基于背景值和初值优化的灰色Verhulst建模方法与应用

Grey Verhulst Model and Application Based on Background Value and Initial Value Optimization

针对灰色Verhulst模型的优化问题,提出从背景值和初值两个方面对灰色Verhulst模型进行优化,分别利用倒数变换和约束优化模型求解模型的背景值参数与初值参数,并给出基于背景值和初值优化的灰色Verhulst建模步骤,最后以案例验证了本文模型的有效性、适用性和优化效果。结果表明,利用背景值和初值的优化方法能够有效地提高Verhulst模型的模拟精度与预测精度。

With respect to the optimization problems of grey verhulst model,both elements of background value and initial value are considered to optimize the traditional grey verhulst model,and then the reciprocal transformation and optimization model without constraint are used respectively and constructed to acquire the parameters of the background value and initial value,thus the modeling steps of grey verhulst model based on background value and initial value optimization is given.Finally an example is exploited to validate the effectiveness,applicability and optimization effect of the proposed model.The results show that compared with the existing grey verhulst model the proposed model possesses much higher simulation and prediction precision by optimizing background value and initial value.