E. Altuntas [1], Y. Tulunay [1], M. Messerotti [2], E. Tulunay [3], M. Molinaro [2], Zeynep Kocabas [1] 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 1 Solar Event Forecasting via ANN [1] METU/ODTÜ Dept. of Aerospace Eng., 06531, Ankara, Turkey [2] INAF Astronomical Observatory of Trieste, Trieste, Italy [3] METU/ODTÜ Dept. of Elect. And Electrn. Eng., 06531, Ankara, Turkey

10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 2 Objective To forecast the maximum flux values of the solar radio bursts. To design a fuzzy inference system (FIS) Ultimate Goal to forecast the radio burtst by using a Recurrent Fuzzy Neural Network (RFNN) provided representative data become available.

Introduction (1) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 3 Mathematical modeling of highly non-linear and time varying processes is difficult or impossible. Data driven modeling methods are used in parallel with mathematical modeling Demonstrated by the authors and others that the data driven NN modeling is very promising (Tulunay, Y., 2004 and references there in).

Introduction (2) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 4 NN and fuzzy systems are motivated by imitating human reasoning processes. NN have been used extensively in modeling real problems with nonlinear characteristics.

Introduction (3) The main advantages of using NNs are their flexibility and ability to model nonlinear relationships. Unlike other classical large scale dynamic systems, the uniform rate of convergence toward a steady state of NN is essentially independent of the number of neurons in the network (Özkök, 2005; Tulunay, E., 1991). 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 5

Introduction (4) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 6 Due to the rapid growth around the world in wireless communications at GHz frequencies, studies of solar noise levels at such freq. have become popular. (Lanzerotti, 2002)

Introduction (5) We started by using the GOES SXR flux data of 2003 and 2004 to train the METU-NN to forecast the number of occurence of large X-ray bursts (events) in specific time-intervals (Tulunay et al., 2005). 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 7

Introduction (6) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria : EA, visited INAF Astr. Obs. of Trieste on a COST 724 STSM MHz (11 cm) Events are typically related to, i. SXR flares, and ii. proxies of EUV enhancement, The data of interest: Trieste Solar Radio System (TSRS) data at 2695 MHz (1 June 2003 – 31 May 2004); (sunrise – sunset)

TRSR Data (1) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 9 Fig 1 A typical Solar Radio Data Record with an event

TRSR Data (2) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 10 Fig 2 Solar Radio Data Record During Halloween Storm

Event Definition (1) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria Consider 1 day long record of data btween sunrise and sunset. 2. Smooth the data by 3 pt. moving averages. 3. Calculate logarithmic gradient (lngrad) (Criterion 1)

Event Definition (2i) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria Calculate the ratio for each successive data points 5. Are (Cr 1&2) are both satisfied? Note: t = t cr1&2 6. Check 10 min. past of the data. (Cr 2)

Event Definition (2ii) Are data non-eventlike? Then event start time: t cr1&2 (-10 min) Event ends when any; |lngrad(i) – lngrad(i-1)| < 0.01 assumes this condition for at least 20 minutes

Event Definition (3) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 15 Fig 3 Logarithmic Gradient During an Event

Event Definition (4) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 16 Fig 4 Ratio during an Event

Events number of record < 360 number of events = 20 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 17

Events (1) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 18 Fig 5 Daily Variation of the flux values observed on the day of the event maxima UT (h:min)

Events (2) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 19 Fig 7 Diurnal variation of the flux values observed at the time of event maxima

Events (3) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 20 Fig 6-a Maximum Flux vs. Sunspot and Kp index

Events (4) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 21 Fig 6-b Maximum Flux vs. Sunspot and Kp index

Fuzzy Inference Model Model, rules: fuzzy clustering (c-means) Each datum belongs to a cluster of some degree that is specified by a membership grade 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 22

C-means Clustering (1) Data points are assigned membership grades between 0 and 1. the membership matrix (U) is randomly initialized according to; 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 23

C-means Clustering (2) The dissimilarity function which is used in FCM is; 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 24 Where;  u ij is between 0 and 1;  c i is the centroid of cluster i;  d ij is the Euclidian distance between i th centroid(c i ) and j th data point;  m є [1,∞] is a weighting exponent.

