面向EMD分解的径流分量重构方法对比研究

水文序列非平稳与非线性的复杂变化导致水文序列中长期预测的准确性备受质疑。"分解-预测-重构"模式作为一种新的有效的预测思路近年来备受业界和学者关注。但受到高频分量预测误差大、趋势走向不确定等问题困扰,这种模式在发展过程中仍有诸多需要改进的地方。其中,径流分量的重构方法是控制高频分量误差,提高整体预测精度的关键性措施,其优劣对预测效果实现有着重要的意义。基于经验模态分解(EMD)和自回归模型(AR)建立"分解-预测"耦合模型,结合粒子群优化(PSO)算法,提出PSO重构系数优化法和高频分量剔除+重构系数优化法两种重构方法,结合前人提出的高频分量剔除法,以陕北丁家沟站、关中华县站、陕南白河站为算例,对不同重构方法的效果进行对比研究。研究结果表明:基于高频分量剔除法、PSO重构系数优化法、高频分量剔除+重构系数优化法三种重构方法的预测效果均较好,五项误差评价指标均优于标准重构法,三种重构方法均可不同程度地提高预测精度。对比研究发现:高频分量剔除法在重构过程中剔除了最不稳定且最难预测的高频分量,提高了预测精度,但提升效果有限;PSO重构系数优化法对所有径流分量赋予优化重构系数并重构,可最大程度地实现分量间的平差,有效提高了预测精度;高频分量剔除+重构系数优化法综合上述两种方法的优势,取得了比其他方法更好的预测效果。

Comparison among reconstruction methods for empirical mode decomposition components in runoff prediction

The accuracy of mid- and long-term forecast on hydrological time series is highly questioned due to the non-stationary and nonlinear complex changes of the series. The "Decomposition - Prediction - Reconstruction" model, as a new and effective forecasting method, has captured the attention of many scholars in related fields in recent years. But troubled by large errors in high-frequency component prediction, uncertain trend and other issues, this model still requires a lot of improvements in the development process. Among all the improvements, reconstruction of runoff component is intensely crucial in controlling high-frequency component prediction error and improving prediction accuracy of the hydrological series. To do this, the "Decomposition - Prediction" hybrid model was established in this paper using empirical mode decomposition (EMD) and autoregressive model (AR). Two reconstruction methods were proposed based on the particle swarm optimization (PSO) algorithm, which were the PSO-based reconstruction coefficient optimization method and the high-frequency component removal & reconstruction coefficient optimization method. These two methods plus the previous high-frequency component removal method were used to compare the efficacy of hydrological forecasting in a case study on Dingjiagou station in northern Shaanxi, Huaxian station in middle Shaanxi and Baihe station in southern Shaanxi. The results showed that the high-frequency component removal method, PSO-based reconstruction coefficient optimization method and high-frequency component removal & reconstruction coefficient optimization method all predict better than the standard reconstruction method, as reflected by five error evaluation indicators. Thus it can be drawn that these three reconstruction methods can improve the prediction accuracy in different degrees. High-frequency component removal method emphasizes removing the high-frequency component, which is the most unstable and unpredictable, so as to enhance the prediction accuracy, but only by a limited margin due to the simple removal process. PSO-based reconstruction coefficient optimization method is to optimize the reconstruction coefficients of all runoff components and to reconstruct the forecasted series. It can reduce errors during components reconstruction to the greatest extent and improve the prediction accuracy effectively. High-frequency component removal & reconstruction coefficient optimization method combines the above two methods and predicts better than all the other methods.