Forecasting of urban water demand based on combining Grey and BP neural network with Markov chain model | 基于灰色神经网络与马尔科夫链的城市需水量组合预测

Chinese. 针对城市需水量预测系统具有非线性和随机波动性的特点,建立基于马尔科夫链修正的组合灰色神经网络预测模型，以提高模型的预测精度。比较分析灰色GM(1,1)模型、BP神经网络模型以及二者线性组合的灰色神经网络预测模型的预测效果，建立基于马尔科夫链修正的组合灰色神经网络预测模型，并以榆林市2000-2009年的用水量实际数据为研究对象，通过实例比较分析模型的检验预测精度。经马尔科夫链修正处理后，建立的基于马尔科夫链修正的灰色神经网络组合模型的预测精度更高，预测误差的绝对值均小于4%，且均方差σ为1.00，小于组合灰色神经网络模型与GM(1,1)模型、BP神经网络模型预测误差值的均方差。基于马尔科夫链修正的组合灰色神经网络需水量预测模型，对城市需水量的预测优于灰色神经网络及各单项预测模型，不仅预测精度高，而且能同时反映出数据序列发展变化的总体趋势和系统各状态之间的内在规律，适合描述随机波动性较大的预测问题。

English. Because water demand forecast model is nonlinear and stochastic, a combination model based on Grey and BP neural network model corrected by Markov chain is established to improve accuracy. On the analysis of Grey GM(1, 1) model, BP neural network and the linear combination of these two methods, a prediction model based on Grey neural network and Markov chain model is set up. The water consumption of Yulin from 2000 to 2009 is used to verify this model and check its precision through some analysis. The result shows that Grey neural network model after Markov chain has higher precision, the absolute forecasting errors are all less than 4%, and its mean square errors of predicting error value is 1.00, less than the mean square errors of predicting error value of Grey GM (1, 1), BP neural network and combination of Grey GM and BP neural network. The Grey neural network and Markov chain model is better than Grey GM and BP neural network model and other 2 single models, which not only gives higher prediction but also shows the data sequence trend and the internal law between system states. This model suits for volatile random questions.