非等间距NGM(1,1,k)模型的改进算法及其应用

Improved Algorithm for Non-equidistant NGM (1, 1, k) Model and Its Applications

针对观测数据的非等间距性以及NGM (1, 1, k)模型建立的不足,本文构建了灰作用量优化的非等间距NGM (1, 1, k)模型.基于数值积分原理,推导出模型背景值改进算法的非等间距Simpson数值积分公式.然后利用原始数据序列的观测值与模拟值的相对误差平方和最小为目标,构建新的效用函数作为求解新模型的时间响应函数中的最优常数表达式,从而形成了完整的非等间距NGM (1, 1, k)模型的改进算法.最后,通过两个算例验证了所提出模型的有效性和实用性,表明了优化模型可以有效地提高预测精度.

According to the non-equidistance of observation data and the de?ciency of NGM(1, 1, k) model, a modeling approach for the grey action quantity with non-equidistant NGM(1, 1, k) model is established in this paper. A new model’s background value optimization method is proposed based on the principle of numerical integration by using non-equidistance Simpson numerical integration formula. Then the desirability function is construsted by the minimizing the square sum of relative error between the raw sequence and the simulative sequence, which is used to determine the optimal constant value in the time response function.Moreover, a complete improved algorithm for non-equidistance NGM(1, 1, k) model is proposed.Finally, the e?ciency and applicability of the proposed optimization model are demonstrated by two examples. The results show that the optimal model is able to signi?cantly improve the simulation and prediction accuracy.