On the Evaluation of Internal Optimizers and Correlation Functions in Kriging

Abstract

Response surfaces are being used to create meta-models of expensive computer experiments (such as CFD of FEM models). The response surfaces can then be used for optimization, or for design space exploration using combinations of responses extracted from the computer experiments. The method of Kriging uses the correlation between the response values to create a best unbiased linear predictor. Normally a function, such as the Gaussian or the Exponential function, is chosen as correlation function, and its variables then fitted to the data. This is done by finding the Maximum Likelihood Estimator (MLE). Finding the MLE means a separate optimization problem, one which can be non-trivial. Several techniques to find the MLE are evaluated, namely LFOPC (a gradient-based trajectory method), Dynamic-Q (a successive quadratic approximation method) and particle swarms. This is done for different correlation functions. Responses from analytical functions and Computational Fluid Dynamic (CFD) simulations of a Submerged Entry Nozzle (SEN) used in the continuous casting of steel are used. The different optimizers are compared according to the MLE, as well as the number of times Φ was calculated to find the optimum. In this comparison the number of times the MLE was calculated for different correlation functions looked at. 2. Keywords