An Investigation of Metamodeling Techniques for Complex Systems Design
Debora Daniela Daberkow, Dimitri N. Mavris · 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization · 2002
In this paper, a new metamodel implementation process to be used in complex systems design, utilizing a Gaussian Process (GP) prediction method is formulated. It is based on a Bayesian probability and inference approach and as such assigns a probability distribution as a new prediction, rather than estimating a single value. This distribution is considered to be Gaussian, and the method returns a variance prediction along with the most likely value. Compared to other metamodeling techniques, it thus gives an estimate also for the confidence in its prediction, in addition to the value of the prediction itself. In this paper, the theory of this prediction via Bayesian regression is introduced, and the method is contrasted to other regression metamodeling techniques, such as Response Surface Equations (RSEs) and Neural Networks (NNs). An implementation process is formulated, making the GP method accessible for complex systems design, its applicability and appropriateness at the theoretical as well as practical level are investigated, and proof-of- concept implementations at the system level are provided. In addition to the capability of giving a confidence estimate, it also shows consistent improvements in the accuracy over a standard quadratic model RSE metamodel implementation.