无偏灰色Verhulst模型及其应用

Unbiased grey Verhulst model and its application

针对灰色Verhulst模型自身所固有的偏差,提出了无偏灰色Verhulst模型.利用递推解法,给出两种初始条件下无偏灰色Verhulst模型的递推预测公式.结果表明,无偏灰色Verhulst模型对传统灰色Verhulst模型预测公式所表达的S型曲线进行模拟和预测具有完全重合性,完全消除了灰色Verhulst模型自身固有的偏差,也避免了以往建模方法由差分方程向微分方程的跳跃导致的误差.实例分析表明,无偏灰色Verhulst模型使得传统模型的模拟与预测精度得到了显著改善.

Abstract As to the inherent simulant error of grey Verhulst model, this paper presents unbiased grey Verhulst model. Recursive solutions are given under two initial conditions of the unbiased the model. The results show thatthe complete coincidence of the prediction and simulation to the original data of S-shaped curve generated form has achieved. The unbiased grey Verhulst model presented in this paper has completely eliminated the inherent simulant error of the traditional model,but also avoided the jumping errors from the differential equation to differential equation in traditional grey modeling. Case Analysis shows that the simulation and prediction accuracy in traditional modeling has been significant improved by unbiased grey Verhulst model. Keywords grey system; grey Verhulst model; recursive solution ; prediction