A geomagnetic variation prediction method based on chaotic VMD-LSTM neural network
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摘要:
针对地磁变化场的非平稳性、非线性以及物理模型难以预测的特点，提出了一种改进的长短期记忆网络预测方法并进行了验证。首先应用变分模态分解方法对地磁台站数据进行去噪，再根据地磁变化的混沌特性引入混沌理论对样本集进行优化，最终以长短期记忆网络预测地磁变化并对改进前后的方法进行了对比。结果显示，优化方法的预测效果较稳定，平均绝对误差小于2 nT，相关指数R2超过0.8，预测值与实测值的拟合度较高，有效预测时长可达2.5天，且在中国大陆的泛用性较好。
Abstract:In view of the nonstationarity and nonlinearity of geomagnetic variation field and the difficulty of physical model prediction, an improved LSTM （long short-term memory） neural network prediction method is proposed and verified by tests. Firstly, the variational mode decomposition （VMD） method is used to denoise the geomagnetic data, and then the chaos theory is introduced to optimize the sample set according to the chaotic characteristics of geomagnetic variation. Finally, the LSTM network is used to predict geomagnetic variation. The results show that the prediction of the optimized method is relatively stable, mean absolute error is less than 2 nT, correlative coefficient R2 is larger than 0.8, the predicted value is well consistent with the measured value, and the effective prediction time can reach 2.5 days, and it has good universality in Chinese Mainland.
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Keywords:
- variational mode decomposition /
- chaos theory /
- LSTM /
- geomagnetic variation
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图 1 长短期记忆网络的单元状态
h表示隐藏状态，C表示单元状态，x表示单元输入，ft为遗忘门，it为输入门，ot为输出门
Figure 1. LSTM unit state
h represents hidden state，C represents unitstate，x represents input，ft is forget gate，it is input gate，ot is otput gate
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图 2 基于广州肇庆站数据使用中心频率法求K值
Figure 2. Calculation of K based on data at Zhaoqing station in Guangzhou by using center frequency method
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图 4 不同分解层数下残余分量与去噪信号的相关系数
Figure 4. Correlation coefficient between residual components and denoised signals with different decomposition layers
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图 5 2020年3月6日肇庆站地磁数据的VMD去噪结果
Figure 5. Denoising results of geomagnetic data at Zhaoqing station on March 6，2020 by VMD
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图 6 自相关系数法确定时间延迟（a）和伪最近邻域法确定嵌入维数（b）
Figure 6. Autocorrelation coefficient method for determining time delay （a） and false nearest neighbor method for determining embedding dimension （b）
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图 7 六个模型的预测结果
（a） 单一LSTM；（b） VMD-LSTM；（c） 混沌优化LSTM；（d） 混沌VMD-LSTM；（e） 自回归差分移动平均模型；（f） 灰色模型
Figure 7. Prediction results of six models
（a） Single LSTM network；（b） VMD-LSTM；（c） Chaotic optimized LSTM network； （d） Chaotic VMD-LSTM；（e） Auto-regressive integrated moving average model；（f） Gray model
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图 8 各台站基于混沌VMD-LSTM方法的预测结果
Figure 8. Prediction results of each station based on the chaotic VMD-LSTM method
表 1 地磁变化预测评估
Table 1 Evaluation of geomagnetic variation prediction
预测方法 MAE/nT RMSE/nT MAPE R2 Ad_R2 RA 单一长短期记忆（LSTM） 6.945 0 9.592 8 0.154 0 0.622 7 0.837 4 0.984 6 VMD-LSTM 6.815 9 9.118 5 0.151 0 0.459 5 0.853 8 0.984 9 混沌优化LSTM 2.944 3 4.752 9 0.006 5 0.614 8 0.612 6 0.993 4 混沌VMD-LSTM 1.936 2 2.876 8 0.004 0 0.854 3 0.853 4 0.995 7 自回归差分移动平均模型 13.655 9 16.298 9 0.030 1 0.346 6 0.349 3 0.969 9 灰色模型 12.197 3 14.872 0 0.026 9 0.271 8 0.274 0 0.973 1 注： MAE为平均绝对误差，RMSE为均方根误差，MAPE为平均绝对百分比误差，R2为相关指数，Ad_R2为调整后的相关系数，RA为相对准确率，下同。 
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表 2 各台站预测评估误差
Table 2 Evaluation error of prediction results for several stations
台站 MAE/nT RMSE/nT MAPE R2 Ad_R2 RA 拉萨站（LAT） 1.705 1 2.714 7 0.002 4 0.802 2 0.801 0 0.997 5 漠河站（MHT） 1.256 3 1.628 6 0.009 9 0.465 6 0.462 4 0.990 0 郫县站（PXT） 1.499 9 2.184 0 0.005 3 0.905 2 0.904 7 0.994 7 十三陵站（SSL） 1.309 7 1.952 5 0.002 1 0.820 5 0.819 5 0.997 9
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