Prediction high frequency parameters based on neural network

Aiming at the shortcomings of the current high frequency communication frequency parameter prediction method, the frequency parameter prediction method based on Gated Recurrent Unit Recurrent Neural Networks (GRU RNN) is proposed. Through the analysis of the ionospheric parameter f0F2 data, the GRU can predict the f0F2 value by long-term memory of the historical data when processing the time series related data. Compared with other prediction methods, the error between the predicted value and the true value is only 2%. The research results show that the model to predict the f0F2 value in advance is feasible.

ICAMMT 2019 IOP Conf. Series: Materials Science and Engineering 631 (2019) 052035 IOP Publishing doi: 10.1088/1757-899X/631/5/052035 2 only consider the monthly law value change of f0F2.The law of f0F2 mid-month changes greatly at dawn and dusk, and the change of the adjacent days are not involved; at the same time, backpropagation neural networks have local minimization, slow convergence, gradient disappearance or explosion, which all cause interference to the final prediction effect and accuracy.
For the above problems, considering the relation between sequential data and the disappearance of gradient in back propagation, this paper proposes an improved approach of Gated Recurrent Unit (GRU) neural network to predict ionospheric parameters.

GRU model construction
Recurrent Neural Networks (RNN) is a widely used artificial neural network model, which is good at processing sequential data. The basic structure is composed of three parts: input layer, hidden layer and output layer. Its structure is shown in figure 1.Unlike traditional neural networks, RNN has "memorability", in which the loop in the hidden layer can transmit historical information backward, making the current moment closely related to historical information. Using this feature, RNN can process sequences composed of any moment. Neurons in RNN are connected by weight U between neurons, they form a loop to train sequence data and predict output. Different from traditional neural networks, each layer in RNN shares parameters W, U and V, which reduces the number of parameters to be learned in the network, but the input of each step is different. When new data is input, the information from time t-1 is calculated to become the output at the current moment, and each data sample is processed according to this process.  (1) and (2) .In the formula, W, U, V are the weight parameters, is the t step state of the hidden layer, it is the memory unit of the network, is the output of the t step, φ is the nonlinear activation function, and generally it is the tanh function.  Figure 2. The hidden layer structure of GRU The external structure of GRU is the same as the traditional RNN structure, with only the improvement of its hidden layer, which has the function of long-term memory of important historical information. In this way, when back propagating, the gradient will not disappear. Its hidden layer structure is shown in figure 2.The GRU network has only two gate structures: the update gate and the reset gate. Compared with other improved circular neural networks, GRU structure is simpler and faster. At time t, the input data and the hidden state transmitted from the previous moment are updated through the gate mechanism to obtain the hidden state and memory contents of the current moment. In this way, according to the weight parameters at each moment, how much information at the previous moment needs to be retained and transmitted can be determined. The mathematical description is as follows: We input data x and hidden state h −1 to get state r by the reset gate, as shown in (3).
We input data x and hidden state h −1 to get state z by the update gate, indicating how much of the previous hidden state information needs to be transferred to the current hidden state h , as shown in equation (4).
After that, the network determines the memory content of the current moment, that is, the important information of the previous moment is recorded, as shown in equation (5).
Finally, the network computes the information vector h to be passed to the next unit, as shown in equation (6).
After iterative calculation, the final output of the network is y , as shown in equation (7).
Through this algorithm, the problem of gradient disappearance or explosion in traditional neural network training is solved, and long-term learning of sequence data is realized. In this paper, the twolayer GRU network is used to predict the ionospheric parameters, with 64 neurons in each layer, which greatly reduces the training time. The input dimension of the first layer network is set as 1, the output dimension is 50, the input dimension of the second layer network is 50, and the activation functions of both layers are tanh functions. Finally, the network outputs a one-dimensional solution. MSE is used as loss function and RMSprop as optimization function to make the model converge as soon as possible. GRU network model is divided into training process and prediction process. Firstly, the program reads data and preprocesses the data, which is divided into test set and training set, and the training set is used to train the model. After training the model, start the prediction, and the results are compared with the real values in the test set to analyse the prediction effect.

Prediction of ionospheric parameters
The main factors which affect the selection of shortwave communication frequency are f0F2 and M(3000)F2 of the ionospheric parameters, and the variation law has nonlinear characteristics. In this regard, we use the actual observed data to train the GRU network to learn the optimal network parameters, and determine the prediction model. In order to verify the usability and prediction accuracy of the model, the simulation experiment uses the monthly median f0F2 data which measured in Beijing in January 2011. The data set has a total of 775 hours as shown in Figure 3. When the data is pre-processed, the missing data points are filled with the corresponding monthly average value. The first 80% of the total data is 620 hours as the training set, and the last 20% is 155 data as the test set, as shown in Table 1. First we normalize the data to enhance the stability of the data set and convert the data into a numpy array for use by the model. Secondly, we started to train the model, inputting 128 data each time, every 24 data as a sequence, and the number of iterations is 400 generations. Finally, after the training, the trained model is used to predict the results, and the predicted values and the true values in the test set are compared to test the accuracy of the model.

Simulation analysis
Footnotes should be avoided whenever possible. If required they should be used only for brief notes that do not fit conveniently into the text. The GRU neural network prediction results and real measured values are shown in Fig. 4. The vertical axis is the frequency value of the predicted sample in MHz, and the horizontal axis is the predicted time point in hours/h. It can be seen that the model has a good prediction effect, especially in the previous predictions and the change trend is well predicted at the position where the change is faster. It can be clearly seen that the shorter the prediction time is, the smaller the error is. On the contrary, the longer the prediction time is, the larger the relative error is, and the prediction value is less reliable.
The mean square error (MSE) between the predicted and actual values are used to describe the accuracy of the prediction, In order to reflect the advantages of the model, the f0F2 value is predicted by using GRU network, BP neural network and Fuzzy Wavelet Neural Network (FWN). By comparing the model complexity and precision, it is found that the two-layer GRU network model has higher prediction accuracy, faster convergence rate and better global convergence, which is superior to the other two models in all aspects. The parameters of models are shown in Table 2.

Conclusion
The deep learning algorithm is a breakthrough in the field of artificial neural networks. By combining low-level features to form more abstract high-level features, the data distribution characteristics are found, which show good prediction results in various data predictions. In order to predict the shortwave communication frequency, the researchers have proposed many prediction methods, this paper proposes to use the GRU network to construct the model to predict the ionospheric parameters, and use the f0F2 data to train and to test, and the experimental results verify the feasibility of the proposed method. The proposed method has the advantages of fast convergence and high prediction accuracy, and provides a new method for predicting short-wave frequencies.
Because many factors can change the ionospheric parameters, this paper does not summarize other factors. In this paper, the GRU model only predicts and verifies the change of median value f0F2, and the subsequent work needs to add more factors affecting the short-wave frequency and further improve the prediction accuracy of the model.