二阶非齐次序列的直接离散模型及灰色预测应用

本文不要白化微分方程和一次累加序列参与建模，提出了二阶非齐次序列的直接离散模型，研究了此模型的模拟预测公式及其性质.经实例验证该模型有可操作性，且有较高的模拟预测精度，同时由该模型递推形式的模拟预测公式出发，采用降阶（二阶降为一阶），化齐次（非齐次转化为齐次）等方法推导出了通项形式的模拟预测公式.该公式直观展示了适用本模型的序列基本形式：指数型序列、线性型序列、抛物线型序列、三次曲线型序列四类基本序列及两个不同底数的指数序列与线性序列三者的和差组合、一个指数序列与抛物线型序列的和差组合、一个指数序列与线性型序列的和差组合、线性型序列与指数型序列的乘积组合序列再与另一线性型序列的和差组合四类组合序列.从理论上证明了当序列严格遵循这些基本形式时，本模型能实现完全模拟，从而近似遵循这些基本形式时，必然有较高的模拟预测精度.

Direct discrete model of second order non-homogeneous sequence and application of grey prediction

In this paper, the direct discrete model of the second order non-homogeneous sequence is proposed without involving in the modeling of the albino differential equation and the one-time accumulation sequence, the simulation prediction formula and its properties are studied. Examples show that the model is operable and has a high accuracy of simulation prediction. At the same time, starting from the recursive form of the model simulation prediction formula, the general term of the simulation prediction formula is derived by reducing the order (second order is reduced to first order), homogeneous (non-homogeneous is transformed to homogeneous) and other methods, the formula shows the intuitive apply basic forms: The sequence of the model with exponential sequence, linear and parabolic sequences, three curve type of four types of basic sequences and the index of two different base sequence and linear sequence and poor combination, an index sequence and combination of parabolic sequence and difference, an index sequence and linear sequence and poor combination, linear sequence and exponential sequence to the product of the combination with another type of linear sequence and poor combination of four types of combination sequence. It is proved theoretically that this model can realize complete simulation when the sequence strictly follows these basic forms, and thus has higher simulation prediction accuracy when these basic forms are approximately followed.