Viscosity Model Data Fitting for Polymer Melt Based on Golden Section Method

Abstract

The viscosity models of polymer melts are adopted popularly in the numerical simulation of plastic injection molding.The data fitting to these models is an important task. Based on golden section method, a kind of fitting method is proposed in order to reduce the restriction on initial values and to eliminate ill-conditioned matrixes. A direct search strategy is applied, with which the derivatives of an objective function need not be calculated. The search process is executed by round, and each round of search is carried out following a group of orthogonal feasible directions in turn. Based on golden section method, a one-dimensional nonlinear search is performed at a parametric interval in each feafible direction, so that a group of stage optimal solutions are attained. The convergence of a search process is guaranteed by continuously shrinking of the intervals and nonincreasing of the objective function values. Better extreme points can be found more easily by this kind of search method that make a current optimal point as the center of a searching interval, and fitting precision is enhanced accordingly. Moreover, a set of simple functions for calculating initial values is supplied for Cross-Arrhenius model. These functions can be employed in all kinds of fitting algorithms to this model. The fitting example shows that this method allows a wide range of feasible initial values, and its fitting precision is higher than Damped Newton's Method and Genetic Algorithm. It can engage in second optimization to the results made by other fitting methods. This fitting process can be accomplished in several seconds with a microcomputer for this example.