3. Available Data for Training ANN and Tests

[20]  The work of the realized method was demonstrated on the 2-month (February-March 2002) database of the half-an-hour values of the ionospheric critical frequency f_oF2 (f _cr ) of the F2 layer (the data are taken from http://www.wdc.rl.ac.uk) for the vertical sounding station Slough (England). The values of PSW, IMF, and magnetic activity indices were taken at http://www.nssdc.gsfc.nasa.gov. A special packet Neural Network Toolbox (which is an applied mathematical expansion of the MATLAB 6 system) was used to realize the ANN method. Currently it is the most powerful universal system of computer mathematics [Dyakonov, 2001; Dyakonov and Kruglov, 2001].

[21]  To train the chosen AAN, the data for February-March 2002 were used. They are a sequences of f _cr (t), f _cr (t) (with the seasonal effect eliminated), d f _cr (t)/dt, DI (ionospheric disturbance, i.e., the difference between the observed and mean values of the critical frequency), intensity of the X-ray radiation, solar wind velocity V and particle concentration N, magnitude of IMF and its z component in the SE coordinate system, Dst and Kp indices of geomagnetic activity, and PC index (index of magnetic activity in the polar cusps). On the whole, more than 2000 values of each parameter with the discreteness of 30 min were used.

[22]  Moreover, to look for valid training, multitude physically background combinations of input sequences were realized. It was necessary to clarify: how the general efficiency of the forecast would depend on an addition of different parameters and what delay time of the PSW and IMF parameters is most acceptable. In each case series of numerical experiments for the forecasts for 1, 2, 3, 12, and 24 hours were performed with experimental search for the best combination from the time sequences available. Evidently, attraction of all parameters together is not rational, because an extra loading of the neuron network leads to an increase of the adaptation time to new data and to a long training. Thus a particular goal was formulated: to determine a limited set of the input databases such that the attraction of these sets would provide a high quality of the forecasting in each time interval.

[23]  The training of the networks was performed using 1661 values (of each input parameter). The forecasting provided obtaining at the ANN output of the values f _cr (t+D t ), where D t is the time to which the forecasting was performed: 1 hour in advance, 2 hours in advance, and so on for 830 values.

[24]  The objective evaluation of the forecast quality was performed computing the so-called forecasting efficiency value PE [Barkhatov et al., 2000]:

where T^m is an aim (really registered) value for the comparison with the output for the m th example in the input sequence, O^m is the value of the m th output of ANN for the m th example of the input sequence, T is the averaged over all aim values of the ANN output, and N is the number of the points of the aim process. Thus the prediction efficiency is understood as the unit reduced by the value of the mean relative variation, the latter being a ratio of the standard deviation to the dispersion of the aim process.

[25]  The forecast accuracy was estimated also calculating the classical correlation coefficient R between the real and forecasted values of the critical frequency. Moreover, in each numerical simulation a half-an-hour correlation coefficient was calculated over the used time interval. The dynamics of the coefficient made it possible to evaluate the reliability of the forecast during the day. The solution of the problem in question involved a search for a valid training multitude of values and their physically reasonable combinations. The main goal of the study was to confirm the correctness of the physical basis for the choice of the algorithm and architecture of AAN and to create a satisfactory for our aims network with the least possible number of connections. The latter makes it possible to exclude the "remembering" effect and make the forecasting process more intellectual.