基于分形理论的城市日用水量预测方法

Prediction Method of Urban Daily Water Consumption Based on Fractional Theory

针对城市日用水量呈现周期性和自相似性的特点,通过对分形理论的研究,提出了基于分形拼贴定理和分形插值函数迭代过程的城市日用水量预测方法.该方法根据分形拼贴定理,由基于仿射变换的分形插值方法求取一个与历史日用水量记录相近的迭代函数系,建立分形预测模型,对城市日用水量进行预测.首先根据日用水量具有以周为周期的特点,应用相似日拟合模型对日用水量进行预测,平均预测误差为2.06%;然后根据日用水量具有以月为周期的特点对日用水量进行预测,平均预测误差为2.94%.应用表明,该方法实用性强,能够为城市供水优化调度提供决策支持.

Considering the periodicity and self-similarity, a method, which is based on fractional theory, for predicting urban daily water consumption was proposed. The fractal interpolation based on fractional collage theory was applied to determine the iterated function system, whose attractor was similar with the historical data, and according to this iterated function system, the fractal predicting model was set up. Firstly, the daily similarity fitting model was used to predict the daily water consumption based on its weekly periodicity, and the resulting average prediction error was 2.06%.Secondly, the same model was used to predict the daily water consumption based on its monthly periodicity, and the resulting average prediction error was 2.94%,. The results of practical application indicate that the method is of high practicality and can serve as the decision making support for optimization operation in urban water supply system.