Abstract: Water demand forecast is the foundation of rational allocation and effective manage for regional water resources. Commonly，there are mainly various methods for water demand forecasting in urban，for example，quota，grey theory，artificial neural network and so on. Various forecasting methods have their own advantages and disadvantages. It is not ideal for traditional prediction method to predict accurately，such as the gray theory. However，artificial neural network model has the advantages of strong generalization ability and stable algorithm. The present study shows that no matter what kind of model，the result of prediction is described by using a single numerical points，which represent the future time requirement water，ignoring the water randomness and uncertainty of model. It is difficult to calculate the accurate water in the future，because the water system in urban is complex，which consist of various factors. Therefore，in this paper，Radial Basis Function （RBF） and Back-Propagation （BP） neural network prediction model are developed to simulate and forecast water demand in Xi’an City，Shaanxi Province，China as an example，where is the semi-arid region in the northwest China and has the serious contradiction between supply and demand. Six key factors which related to water demand are inputs for both models，and water demand is outputs. 20 groups of data from 1990-2009 are used for training the networks and three groups of data from 2010-2012 are used for testing. The results show that the root mean square error （RMSE） of RBF and BP are 0.223 and 0.206 respectively in the period of 1990-2009，and 0.08 and 0.26 for those in the period of 2010-2012. The relative errors of RBF are all less than 5%，while the maximum relative error of BP is more than 10%. It makes clear that the simulation and prediction results of RBF neural network are more accurate than those of BP. Furthermore，the evaluation index （d-factor） and confidence intervals are calculated to measure and compare the uncertainty related to the outputs of the two models. The results show that the d-factor is 0.74 and 1.02 for RBF and BP separately which means the RBF model has less uncertainty than the BP model. Based on the results of simulation and forecasting，the 95% confidence interval is applied for analyzing the reliability of results，which can make the result in the special range change and provide the reliable water demand variation range in different situations. It is important significance for water resources management of Xi'an to get reference information from this method. 搜索 #oXBr5L4gjSTips { Z-INDEX: 999999999; POSITION: absolute; WIDTH: 56px; HEIGHT: 24px; LEFT: 1342177.27em } #oXBr5L4gjSTips A { POSITION: relative; LINE-HEIGHT: 24px; MARGIN: -32px 0px 0px; PADDING-LEFT: 23px; WIDTH: auto; DISPLAY: block; BACKGROUND: url(http://mat1.gtimg.com/www/sogou/sogou_tips_v1.png) no-repeat 0px 0px; HEIGHT: 24px; COLOR: #000; FONT-SIZE: 12px; TEXT-DECORATION: none } #oXBr5L4gjSTips A:hover { BACKGROUND-POSITION: 0px -34px; COLOR: #45a1ea }

Key words: water demand, RBF neural network, BP neural network, uncertainty analysis, Xi’an City