Approximated optimal design using local polynominal regression

Abstract

In this paper, local polynominal regression is proposed as a metamodel for the optimal design. Local polynominal regression is often used for smoothing. Smoothing and approximation are applied for the different purpose, however these two methods are based on the similar theory. Therefore local polynominal regression is forecasted to be able to approximate functions. So the theory of local polynominal regression is extended to multivariate predictors for optimal design, and its effectiveness for approximation is verified. Next, more suitable optimization method that uses characteristics of local polynominal regression is suggested. Additionally, the comparison of local polynominal regression and other metamodels shows its features. As a result of the consideration, next four points are clarified. (l)LOESS that uses local quadratic regression and tricube weight function is most suitable for the approximation. (2)The metamodels based on local polynominal regression are able to use for the structural optimization and its characteristics are available for the optimization based on the gradient. (3)The accuracy of local polynominal regression is better than Kriging and RBF interpolation when the sample size is small. However, the property is reversed when the sample size is large. (4)The accuracy of local polynominal regression is better than Kriging and RBF interpolation when the response has noises. The fact shows local polynominal regression is suitable for the metamodel of montecarlo simulations and experiments. © 2012 The Japan Society of Mechanical Engineers.