优化BP与LSTM神经网络模型电离层TEC长短期预测

Optimizing BP and LSTM neural network model for long-term and short-term prediction of ionospheric TEC

  • 摘要: 电离层总电子含量(total electron content, TEC)对电波通信、卫星导航定位等领域都有着重要影响,因此,对其进行准确的预测至关重要. 针对电离层TEC难以有效预测的问题,基于深度学习方法,通过欧洲定轨中心(Center for Orbit Determination in Europe, CODE)分布的TEC网格模型全球电离层地图(global ionospheric map, GIM),利用后向传播(back propagation, BP)神经网络、K折交叉验证(K-fold cross validation KCV)-BP神经网络,遗传算法 (genetic algorithm, GA)-BP神经网络和长短时记忆(long short-term memory, LSTM)神经网络,结合滑动窗口策略,进行电离层TEC长短期预测,开展不同纬度区域、不同经度区域、不同太阳活动状态下电离层TEC的1 h短期预测和7~15 d长期预测,引入均方根误差(root mean square error, RMSE)、拟合优度R2、平均绝对百分误差(mean absolute percentage error, MAPE)指标评估不同模型预测的适用性. 研究结果表明:短期预测中,从不同模型来说,预测效果由高至低依次为GA-BP、LSTM、KCV-BP、BP和普通最小二乘(ordinary least squares, OLS),最优预测误差在1 TECU以内. 在长期预测中,OLS预测效果最好,特别是15 d优势明显,而GA-BP具有最优的长时效性,预测稳定性好. 通过MAPE指标说明南北半球对模型的预测适用性有明显差异. 最后,在评估模型对区域的适用性时,通过单一的RMSE来衡量具有片面性,需要综合使用R2、MAPE等综合指标来衡量.

     

    Abstract: The total electron content (TEC) of the ionosphere has a significant impact on fields such as radio communication and satellite navigation positioning, therefore, accurate prediction is crucial. In response to the problem of difficult effective prediction of ionospheric TEC, the research introduces deep learning methods and constructs ionospheric TEC prediction models based on back propagation (BP) neural network, K-fold cross validation (KCV)-BP neural network, genetic algorithm (GA)-BP neural network, and long short-term memory (LSTM) neural network using ionospheric TEC grid data (global ionospheric map (GIM)) provided by the Center for Orbit Determination in Europe (CODE). These models are used for 1 h short-term prediction and 7-15 d long-term prediction of ionospheric TEC in different latitude regions, different longitude regions and different solar activity period. Indicators such as root mean square error (RMSE), goodness of fit R2, mean absolute percentage error (MAPE) are introduced to evaluate prediction applicability of different models. Research has shown that in short-term forecasting, among different models, the prediction performance from high to low is GA-BP, LSTM, KCV-BP, BP, and ordinary least squares (OLS), and the optimal prediction error is within 1 TECU. In long-term forecasting, OLS has the best prediction performance, especially with a significant advantage at 15 d, while GA-BP has the best long-term timeliness and good prediction stability. The MAPE indicators demonstrate significant differences in the predictive applicability of the model between the northern and southern hemispheres. Finally, when evaluating the applicability of the model to the region, using a single RMSE to measure it is one-sided and requires the comprehensive use of indicators such as R2 and MAPE to measure it.

     

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