• 关键词：灰色模型  马尔柯夫模型  预测  富营养化

• 基金项目：国家自然科学基金资助项目(No.50778009)

• 邹志红
• 北京航空航天大学经济管理学院, 北京 100083

• 王乐娟
• 北京航空航天大学经济管理学院, 北京 100083

• 摘要：根据水质时间序列具有趋势性和波动性的特点,将灰色马尔柯夫模型应用于太湖、滇池、巢湖三大湖泊水质富营养化趋势预测,其预测值可看成趋势项和随机波动项之和.预测过程如下:①用t检验准则判断并剔除序列中的异常数据,保证GM(1,1)模型精度;②建立GM(1,1)模型,对时序数据进行拟合,找出其变化趋势并建立趋势项;③根据最大残差划分状态空间,进行马尔柯夫预测,找出波动性规律并建立随机波动项.预测结果显示:太湖、滇池、巢湖预测结果的相对误差分别为3.59%、1.73%、2.20%,平均相对误差为2.50%,比单纯的灰色GM(1,1)模型降低了0.32%.

• Abstract：Because water quality time series have characteristic trends and fluctuations, the Gray Markov Model was used to forecast the eutrophication trend for three lakes: Tai Lake, Dian Lake and Chao Lake. The forecast value can be seen as the sum of the trend and fluctuation components. The main procedures of this approach include: ① abnormal data are identified and removed using t-test criteria; ② the GM(1,1) model is built and trend items established through finding the various trends; ③ state space is divided according to the maximum error and fluctuation items are established using the Markov forecast. The forecast results show: the relative errors of the three lakes are 3.59%, 1.73% and 2.20%. The average relative error is 2.50%, which is 0.32% lower than the pure GM(1,1) model.

• Key words：GM(1,1) Model  Markov Model  forecast  eutrophication

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