C-means Clustering (3) To reach a minimum of dissimilarity function there are two conditions; 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 25 and

C-means Clustering (4) Detailed algorithm of fuzzy c-means proposed by Bezdek in 1973; 1. Randomly initialize the membership matrix (U) that has constraints 2. Calculate centroids (c i ) 3. Compute dissimilarity between centroids and data points 4. Stop if its improvement over previous iteration is below a threshold 5. Compute a new U, go to step 2 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 26

Training the model Inputs to the model 1. Solar sunspot number, 2. Planetary 3h-Kp Index 3. Hour of Event 4. Day of Event Output 1. Maximum flux value of an Event 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 27

Training The fuzzy model is trained for better performance using a training routine for Sugeno-type fuzzy inference systems (FIS) Training method applies a combination of the least- squares method and the backpropagation gradient descent method for training FIS membership function parameters to emulate a given training data set 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 28

Fuzzy Model 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 29 Fig 8 Sugeno Type Fuzzy Model Employed

Membership Functions 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria Gaussian type membership functions are used for the inputs 1. Linear membership function is used for the output 2. Weighted average defuzzification method is used 3. Clustering produces 3 clusters for each input and output;

Membership Func. (1) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 31

Membership Func. (2) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 32

Membership Func. (3) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 33

Membership Func. (4) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 34

Fuzzy Rules 3 Fuzzy rules are obtained during training; 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 35

Surface Plots of Fuzzy Rules (1) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 36

Surface Plots of Fuzzy Rules (2) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 37

Surface Plots of Fuzzy Rules (3) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 38

Operating the Model 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 39 Inputs to the model for a specified period of time 1. Solar sunspot number, 2. Planetary 3h-Kp Index 3. Hour of Day 4. Day of Year Output 1. Maximum flux value

Results (1) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 40

Results (2) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 41

Scatter Plot 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 42 R = 0.81 H S

Note the Halloween and Superstorm Effect Fuzzy model creates a cluster for the high flux events Halloween 2003 (H) and November 2003 Superstorm (S) events. As a result model performs very well for this kinds of events Excluding these events from the error calculation produces higher error values 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 43

Scatter Plot (H&S Excluded) 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 44 R = 0.71

Performace Number of Events Number of Clusters R Performance (normalized error %) Comments Model can get better The model is succesful The model memorizes 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 45 Table 1 Performance Table

Conclusions 1. Fuzzy model can be improved if more representative data available, 2. RFNN is planned for future work 10/1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 46

References Altuntas E., Messerotti M., Tulunay Y., Molinaro M., Neural Network Modeling in Forecasting the Near Earth Space Parameters: Forecasting of Solar Radio Bursts (“Events”), COST724 STSM Report Bezdec J.C., Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, Bezdec J.C., Fuzzy Mathemathics in Pattern Classification, PhD Thesis, Applied Math. Center, Cornell University, Ithaca, Jang J.-S. R., Sun C.-T., Mizutani E., Neuro-Fuzzy and Soft Computing, pp , Prentice Hall, 1997 Lanzerotti L. J., Gary D. E., Thomson D. J., Maclennan C. G., Solar Radio Burst Event (6 April 2001) and Noise in Wireless Communications Systems, Bell Labs Technical Journal 7(1), pp , Tulunay Y., Messerotti M., Senalp E.T., Tulunay E., Molinaro M., Ozkok, Y.I., Yapici T., Altuntas E., Cavus N., Neural Network Modeling in Forecasting the Near Earth Space Parameters: Forecasting of the Solar Radio Fluxes, COST 724 MCM, Oct. 2005, Athens. Tulunay Y., Tulunay E., Senalp E.T., The Neural Network Technique - 1: A General Exposition, Adv. 284 Space Res., 33, pp. 983–987, /1/2015 COST 724 9th MCM, May, Sofia, Bulgaria 47