基于PCA-RBF神经网络模型的城市用水量预测

摘要

针对城市用水量影响因素众多、关联性较强以及BP神经网络收敛速度慢、易陷入局部极小值等问题,采用组合主成分分析(PCA)与RBF神经网络的方法预测城市用水量.利用主成分分析对用水量影响因素进行降维,消除多重共线性,选取能够替代原用水量影响因素的前三个主成分作为输入因子,选用学习和收敛速度快、模式识别能力强的RBF神经网络进行预测.研究结果表明,该模型的相对误差平均值在训练和预测阶段均最小,分别为0.165 4％和0.677 5％,学习和预测能力均优于RBF和BP神经网络模型,提高了收敛速度和预测精度;主成分数量从3个增加到5个,信息量累积贡献率从93.09％增加到98.37％,平均相对误差从0.250 7％降至0.206 0％,预测精度略有提高.对2015-2020年枣庄市用水量进行预测,总用水量先有小幅上升,后又下降,呈现“倒U型”增长.该模型对城市区域水资源规划具有参考价值.%Aiming at the problems,such as many factors of influence on the urban water consumption,strong correlation and slow convergence speed of BP neural network,being prone to trapping in the local minima,etc.,the urban water consumption is predicted herein by means of combining the principal components analysis (PCA) with the RBF neural network;for which the dimension reduction is made on the factors of the influence on the water consumption for eliminating the multicollinearity,and then the former three principal components which can replace the original factors of the influence on the water consumption are selected as the input factors,while the RBF neural network with quick learning and convergence speed and strong capacity of mode identification is selected for the prediction.The study result shows that the mean relative errors of the model are minimum within the phases of the training and the prediction,which are 0.165 4％ and 0.677 5％ respectively,while both the earning and prediction capacities are better than those from the models of RBP and BP neural networks,thus enhance both the convergence speed and the prediction accuracy;from which the number of the principal components increases from 3 to 5 along with the increase of the contribution rate of information accumulation from 93.09％ to 98.37％ and the decreases of the mean relative error from 0.250 7％to 0.206 0％,thus the prediction accuracy is slightly enhanced.During the prediction made on the water consumption of Zaozhuang City from 2015 to 2020,the total water consumption therein is increased with small amplitude at first,and then is decreased,which shows an increase with the shape of inversed U.Generally,this model has reference value for the urban regional water resources planning concerned.