ASME04.kriging - Proceedings of DETC04 ASME 2004...

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1 Copyright © 2004 by ASME Proceedings of DETC’04: ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference Salt Lake City, Utah USA, September 28 - October 2, 2004 DETC2004/DAC-57300 ON THE USE OF KRIGING MODELS TO APPROXIMATE DETERMINISTIC COMPUTER MODELS Jay D. Martin 1 Research Assistant Applied Research Laboratory State College, PA 16805 USA Timothy W. Simpson Associate Professor of Mechanical Engineering and Industrial Engineering The Pennsylvania State University University Park, PA 16802 USA ABSTRACT 1 The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models. KEYWORDS: Kriging, Metamodel, Maximum Likelihood Estimation, Cross-Validation, Metamodel Error Assessment 1 INTRODUCTION Kriging models have become a popular method for approximating deterministic computer models [1-7]. They have been used in a wide variety of applications including conceptual design [8], structural optimization [9], multidisciplinary design optimization [10], aerospace engineering [11], and mechanical engineering [12]. Kriging models offer a good choice for these types of applications due to their flexibility to approximate many different and complex response functions. They are also a good choice for approximating deterministic computer models since they interpolate the observed or known data points [13,14]. The widespread usage of kriging models appears to be 1 Please address all correspondences to this author: [email protected] . hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model (see Section 2.1), (2) a computationally efficient algorithm for estimating the model’s parameters (see Section 2.2), and (3) a method to effectively assess the resulting model’s quality (see Section 2.3). In this work we investigate these three aspects of using kriging models to approximate deterministic computer models and attempt to draw conclusion based upon the results of creating kriging models for six test problems: a 1-D, four 2-D, and one 5-D functions (see Section 3). For each test problem, many different
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

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ASME04.kriging - Proceedings of DETC04 ASME 2004...

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