基于时频分析的LSTM组合模型径流预测

doi:10.12118/j.issn.1000–6060.2021.06.18

摘要/Abstract

摘要：

针对变化环境下径流时间序列复杂的非线性、非平稳性特征,为提高中长期径流预测的准确性,运用多种时频分析方法构建组合预报模型以探究适用性。以干旱区典型内陆河玛纳斯河为例,利用经验模态分解（EMD）、变分模态分解（VMD）、离散小波变换（DWT）时频分析方法对径流时间序列进行多尺度分解,得到不同频率和特征的子序列。以前期径流、降水量、气温、大气环流因子等作为长短期记忆神经网络模型（LSTM）的输入变量,采用随机森林法和Pearson相关系数法确定各子序列的最佳预报因子,基于时频分析方法分别构建EMD-LSTM、VMD-LSTM、DWT-LSTM组合预报模型,通过LSTM模型对各子序列进行预测,加和重构获得最终预测结果,并与单一的误差反向传播神经网络（BP）、极限学习机（ELM）、LSTM模型的预测结果进行对比分析。结果表明：组合模型VMD-LSTM预报误差最小、精度最高,纳什系数保持在0.9以上,有效避免了过拟合等问题,其径流极值预测误差在15%以内,对径流总体趋势预测和极值的追踪均有良好效果。研究结果可为流域水资源规划与调度提供参考。

关键词: 径流预测, 组合模型, 时频分析, 长短期记忆神经网络

Abstract:

This study investigated the complex nonlinear and nonstationary characteristics of runoff time series in a changing environment. We obtained accurate and reliable runoff prediction results by constructing long-short term memory (LSTM) combination models on the basis of time frequency analysis methods. The combination models were then applied to the Manas River, Xinjiang, China, a typical inland river in an arid area. Empirical mode decomposition (EMD), variational mode decomposition (VMD), and discrete wavelet transform (DWT) were first applied to decompose the original runoff series into several subsequences with different frequencies and characteristics. Second, we used the previous runoff, precipitation, temperature, and atmospheric circulation factors as the input variables of the LSTM model. At the same time, the optimal predictor of each subsequence was determined according to random forest classification and the Pearson correlation coefficient. Finally, the combined models were based on a combination of VMD, EMD, and DWT with LSTM. Accordingly, they were called VMD-LSTM, EMD-LSTM, and DWT-LSTM and are proposed and applied for runoff forecasting. The total output of all submodules was treated as the final forecasting result for the original runoff. A single back propagation neural network, a single extreme learning machine, and a single LSTM were adopted as comparative forecast models. The results indicated that the VMD-LSTM model had the best forecasting performance among all the models in terms of its Nash-Sutcliffe error (NSE=0.930), root mean square error (RMSE=0.385), and coefficient of determination (R²=0.940). The extreme value prediction error for the runoff of the VMD-LSTM model was within 15%, and it had a good effect on the overall trend prediction and extreme value tracking regarding the runoff. This result further verified the accuracy and stability of the VMD-LSTM model. On the basis of the above results, the accuracy and stability of the VMD-LSTM model were further verified. Thus, on the basis of sequence decomposition, considering the influence of predictors on subsequences can help promote accurate and stable prediction results. These research results will provide a reference for river basin water resource planning and dispatching.

Key words: runoff prediction, combination model, time-frequency analysis, long short-term memory

蔡文静,陈伏龙,何朝飞,骆成彦,龙爱华. 基于时频分析的LSTM组合模型径流预测[J]. 干旱区地理, 2021, 44(6): 1696-1706.

CAI Wenjing,CHEN Fulong,HE Chaofei,LUO Chengyan,LONG Aihua. Runoff prediction with LSTM-based combination model on time-frequency analysis[J]. Arid Land Geography, 2021, 44(6): 1696-1706.

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分解方法	时间序列	大气环流因子（滞时月数）
	原始径流序列	G（0）、Q（0）、R（0）、D（0）、K（1）
EMD	IMF1	F（0）、F（3）、K（3）、C（10）、C（9）
	IMF2	K（1）、J（0）、J（6）、B（0）、L（6）
	IMF3	E（2）、M（6）、M（7）、E（1）、N（1）
	IMF4	O（0）、O（1）、P（0）、P（1）、N（0）
	IMF5	P（0）、P（1）、P（2）、P（3）、P（5）
	IMF6	P（0）、P（1）、N（10）、N（0）、N（1）
	R	F（0）、F（1）、F（6）、F（7）、Q（0）
VMD	IMF1	A（0）、A（1）、A（2）、A（6）、A（7）
	IMF2	B（2）、B（8）、C（1）、D（7）、E（8）
	IMF3	F（0）、F（3）、F（6）、F（9）、G（0）
	IMF4	F（0）、F（4）、F（6）、F（8）、F（10）
	IMF5	F（0）、F（3）、F（6）、F（9）、B（5）
	IMF6	F（0）、F（1）、F（6）、F（7）、B（8）
	IMF7	H（3）、I（0）、J（2）、D（0）、E（6）
DWT	A3	L（0）、S（10）、S（7）、C（10）、O（10）
	D1	J（1）、F（0）、F（9）、Q（0）、D（1）
	D2	F（0）、F（10）、F（9）、F（7）、Q（9）
	D3	J（0）、J（1）、K（6）、C（0）、E（0）

模型名称	训练期			验证期
模型名称	RMSE	NSE	R²	RMSE	NSE	R²
BP	0.514	0.833	0.845	0.637	0.808	0.865
ELM	0.486	0.851	0.856	0.576	0.843	0.872
LSTM	0.406	0.896	0.902	0.505	0.879	0.884
EMD-LSTM	0.307	0.940	0.941	0.457	0.901	0.906
VMD-LSTM	0.328	0.932	0.935	0.385	0.930	0.940
DWT-LSTM	0.444	0.876	0.900	0.463	0.898	0.901

组合模型	训练期			验证期
组合模型	RMSE	NSE	R²	RMSE	NSE	R²
EMD-LSTM	0.353→0.307	0.923→0.940	0.925→0.941	0.483→0.457	0.890→0.901	0.896→0.906
VMD-LSTM	0.337→0.328	0.929→0.932	0.923→0.935	0.448→0.385	0.905→0.930	0.907→0.940
DWT-LSTM	0.484→0.444	0.853→0.876	0.862→0.900	0.499→0.463	0.884→0.898	0.899→0.901