基于加权灰色-马尔可夫链模型的城市需水预测

城市需水量预测是区域水资源规划及优化配置的基础内容。在基于灰色GM(1,1)模型预测城市需水量总体趋势的基础上,引入加权马尔可夫链预测理论,建立了加权灰色马尔可夫GM(1,1)预测模型。该模型既考虑了GM(1,1)模型较强的处理单调数列的特性,又考虑了通过相对误差的状态转移概率矩阵的变换提取数据随机波动响应的特点。成都市城市需水量预测结果表明:加权灰色马尔可夫GM(1,1)模型充分利用需水量数据给予的信息,实现了对相对误差的状态转移的预测,并提高了修正灰色模型预测值的精度;通过与其它2种灰色预测模型预测结果比较,加权灰色马尔可夫GM(1,1)模型精度更高,预测得到2012年和2013年成都市城市需水量分别为74 250.91万m3和79 818.34万m3,呈明显增长趋势。因此该模型提高了随机波动较大数据序列的预测精度,拓宽了传统灰色模型预测的应用范围,更具科学性。

Prediction of Urban Water Demand by Using Weighted Grey-Markov Chain Model

Forecast of urban water demand is a basic content of optimal allocation and planning for regional water re-sources.On the basis of gray GM(1,1)model of trend prediction,the weighted Markov chain prediction method is introduced to establish a weighted grey Markov GM(1,1 )model for predicting urban water demand.This model combines the feature of dealing with numbers of strong monotonous series with the feature of random wave response in extracting relative residuals through state transfer probability matrix.The model is applied to the prediction of ur-ban water demand in Chengdu city and the result indicates that the weighted grey Markov GM(1,1)model makes full use of the information given by urban water demand sequence and forecasts the transfer regularity of relative re-siduals sequence among system states,by which it enhances the precision correcting value of grey model prediction. Furthermore we compared this model with other two grey models and the prediction result suggests that the weighted gray Markov GM(1,1)model has higher accuracy.The urban water demand forecast in 2012 and 2013 is 742. 5091 million m3 and 798.1834 million m3 in Chengdu city respectively,presenting a significant increasing trend. Therefore this model improves the accuracy when dealing with stochastic fluctuating data,and broadens the applica-tion scope of grey model prediction and makes it more scientific.