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针对GM(1,1)模型对原有数据信息利用不充分、模拟序列首项固定不符合最小二乘法要求两个问题,以原始序列与模拟序列差值平方和最小为条件,利用最小二乘法确定了GM(1,1)白化权函数的时间响应函数中的常数,构建了改进的GM(1,1)模型,并应用于宁波市用水量预测中。结果表明,改进的GM(1,1)模型预测精度大幅提高,具有较好的可行性和实用性,可用于预测城市未来用水量。
In order to solve the problem that the GM (1,1) model does not fully utilize the original data and the first fixed sequence does not meet the requirements of the least square method, the least square method is used to solve the problem that the sum of squares of the difference between the original sequence and the simulated sequence is the minimum. The constant in the GM (1,1) whitening weight function time response function was determined. An improved GM (1,1) model was constructed and applied to predict the water consumption in Ningbo. The results show that the improved prediction accuracy of GM (1,1) model is greatly improved, and it has good feasibility and practicability. It can be used to predict the future urban water consumption.