函数变换法GM（1，1）灰色模型及其在污水排放预测中的应用

为克服传统的灰色动态GM（1，1）模型方法的不足之处，本文提出不需累加生成，累减生成，且适合于非等间距建模的相除法，分析相除法拟合数据误差产生的机理，建立标准差系数进行评价，标准差系数反映了原始数据的指数规律性，当原始数据的指数规律性较强时，拟合精度高，然后，相除法和标准差系数相结合，建立了GM（1，1）模型参数估计的函数变换法，相除法和函数变换法，不需要对原始数据进行预处理，不需要累加生成，累减生成，不仅适应于等间距建模，也适应于非等间距建模，实例表明，两种方法简单实用，值得在污水排放预测中推广使用。

Grey GM(1, 1) Model of Function-Transfer Method and Its Application in Forecast of Sewerage Drainage

In order to overcome these shortcomings of tradition method of establishing grey dynamic GM(1,1) model, the mutual division estimating model parameter was proposed. Data needs not be preprocessed and operation on accumulate plus generation and accumulate subtract generation needs not be done. It was suit not only for establishing model on equal interval but also for establishing model on differ interval. And it had the same accuracy as GM(1,1) on estimating parameter in accumulate plus generation. In the light of constructing a new number line, and then analyzing its criterion difference coefficient, at the time that fitting accuracy was high or low could be judged. Criterion difference coefficient reflected index law of original number line. If it was relatively strong, fitting forecasting accuracy was relatively high. On the contrary, it was low. Criterion difference coefficient could be effectively decreased in the method of function exchange. Further, the function transfer method of parameters estimation of GM(1,1) was established. The applied examples of mutual division and function transfer method were given. The practical results show that two methods are simple and feasible, and have extensive value.