灰色欧拉优化模型及其应用

An optimized grey Euler model and its applications

针对一类具有近似幂函数特征的序列建模预测问题,通过引入非齐次欧拉方程,提出一种优化的灰色欧拉模型.对该模型的建模机理、参数估计和时间响应式等进行研究,讨论以误差平方和最小为目标,对灰色欧拉模型的初始点进行优化,研究灰色欧拉模型的3种基本形式和3种优化形式.该模型能很好地拟合幂函数特征的序列,拓展灰色预测理论的体系,扩大灰色预测理论的应用范围.最后,利用中国能源消费量和幂函数拟合两个实例来测试模型的有效性,结果表明,所提出的新模型具有更好的拟合和预测精度.

Aiming at solving the predicting problems for the power function series,the grey Euler model(GEM(1,1))with grey action optimization is proposed by introducing the nonhomogeneous Euler equation.The modeling mechanism,parameter estimation and the time response function are studied.The initial point of GEM(1,1)is optimized with the minimum of the square sum of the error as the target.And further studies on three basic forms and three optimized forms of the GEM(1,1)model are also discussed.Researches show that the OSGEM(1,1)model can fit the series of power function characteristics well,which expands the system of gray prediction theory and the application scope of gray prediction theory.Finally,in the case studies,the natural gas consumption of China and the fitting of the power function series data are adopted to test the effectiveness of this model,and the good results obtained show the effectiveness and practicality of the proposed optimization model.