基于复合辛普森公式的GM(1,1)模型背景值的优化

Optimization of background value in GM(1,1) model based on compound Simpson quadrature formula

背景值是导致GM(1,1)模型产生系统误差的主要原因之一,为提高模型的模拟效果和预测精度,根据灰色系统理论建模机理以及数据累加生成具有非齐次灰指数规律,构建灰色系统模型。基于GM(1,1)模型背景值的几何意义,结合复合辛普森求积公式和动态序列模型,提出一种新的GM(1,1)模型背景值优化方法。实例表明,基于复合辛普森公式的背景值优化算法所建立的GM(1,1)模型,可以有效地提高模型的预测精度和适用性。

The formula of background value is one of the main factors causing systematic error of GM(1,1) model. In order to improve the simulation results and prediction accuracy of the model, the grey system model was con?structed according to the grey system theory modeling mechanism and the data accumulated generating operation with non-homogeneous grey exponent. A new GM(1,1) model background value optimization method was proposed based on geometric meaning of GM(1,1) background value, and combining the compound Simpson quadrature for?mula and dynamic series model. In case study, the results show that GM(1,1) model based on the background val?ue optimization algorithm of the compound Simpson formula can effectively improve the accuracy and applicability.