Bayesian Meta-Modeling of Engineering Design Simulations : A Sequential Approach with Adaptation to Irregularities in the Response Behavior

A Sequential Approach with Adaptation to Irregularities in the Response Behavior A. Farhang-Mehr S. Azarm Postdoctoral Research Associate Professor Department of Mechanical Engineering University of Maryland College Park, Maryland 20742 U.S.A. Abstract Among the current meta-modeling approaches, Bayesian-based interpolation models have received significant attention in the literature. A Bayesian model is valid for an entire range of design space. Also, a Bayesian model has the ability to adapt to the behavior of a response function and thus obtain a more accurate meta-model with a fewer number of experiments. However, the current adaptive methods in the literature are mainly based on the assumption that some variables are more important (or sensitive) than others and accordingly less sensitive variables can be weighted less or ignored. This dramatically limits the scope and applicability of these models since in many practical cases none of the variables can be ignored or weighted less than others for the entire range of design space. A more pragmatic model is one that identifies regions of the design space where more experiments are needed. In this paper, a new Bayesian meta-modeling approach is developed that designs and performs sets of experiments in a sequentially adaptive manner. In order to achieve the best possible meta-model, the approach adaptively utilizes the information obtained from previous experiments, builds interim meta-models, and identifies “irregular” regions of the design space in which more experiments are needed. The behavior of the interim meta-model is then quantified as a spatial function and incorporated into the next stage of the design to sequentially improve the accuracy of the obtained meta-model. The performance of the meta-modeling approach is demonstrated using numerical and engineering examples. 1 Corresponding authorphone: (301)405-5250, fax: (301)314-9477, e-mail: azarm@umd.edu

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