e. altuntas [1], y. tulunay [1], m. messerotti [2], e. tulunay [3], m. molinaro [2], zeynep kocabas...

E. Altuntas[1], Y. Tulunay[1], M. Messerotti[2], E. Tulunay[3], M.

Molinaro[2],Zeynep Kocabas[1]

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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

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Objective

To forecast the maximum flux values of the solar radio bursts.

To design a fuzzy inference system (FIS)

Ultimate Goalto forecast the radio burtst by using a

Recurrent Fuzzy Neural Network (RFNN) provided representative data become available.

Introduction (1)

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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)

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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).

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Introduction (4)

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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).

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Introduction (6)

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2006 : EA, visited INAF Astr. Obs. of Trieste on a COST 724 STSM.

2695 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)

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Fig 1 A typical Solar Radio Data Record with an event

TRSR Data (2)

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Fig 2 Solar Radio Data Record During Halloween Storm

Event Definition (1)

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1. 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)

0.12

11 11

ii

i

i

i

nn

ndt

dn

n(Criterion 1)

Event Definition (2i)

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4. Calculate the ratio for each successive data points

5. Are (Cr 1&2) are both satisfied? Note: t = tcr1&2

6. Check 10 min. past of the data.

4.11

i

i

n

n(Cr 2)

Event Definition (2ii)

Are data non-eventlike?

Then event start time: tcr1&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)

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Fig 3 Logarithmic Gradient During an Event

Event Definition (4)

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Fig 4 Ratio during an Event

Events

number of record < 360

number of events = 20

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Events (1)

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Fig 5 Daily Variation of the flux values observed on the day of the event maxima

UT (h:min)

Events (2)

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Fig 7 Diurnal variation of the flux values observed at the time of event maxima

Events (3)

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Fig 6-a Maximum Flux vs. Sunspot and Kp index

Events (4)

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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

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C-means Clustering (1)

Data points are assigned membership grades between 0 and 1.

the membership matrix (U) is randomly initialized according to;

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c

iij nju

1

,...,1,1

C-means Clustering (2)

The dissimilarity function which is used in FCM is;

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c

i

n

jij

mij

c

iic duJcccUJ

1 1

2

121 ),...,,,(

Where;

uij is between 0 and 1;

ci is the centroid of cluster i;

dij is the Euclidian distance between ith centroid(ci) and jth data point;

m є [1,∞] is a weighting exponent.

C-means Clustering (3)

To reach a minimum of dissimilarity function there are two conditions;

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n

j

mij

n

j jmij

iu

xuc

1

1

c

k

m

kj

ij

ij

d

du

1

)1/(2

1and

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 (ci)

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

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Training the model

Inputs to the model

1. Solar sunspot number,2. Planetary 3h-Kp Index3. Hour of Event4. Day of Event

Output

1. Maximum flux value of an Event

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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

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Fuzzy Model

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Fig 8 Sugeno Type Fuzzy Model Employed

Membership Functions

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1. 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)

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Membership Func. (2)

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Membership Func. (3)

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Membership Func. (4)

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Fuzzy Rules

3 Fuzzy rules are obtained during training;

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Surface Plots of Fuzzy Rules (1)

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Surface Plots of Fuzzy Rules(2)

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Surface Plots of Fuzzy Rules(3)

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Operating the Model

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Inputs to the model for a specified period of time

1. Solar sunspot number,2. Planetary 3h-Kp Index3. Hour of Day4. Day of Year

Output

1. Maximum flux value

Results (1)

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Results (2)

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Scatter Plot

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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

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Scatter Plot (H&S Excluded)

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R = 0.71

Performace

Number of

Events

Number of Clusters

R

Performance

(normalized error %)

Comments

20

2 0.56 39 Model can get better

3 0.81 30 The model is succesful

5 0.99 0.04 The model memorizes

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Table 1 Performance Table

Conclusions

1. Fuzzy model can be improved if more representative data available,

2. RFNN is planned for future work

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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, 1981.

Bezdec J.C., Fuzzy Mathemathics in Pattern Classification, PhD Thesis, Applied Math. Center, Cornell University, Ithaca, 1973.

Jang J.-S. R., Sun C.-T., Mizutani E., Neuro-Fuzzy and Soft Computing, pp. 426-427, 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 159-163, 2002.

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, 10-13 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, 2004.

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