[关键词]
[摘要]
以往的预测模型对数据长度有较强的依赖性,且数据出现较强的非线性时,将增加预测的复杂程度。为使监测数据呈现出一定的线性关系,基于分形理论,将常维分形改进为变维分形,并据此建立相应的数学模型,通过短期监测数据进行预测。考虑到变维分形得到的预测结果不可避免地存在一定的波动误差,对此,利用马尔科夫链(Markov)无后效性的特点对预测结果进行修正,从而提高预测精度。以西溪水库的监测资料数据为样本,建立其马尔科夫链-变维分形预测模型,结果显示最大误差修正值可达0.89%,占原预测误差的67.9%,表明利用马尔科夫链修正的变维分形模型能有效地减小误差,提高预测精度。
[Key word]
[Abstract]
Previous forecast models have strong dependence on the length of the data, and the data often appears strong nonlinear. Both of these will increase the complexity of the prediction. So in order to make the monitoring data to show a certain linear relationship, this paper changed constant dimension fractal method to variable dimension fractal method to predict short-term monitoring data based on fractal theory short-term monitoring data. The corresponding mathematical model was set up. However, inevitably, there were some fluctuation errors in the results predicted by the variable dimension fractal method. This paper used the Markov chain to modify these predicted results based on the characteristic of no aftereffect. The results analyzed by Xixi reservoir monitoring data showed that the revised error could be optimized by 0.89%. Obviously, it could be concluded that the variable dimension fractal method modified by Markov chain could effectively reduce error and improve the precision of prediction.
[中图分类号]
[基金项目]
水利部公益性行业专项(201401022);南京水利科学研究院中央级公益性基本科研业务费专项(Y715012, Y715018)