基于自相关的GM(1,1)与GM(1,N)联合模型优化及应用

Optimization of GM(1,1) and GM(1,N) based on self-correlation theory and its application

分析基于自相关理论的GM(1,1)与GM(1,N)联合模型,将仅适合GM(1,1)模型的数据拓展到适合GM(1,N)模型。用数值积分中的Simpson公式来重建GM(1,1)与GM(1,N)的联合模型,在参数辨识过程中引入累积法,降低线性方程组系数矩阵的条件数,使联合模型求解更加稳定,提高了模拟及预测精度,并且克服了原GM(1,N)模型必须获得预报时刻点相关数据列的值的缺陷,有利于新息GM(1,N)模型的应用。数值实验结果表明,优化后模型数值稳定性好,其系数矩阵的条件数在数值上比通用的最小二乘法有所降低,且模拟平均相对误差也有所降低,预测精度得到提高。

This paper made an analysis on the model uniting GM（1,1） and GM（1,N） based on self？correlation theory. The model expands the data only suitable for GM （1,1） model to make it suitable for GM （1,N） model. The united model of GM（1,1） and GM（1,N） was rebuilt using the Simpson formula in numerical integration. The introduction of cumulative method in parameter identification process reduces the condition number of the coefficient matrix in linear equations, which makes the solution to the united model more stable and improves the accuracy of simulation and prediction. This method also overcomes the limitation that GM （1,N） model must obtain the related column value of the prediction time point and promotes the application of the new information GM （ 1,N） model. Numerical experiment shows that the condition number of coefficient matrix computed by cumulative method is lower than that evaluated by the general least square method. Besides, the present method decreases the average relative error of simulation and improves the prediction accuracy.