近似非齐次指数递减序列NGOM(1,1)模型的构建与优化

Modeling and optimizing the grey model NGOM(1,1) for the approximation non-homogenous decreasing series

针对一类具有近似非齐次指数特征的衰减序列建模预测问题,构建NGOM(1,1)模型,推导出其参数估计的最小二乘解与时间响应函数的表达式.鉴于背景值和初始条件对于该模型作用的复杂性和噪声扰动的不确定性,运用方程组的数据融合技术对背景值进行全局性优化,并利用平均相对误差平方和构建期望函数,实现模型优化目标函数和平均相对误差最小两个准则一致性条件下模型初始条件的最优选择.实例研究表明了所提出模型在处理衰减非齐次序列时具有较高的精度.

Aiming at solving the predicting problems for the decreasing non-homogenous series, the grey model NGOM（1,1） is proposed with the method of accumulated generating operation in opposite-direction. The parameters and time response function are estimated. For the background value and the initial condition have a great effect on the simulating and predicting accuracy of the grey model, the background value is optimized by using the equations, and the initial condition is modified by using the expectation function, which ensures the consistency between the two rules, namely, the minimum values of optimized objective function and the minimum average relative errors. The results of the case study show that the NGOM（1,1） model has better simulating accuracy compared to other optimized models, which demonstrates the effectiveness and practicability of the proposed model dealing with the decreasing non-homogeneous sequences.