基于黄金分割法的聚合物熔体黏度模型数据拟合

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

注塑成型加工过程数值模拟广泛使用聚合物熔体的黏度模型,其数据拟合是一项重要工作。为降低传统迭代算法对初值的严苛要求,消除迭代过程中可能出现的病态矩阵现象,提出基于黄金分割法的拟合算法。拟合采用直接搜索法,不需要对目标函数进行求导运算。搜索过程分轮次进行,每一轮搜索在一组正交的可行方向上依次进行。在每一个可行方向上,利用黄金分割法在一个参数区间内进行一维非线性搜索。搜索区间的持续缩小,以及目标函数值的非增性,保证了算法的收敛性。以当前最优点为中心的搜索方法有利于发现更优的极小点,从而提高拟合精度。此外,针对Cross-Arrhenius黏度模型,给出一套简洁的初值计算公式,可为该模型的各种拟合算法提供合适的初值。算例表明,算法适用的初值范围广,拟合精度高于阻尼Newton法和遗传算法,而且能对其他算法的拟合结果进行二次优化。算例的计算机用时仅需数秒即可。

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 microcomouter for this examnle.