Response surface approximations for structural optimization

Response surface methodology can be used to construct global and midrange approximations to functions in structural optimization. Since structural optimization requires expensive function evaluations, it is important to construct accurate function approximations so that rapid convergence may be achieved. In this paper techniques to nd the region of interest containing the optimal design, and techniques for nding more accurate approximations are reviewed and investigated. Aspects considered are experimental design techniques, the selection of the `bestʹ regression equation, intermediate response functions and the location and size of the region of interest. Standard examples in structural optimization are used to show that the accuracy is largely dependent on the choice of the approximating function with its associated subregion size, while the selection of a larger number of points is not necessarily cost-e ective. In a further attempt to improve e ciency, di erent regression models were investigated. The results indicate that the use of the two methods investigated does not signi cantly improve the results. Finding an accurate global approximation is challenging, and su cient accuracy could only be achieved in the example problems by considering a smaller region of the design space.