Using the fuzzy inference system to model the ionosphere total electron content in IRAN

Ionosphere is a layer in the upper part of the atmosphere wide-ranging from 60 km to 2000 km. It has a very significant role in radio wave propagation because of its electromagnetic attributes. Ionosphere is mainly affected by solar zenith angle and solar activity. In the day-time, ionization in ionosphere is at the highest level and the ionospheric effects are stronger. In the night-time, ionization decreases and the effects of ionosphere gets weaker. One of the most important parameters that defines the physical structure of ionosphere is Total Electron Content (TEC). TEC is a line integral of electron density along signal path between satellite to the receiver on the ground. The unit of TEC is TECU and 1 TECU equals 1016 electrons/m2. The TEC values can be computed from dual frequency Global Positioning System (GPS) stations, which are the most available observations for studying the Earth’s ionosphere. However, because of scattered repartition of dual frequency of GPS stations, precise information on TEC over the favorable region is unknown.
   Fuzzy inference systems (FIS) take inputs and process them based on the pre-specified rules to produce the outputs. Both the inputs and outputs are real values, whereas the internal processing is based on fuzzy rules and fuzzy arithmetic. FIS is the key unit of a fuzzy logic system having decision making as its primary work. It uses the “IF…THEN” rules along with connectors “OR” or “AND” for drawing essential decision rules. A FIS is defined according to the following five main sections:
•   Rule Base − It contains fuzzy IF-THEN rules;
•   Database − It defines the membership functions of fuzzy sets used in fuzzy rules;
•   Decision-making Unit − It performs operation on rules;
•   Fuzzification Interface Unit − It converts the crisp quantities into fuzzy quantities; and
•   Defuzzification Interface Unit − It converts the fuzzy quantities into crisp quantities.
   In this paper, the TEC of the ionosphere is modeled using FIS. The fuzzy inference system uses the rules IF-THEN to recognize the characteristics of dynamic phenomena. This feature, along with the simplicity of computing, has made it possible for this model to study the temporal and spatial variations of the ionosphere. In fact, the main innovation of the paper is the time series modeling of TEC in Iran using FIS. Hybrid particle swarm optimization training (BP-PSO) algorithm is used to train fuzzy network. This algorithm uses the PSO in the early stages of searching for solution and uses the back propagation (BP) near the optimal solution. From the observations of 2015, the Tehran GPS station, which is one of the IGS global stations, was used for evaluation of the proposed model. Also, the results were compared with the results of the global ionosphere map (GIM) TEC as well as artificial neural network model (ANN). In order to evaluate the accuracy of the fuzzy model presented in this paper, 5 days of each season were selected as the test data and model validation was performed in these 20 days. Based on the results, the average relative error calculated in the 20 test days for FIS, ANN and GIM models compared to GPS were 11.25%, 19.68% and 16.03%, respectively. Besides, the average absolute error calculated for FIS, ANN and GIM models compared to GPS in the 20 test days was 1.32 TECU, 3.33 TECU and 1.98 TECU, respectively. The calculated correlation coefficients between TEC obtained from FIS, ANN and GIM compared to GPS were 0.9474, 0.6960 and 0.831, respectively. The results of the analysis show that the FIS model is superior to the ANN and GIM models. Using the proposed model of this research, the time series of the ionosphere TEC can be modeled and investigated with high accuracy. This model can also be a good alternative to the outputs of the IGS network in Iran.