A Prediction Model of Ionospheric f_oF₂ Based on Extreme Learning Machine

Abstract

The highly nonlinear variation of the ionospheric F 2 layer critical frequency (f o F 2 ) greatly limits the efficiency of communications, radar, and navigation systems that employ high-frequency radio waves. This paper proposes an effective method to predict the f o F 2 using the extreme learning machine (ELM). Compared with the previous neural network model based on feedforward algorithm, the ELM model offers the advantages of faster training speed and less manual intervention. The ELM model is trained with the daily hourly values of f o F 2 at Darwin (12.4°S, 131.5°E) in Australia. The training data are selected from 1995 to 2012, except 1997 and 2000, which includes all periods of quiet and disturbed geomagnetic conditions. The f o F 2 data to verify model performance are selected in 1997, 2000, and 2013, which are low, high, and moderate solar activity years, respectively. The prediction results have shown that the proposed ELM model can achieve faster training process while maintaining the similar accuracy compared with BPNN. In addition, the proposed ELM model is compared with the International Reference Ionosphere model prediction. The ELM model predicts the f o F 2 values more accurately than the International Reference Ionosphere model in low (1997), moderate (2013), and high (2000) solar activity years, as clearly seen on the yearly root-mean-square error. As far as the author's knowledge, this is the first time that the ELM model is applied to predict f o F 2 .Plain Language Summary The spatiotemporal variability of the ionospheric F 2 layer critical frequency (f o F 2 ) affects the efficiency of communications, radar, and navigation systems that employ high-frequency radio waves. Therefore, many researchers have established different kinds of models to predict the changes in f o F 2 based on historical data. However, these studies only focus on how to improve the prediction accuracy of the model. In fact, for a predictive model, it is also crucial to increase the training speed of the model on the premise of ensuring prediction accuracy, especially when dealing with a large amount of data (such as f o F 2 data). For this reason, a modeling method using extreme learning machine (ELM) for the prediction of f o F 2 is proposed in this paper. This proposed method has fast learning speed and good generalization performance. The results show that the proposed method provides a successful prediction of the f o F 2 . Compared with the International Reference Ionosphere model, the average prediction accuracy has increased by 34%. Compared with the backward propagation neural network, the ELM model accelerates the model training speed by 61 times while maintaining the similar predicting accuracy. In summary, the modeling method using ELM for the prediction of the f o F 2 provides a new idea for the modeling problems of the ionospheric parameters.

Modeling of the Ionospheric Critical Frequency of the F2 layer over Asia based on Modified Temporal‐Spatial Reconstruction

“…Compared with other expansion methods, the modeling approach not only reduces the number of modeling parameters but also reduces the computation time (Zhang et al, 2009). In particular, the mathematical procedure involved in empirical orthogonal function transforms a dataset into a number of uncorrelated orthogonal principal components (Bai et al, 2018;Liu et al, 2004), which well suits the prediction of f o F 2 . The empirical orthogonal function is therefore introduced to our modeling.…”

“…Moreover, the Asia-Oceania method and its modified version were proposed to describe the monthly median values of f o F 2 and M3000F2, which apply well to the Asia and Oceania region (Cao & Sun, 2009;Yan et al, 2011). Oyeyemi et al (2005Oyeyemi et al ( , 2007; Oyeyemi and McKinnell (2008) and Bai et al (2018) used a neural network and extreme learning machine to develop new models of F 2 layer parameters. Another way of predicting critical frequency (Ercha et al, 2011), peak height (Zhang et al, 2009;Zhang et al, 2010;Zhang et al, 2012), Propagation factor of 3,000 km (Liu et al, 2008;Zhang et al, 2010), total electron content (Ercha et al, 2012 ), and other parameters are based on empirical orthogonal function.…”

Forecasting Ionospheric foF2 Using Bidirectional LSTM and Attention Mechanism

“…However, the NN models which are mainly based on gradient descent are generally very slow due to improper learning steps or may easily converge to local minimums (Huang et al., 2004). To overcome the disadvantage of the NN models, the extreme learning machine model is used to predict the ionospheric foF2, which can reduce training time, especially with large sets (Bai et al., 2018).…”

An Ionospheric TEC Forecasting Model Based on a CNN-LSTM-Attention Mechanism Neural Network

“…The prediction of ionospheric TEC is necessary to indicate adverse space weather conditions for initiating necessary measures in GNSS applications. Significant research studies were carried out to evaluate the utility of using different neural networks to investigate the ionospheric parameters forecasting [2][3][4][5][6][7][8][9][10][11][12][13]. Francis et al [3] performed ionospheric parameter prediction and provided a technique to fill in missing data points, while minimizing the impact on data dynamics.…”