灰色Verhulst模型背景值优化的建模方法研究

本文对传统灰色Verhulst模型背景值的误差来源进行分析,对模型的背景值进行优化,以期提高模型的模拟预测精度。基于灰色Verhulst模型时间响应式的Logistic函数形式,文章利用Logistic函数拟合模型中的一阶累加生成序列,经过一系列的数学推导,借助反向累加生成的思想,解出了Logistic函数中的三个参数,得到了灰色Verhulst模型背景值的优化公式,并建立了优化的灰色Verhulst模型。最后分别通过算例和应用实例验证本文的优化效果,结果表明,利用优化的背景值公式可以有效地提高传统灰色Verhulst模型的模拟预测精度。

The Research on the Modeling Method of Background Value Optimization in Grey Verhulst Model

In this study, the error sources of background value of traditional grey Verhulst model and optimizes the background value of the model are analyzed, in order to improve the simulation and prediction accuracy of the model. Based on the Logistic function structure of the time response formula in the grey Verhulst model, the Logistic function is used to fit the accumulated sequence, three parameters in Logistic function are solved through a series of mathematical derivation and the idea of accumulated generating operation in opposite direction, and then the optimal formula of background value of grey Verhulst model is got and the optimal grey Verhulst model is constructed. Finally, the optimization effect in this paper is verified by an example and an application example respectively. The result shows that it can effectively improve the simulation and prediction accuracy of the traditional grey Verhulst model to use the optimization background value.