基于灰色马尔科夫模型的天津市供水总量预测

Prediction of total water supply quantity of Tianjinbased on Grey Markov Model

为了解决GM(1,1)模型预测波动大序列精度低的问题,引入了马尔科夫链理论,通过对二者算法的合理结合,建立了灰色马尔科夫模型。将优化前后的灰色模型运用到天津市供水总量预测中,首先使用GM(1,1)模型拟合2001—2016年供水总量,在供水总量递增区间的相对误差在±5%以内,在供水总量波动区间的相对误差大于±5%。分别使用GM(1,1)模型、灰色马尔科夫模型预测2017年、2018年的供水总量,GM(1,1)模型预测的相对误差分别为-7.04%、-7.73%,灰色马尔科夫模型预测的相对误差分别为-3.99%、-4.70%。结果表明:灰色马尔科夫模型在一定程度上提高了对波动性较大序列的适应性,采用其预测天津市供水总量对该市水资源规划具有一定的指导意义。

To solve the issue of low accuracy of predicting the fluctuating large sequence by GM(1,1)model,the Markov Chain Theory was introduced and the Grey Markov Model was established by reasonable combination of the two algorithms.The grey model before and after optimization were applied to forecast the total water supply quantity of Tianjin City,the relative error of the GM(1,1)model fitting result was within±5%in the increasing range and greater than 5%in the total fluctuation range of the water supply quantity from the year of 2001 to 2016.For 2017 and 2018,the relative errors were-7.04%and-7.73%of the GM(1,1)model and-3.99%and-4.70%of the Gray Markov Model of respectively.The results showed that the Gray Markov Model improved the adaptability to the large fluctuation sequence,and using it to to predict the total water supply quantity in Tianjin had a certain guiding significance to the city′s water resources planning.