基于经验模态分解的非平稳水文序列预测研究

A modified method for non-stationary hydrological time series forecasting based on empirical mode decomposition

在全球气候变化和人类活动影响下,降雨和径流过程的非平稳特征日趋显化,如何通过有效的方法提高预测精度,准确地预测非平稳时间序列变化,为管理者提供决策支持至关重要。经验模态分解(EMD)是"分解—预测—重构"预测模式中的重要方法之一,通过其与径向基神经网络(RBF)的耦合,构建了改进RBF预测方法,研究了"分解—预测—重构"预测模式对渭河流域降雨(弱趋势)和径流(强趋势)两种非平稳时间序列的预测效果,总结了"分解—预测—重构"模式的适应范围。同时,针对重构过程中高频分量误差偏大的问题,提出了误差控制的改进措施。计算结果显示,RBF神经网络对具有弱趋势的非平稳时间序列(降雨)可获得比较满意的预测效果,平均相对误差为11%,是否分解预测对其预测精度影响不大;而对具有强趋势的非平稳时间序列(径流),RBF神经网络模型的预测效果并不理想,平均相对误差达到54%,而经过分解—预测—重构处理后,平均相对误差可降至30%,基本满足中长期水文预测精度要求。且若实施误差控制,平均相对误差可再减小2%。研究表明,"分解—预测—重构"的处理方法适用于具有强趋势变化的非平稳时间序列,其特点在于可有效分离时间序列中的周期和趋势变化成分,预测中使不同成分得到有效外延。同时,这种处理思路与径流序列基于物理驱动机制的普遍认识较为相符,更有利于开展有关水文过程的扩展性分析。误差控制方法在径流预测中能有效降低高频分量预测误差对整体预测效果的影响,可为其他类似的非平稳时间序列预测提供借鉴。

Influenced by global climate change and human activities, the processes of rainfall and runoff show non-stationary characteristics that are increasingly remarkable. To provide necessary and useful decision making information, it is crutial to improve forecasting accuracy of the future changes in hydrological time series using more effective methods. Empirical mode decomposition（EMD） is a key technique of the decomposition-prediction-reconstruction approach. This paper decribes a modified radial basis function（RBF） prediction model that integrates EMD and the RBF neural network. Using this model, we have examined the efficiencies of such an approach in prediction of two non-stationary time series for the Wei River basin, a precipitation series showing weak-trend changes, and a runoff series showing strong-trend changes, and compared our modfied RBF method with the original RBF. In addition, a new measure was adopted to reduce errors in prediction of high-frequency components decomposed by EMD. The results show that for weak-trend precipitation series, RBF gave a satisfactory prediction with a mean relative error of 11% and the modified RBF behaved similar. For strong-trend runoff series, the modified RBF was better, reducing the errors from 54% to 30%. This error can be decreased further by 2% if using error control measures. The comparison shows that the modified RBF method is applicable to nonstationary time series featured with strong-trend changes and it can easily decompose a time series into random, periodic and trend components and extrapolate each of them effectively. But beyond that, error control measures improve the efficiency of a prediction approach and can be used as a general technique for non-stationary time series forecasting.