Considerations of Accuracy and Uncertainty with Kriging Surrogate Models in Single-Objective Electromagnetic Design Optimization

The high computational cost of evaluating objective functions in electromagnetic optimal design problems necessitates the use of cost-effective techniques. This paper discusses the use of one popular technique, surrogate modelling, with emphasis placed on the importance of considering both the accuracy of, and uncertainty in, the surrogate model. After briefly reviewing how such considerations have been made in the single-objective optimization of electromagnetic devices, their use with kriging surrogate models is investigated. Traditionally, space-filling experimental designs are used to construct the initial kriging model, with the aim to maximize the accuracy of the initial surrogate model, from which the optimization search will start. Utility functions, which balance the predictions made by this model with its uncertainty, are often used to select the next point to be evaluated. In this paper, the performances of several different utility functions are examined using experimental designs which yield initial kriging models of varying degrees of accuracy. It is found that no advantage is necessarily achieved through searching for optima using utility functions on initial kriging models of higher accuracy, and that a reduction in the total number of objective function evaluations may be achieved by starting the iterative optimization search earlier with utility functions on kriging models of lower accuracy. The implications for electromagnetic optimal design are discussed

The Meta-Model Approach for Simulation-based Design Optimization.

The design of products and processes makes increasing use of computer simulations for the prediction of its performance. These computer simulations are considerably cheaper than their physical equivalent. Finding the optimal design has therefore become a possibility. One approach for finding the optimal design using computer simulations is the meta-model approach, which approximates the behaviour of the computer simulation outcome using a limited number of time-consuming computer simulations. This thesis contains four main contributions, which are illustrated by industrial cases. First, a method is presented for the construction of an experimental design for computer simulations when the design space is restricted by many (nonlinear) constraints. The second contribution is a new approach for the approximation of the simulation outcome. This approximation method is particularly useful when the simulation model outcome reacts highly nonlinear to its inputs. Third, the meta-model based approach is extended to a robust optimization framework. Using this framework, many uncertainties can be taken into account, including uncertainty on the simulation model outcome. The fourth main contribution is the extension of the approach for use in integral design of many parts of complex systems.