (iii) three-pane window design; and (iv) onshore wind farm cost estimation. We use three differing sampling techniques to investigate their influence on the quality of the resulting surrogates. These sampling techniques are (i) Latin Hypercube Sampling (LHS), (ii) Sobol’s quasirandom sequence, and (iii) Hammersley Sequence Sampling (HSS). Cross-validation is used to evaluate the accuracy of the resulting surrogate models. As expected, the accuracy of the surrogate model was found to improve with increase in the sample size. We also observed that, the Sobol’s and the LHS sampling techniques performed better in the case of high-dimensional problems, whereas the HSS sampling technique performed better in the case of low-dimensional problems. Overall, the AHF method was observed to provide acceptable-to-high accuracy in representing complex design systems.