偏最小二乘与灰色模型组合预测城市生活需水量

Urban Domestic Water Demand Forecasting by Combining Partial Least Squares Regression and Grey Model

为了克服普通多元回归方法用于中长期预测时自变量多重共线性对拟合模型的干扰,引入了更易于辩识系统信息与噪声的单因变量偏最小二乘回归(PLS1),同时将两次拟合等维灰数递补(DEMGM(1,1))模型用于自变量的中长期预测,建立了一套PLS1与DEMGM(1,1)组合预测方法.采用1986年—2000年某市生活用水量历史数据对该方法进行验证,预测结果表明,平均相对误差仅为1.03%.将该方法引入城市生活需水量研究,预测2005年和2010年某市生活需水量将分别达到0.92×109m3与1.1×109m3,为该市给水工程规划与决策提供了参考依据。

In order to eliminate the bad impact of serious multi collinearity among independent variables, this paper described a model of simple partial least squares regression(PLS1)in medium and long term forecasting . It is an effective method to distinguish the system information from the noisy datum. At the same time, double-fit equi-dimensional grey number progressive complement model(DEMGM(1,1)) was used to forecast depen-(dent) variables. A forecasting method was built by combining PLS1 and DEMGM(1,1). The combined method was validated by using the data of domestic water demand in a certain city from 1986 to 2000, and the result shows that the average relative error is just 1.03%. Furthermore, the method was applied to forecast the domestic water demand in this city. As a result, domestic water demand of this city is 0.92 billion m^3 in 2005 and 1.10 billion m^3 in 2010. All these lay the foundation for water supply engineering planning and decision-making in this city.