城市需水量的灰色非线性预测

Grey Nonlinear Forecasting of Metropolis Water Demand

应用灰色理论建立了连云港市年需水量的单变量一阶灰色预测模型，在分析其缺陷的基础，引入了使平均相对误差为最小的灰元，作方程的指数，从而建立起灰色非线性常微分方程模型，它弱化了模型以原始样本序列呈指数规律的要求，经误差分析表明它具有比单变量一介灰色预测模型更高的精度，适用范围更广，灰色非线性预测模型用于城市年需水量预测，其结果令人满意。

The grey model with GM(1,1) for forecasting yearly water demand of certain metropolis is set up according to the theory of grey system. Based on analysis of defects, a grey element  a is introduced as an exponent, which minimizes the average relative errors. The grey nonlinear differential equation model of G aM(1,1) weakens the requirement on data of sample series, which originally should be followed the exponential distribution. It is shown by error analysis that the accuracy of the model is better than that of GM(1,1) and its applicable range larger than the latter. When the G aM(1,1) model is used in forecasting the metropolis water demand, the results are satisfactory.