Construction of stochastic simulation metamodels with segmented polynomials

Abstract

Metamodels are an important tool in simulation analysis as they can provide insight about the behavior of the simulation response. Modeling the response with low-degree polynomial segments allows the identification of different behavior zones and the parameters still have relation with the physical world. The purpose of this paper is to extend the use of segmented polynomial functions for simulation metamodeling, where the segments have at most identical value and slope at the breaks. Our approach is to build segmented polynomials metamodels where the hypothesis of degree and continuity of splines are less exigent, allowing more flexibility of the approximation. When breaks are known, constrained least squares are used for metamodel estimation, taking into account the linear formulation of the problem. If breaks have to be estimated, the unconstrained nonlinear regression theory is used, when it can be applied. Otherwise, the estimation is performed using an iterative algorithm which is applied repeatedly in a cyclic manner for estimating the breaks, and jackknifing yields the confidence intervals.