基于残差灰色-马尔可夫链的生活用水量预测研究

Study on Prediction of Domestic Water Consumption Based on Residual Grey Markov Chain Model

针对传统GM(1,1)模型在用水量预测方面对非增长序列预测精度差、出现过拟合等问题,采用结合马尔可夫链修正的残差灰色模型预测生活用水量。首先在传统灰色理论预测的基础上,建立了改进残差灰色预测模型:对残差绝对值建立灰色模型,再结合马尔可夫状态转移矩阵判断残差预测值在t>n时的正负号,对灰色预测值进行修正。将模型运用于河南省2007—2018年生活用水量预测,结果表明,传统灰色预测模型与改进残差灰色预测模型的平均相对误差分别为4.14%、2.04%,改进残差灰色预测模型的精度等级为"良";同时,改进后模型的后验方差也小于传统模型。这表明改进模型比传统灰色预测模型有更高的精度,拥有更好的可靠性,可以为用水量预测提供新的方法。

Aiming at the problems of traditional GM(1,1)model in forecasting non-growth sequences in terms of water consumption,such as poor precision and over-fitting,a residual grey prediction model corrected with Markov chains is used to predict domestic water consumption.Based on the traditional grey prediction model,this paper firstly establishes an improved residual grey prediction model as follows:establish grey model on the absolute residual,and judge the sign of the predictive residual when t>n based on Markov state transition matrix to correct the predictive value from grey model,and then apply the model to the prediction of domestic water consumption in Henan Province from 2007 to 2018.The results show that the average relative error of the traditional grey prediction model is 4.14%,while that of the improved residual grey prediction model is only 2.04%.The precision class of improved residual grey prediction model is"good",meanwhile,the posterior variance of improved model is also smaller than that of the traditional model,which indicating that the improved model has higher precision and better reliability than the traditional grey prediction model,therefore,it is a new method for water consumption prediction.