e. altuntas [1], y. tulunay [1], m. messerotti [2], e. tulunay [3], m. molinaro [2], zeynep kocabas...
TRANSCRIPT
E. Altuntas[1], Y. Tulunay[1], M. Messerotti[2], E. Tulunay[3], M.
Molinaro[2],Zeynep Kocabas[1]
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria1
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
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria2
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)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria3
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)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria4
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).
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria5
Introduction (4)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria6
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).
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria7
Introduction (6)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria8
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)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria9
Fig 1 A typical Solar Radio Data Record with an event
TRSR Data (2)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria10
Fig 2 Solar Radio Data Record During Halloween Storm
Event Definition (1)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria11
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)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria12
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)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria15
Fig 3 Logarithmic Gradient During an Event
Event Definition (4)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria16
Fig 4 Ratio during an Event
Events
number of record < 360
number of events = 20
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria17
Events (1)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria18
Fig 5 Daily Variation of the flux values observed on the day of the event maxima
UT (h:min)
Events (2)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria19
Fig 7 Diurnal variation of the flux values observed at the time of event maxima
Events (3)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria20
Fig 6-a Maximum Flux vs. Sunspot and Kp index
Events (4)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria21
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
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria22
C-means Clustering (1)
Data points are assigned membership grades between 0 and 1.
the membership matrix (U) is randomly initialized according to;
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria23
c
iij nju
1
,...,1,1
C-means Clustering (2)
The dissimilarity function which is used in FCM is;
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria24
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;
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria25
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
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria26
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
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria27
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
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria28
Fuzzy Model
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria29
Fig 8 Sugeno Type Fuzzy Model Employed
Membership Functions
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria30
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)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria31
Membership Func. (2)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria32
Membership Func. (3)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria33
Membership Func. (4)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria34
Fuzzy Rules
3 Fuzzy rules are obtained during training;
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria35
Surface Plots of Fuzzy Rules (1)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria36
Surface Plots of Fuzzy Rules(2)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria37
Surface Plots of Fuzzy Rules(3)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria38
Operating the Model
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria39
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)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria40
Results (2)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria41
Scatter Plot
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria42
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
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria43
Scatter Plot (H&S Excluded)
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria44
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
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria45
Table 1 Performance Table
Conclusions
1. Fuzzy model can be improved if more representative data available,
2. RFNN is planned for future work
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria46
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.
04/21/23COST 724 9th MCM, 21-25 May, Sofia, Bulgaria47