The Elman Neural Network Based on VMD for Short-Term Forecasting of Ionospheric foF2 in Sanya

An Elman neural network model based on variational mode decomposition (VMD) is established to realize the 1-h accurate forecasting of the critical frequency of the ionosphere F2 layer (foF2). The model processes foF2 time series data through the VMD algorithm, which can effectively avoid the influence of noise in foF2 data. Based on the 2014–2017 data of the Sanya station, the model achieves a high-precision forecasting 1 h advance only through the foF2 data. The forecasting results of foF2 show: In the diurnal variation, the forecasting value of the proposed model is consistent with the actual observation value, and the fluctuation is smaller than that of the Elman and backpropagation NN (BPNN) models. Under the seasonal time scale, the proposed model has the highest forecasting accuracy and the slightest variation in the four seasons. The RMSE on the test set is 0.50 MHz; the accuracy is 0.45 and 0.47 MHz higher than Elman and BPNN models. Moreover, the MAPE is only 6.77%, compared with Elman and BPNN models; the accuracy is increased by 5.62% and 6.46%. The above shows that the proposed VMD-Elman model has good applicability and can improve the accuracy of the foF2 short-term forecast.