Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2011 August 28-31, 2011, Washington, DC, USA DETC2011-48608 SURROGATE MODELING OF COMPLEX SYSTEMS USING ADAPTIVE HYBRID FUNCTIONS Jie Zhang ∗ Rensselaer Polytechnic Institute Troy, New York 12180 Email: zhangj17@rpi.edu Souma Chowdhury ∗ Rensselaer Polytechnic Institute Troy, New York 12180 Email: chowds@rpi.edu Achille Messac † Syracuse University Syracuse, NY, 13244 Email: messac@syr.edu Junqiang Zhang ∗ Rensselaer Polytechnic Institute Troy, New York 12180 Email: zhangj18@rpi.edu Luciano Castillo ‡ Rensselaer Polytechnic Institute Troy, New York 12180 Email: castil2@rpi.edu ABSTRACT This paper explores the effectiveness of the recently devel- oped 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 mod- els: (i) the Radial Basis Functions (RBF), (ii) the Extended Ra- dial 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 engineer- ing systems and an economic system, namely: (i) wind farm de- sign; (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 inves- tigate their influence on the quality of the resulting surrogates. These sampling techniques are (i) Latin Hypercube Sampling ∗ Doctoral Student, Multidisciplinary Design and Optimization Laboratory, Department of Mechanical, Aerospace and Nuclear Engineering, ASME student member. † Distinguished Professor and Department Chair. Department of Mechanical and Aerospace Engineering, ASME Lifetime Fellow. Corresponding author. ‡ Associate Professor, Department of Mechanical Aerospace and Nuclear En- gineering, ASME member (LHS), (ii) Sobol’s quasirandom sequence, and (iii) Hammers- ley Sequence Sampling (HSS). Cross-validation is used to evalu- ate 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 tech- nique 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. KEYWORDS: Complex engineered systems; hybrid surro- gate modeling; optimization; product family; response surface; wind farm; INTRODUCTION Complex systems such as human bodies, rain forests, aerospace-systems, energy systems and wireless networking generally tend to be highly interdisciplinary. Understanding, de- signing, building and controlling such complex systems remains a central challenge in the academia and the industry [1]. The determination of complex underlying relationships be- tween system parameters from simulated and/or recorded data 1 Copyright c  2011 by ASME