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Use of exogenous data to improve an artificial neural network dedicated to daily
global radiation forecasting C. Paoli*, C. Voyant**, M. Muselli*, M-L. Nivet*
Université de Corse - Pasquale PAOLI{christophe.paoli, cyril.voyant, marc.muselli, marie-laure.nivet}@univ-
corse.fr *CNRS UMR 6134 SPE **Hospital of Castelluccio Radiotherapy Unit
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 2/12
Objectives
Forecast the global radiation at daily time step using an Artificial Neural Networks (ANNs)
Look at the Multi-Layer Perceptron (MLP) which has been the most used of ANNs architecture
Optimize the MLP and define an ad-hoc time series preprocessing
Add exogenous meteorological data to improve the predictor
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 3/12
Outline
Data and context Methodology
– Time Series Preprocessing – MLP configuration – Use of correlation criteria to add
endogenous data and exogenous meteorological data at different time lags
Results and discussion Conclusion and perspectives
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 4/12
Data and context Measured global daily radiation
data from two meteorological stations equipped with standard meteorological sensors (pressure, nebulosity, etc.) – Ajaccio
• 41°55’N and 8°48’E, seaside, 4 m
– Bastia • 42°33’N, 9°29’E, seaside, 10 m
– Mediterranean climate • hot summers with abundant
sunshine and mild, dry, clear winters
– Near the sea and relief nearby : 40 km from Ajaccio and 15 km from Bastia
– Data from January 1998 to December 2007
Nebulosity difficult to forecast
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 5/12
Methodology
Time series preprocessing – Prediction of the solar
energy time series perturbed by the non-stationarity of the signal and the periodicity of the phenomena
– Use of a stationary method to increase the prediction quality, based on the clear sky model
measured data ; VC=0,539
0
10002000
300040005000
60007000
80009000
1 48 95 142 189 236 283 330 377 424 471 518 565 612 659 706
Time (Days)
Glo
bal
Rad
iati
on
(W
.h/m
²)
clearness index ; VC=0,326
00,10,20,30,40,50,60,70,80,9
1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691
Time (Days)
clea
rnes
s in
dex
clearness index, with mobil average and periodic coefficients ; VC=0,323
0
0,2
0,4
0,6
0,8
1
1,2
1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691
Time (Days)
det
ren
ded
dat
a (n
o u
nit
)
measured data ; VC=0,539
0
10002000
300040005000
60007000
80009000
1 48 95 142 189 236 283 330 377 424 471 518 565 612 659 706
Time (Days)
Glo
bal
Rad
iati
on
(W
.h/m
²)
clearness index ; VC=0,326
00,10,20,30,40,50,60,70,80,9
1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691
Time (Days)
clea
rnes
s in
dex
clearness index, with mobil average and periodic coefficients ; VC=0,323
0
0,2
0,4
0,6
0,8
1
1,2
1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691
Time (Days)
det
ren
ded
dat
a (n
o u
nit
)
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 6/12
Methodology
MLP configuration – Choice of the hidden layer
number and activation function – Choice of the time lag numbers
for the endogenous input – Choice of the time lag numbers
for the exogenous meteorological inputs
• Daily Pressure Variation• Wind Direction, Humidity, • Insulation, Nebulosity, • Precipitation, Mean Pressure• Min-Max-Mean Temperatures• Night Temperature, Wind
Speed
Xt-1
Xt-2
Xt-3
Xt-p
xt
t
Input windows
Error
Xt
Sliding window technique
tX̂
1 hidden layer, hyperbolic tangent (hidden) and linear (output), Levenberg-Marquardt.
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 7/12
Methodology
Use of correlation criteria to efficiently add endogenous data and exogenous meteorological data at different time lags – Use of the Partial Auto Correlation Factor
(PACF) in the endogenous case– Use of the Pearson correlation coefficient
method to select the exogenous variables
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 8/12
Methodology
Partial Auto Correlation Function : PACF– Plays an important role in
time series analysis– Allows to identify the
extent of the time lag in an autoregressive model
– We have used PACF to determine the best time lags for the endogenous input of the MLP
On figure, we can see the need to use St, St-1, St-2 and St-3 as input of the MLP to predict St+1.
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 9/12
Methodology
Pearson correlation– Determines the extent
to which values of two variables are "proportional" to each other
– Choice of a threshold R = 20%
On figure, we can see that a threshold R = 20% implies that the time lag 1 is sufficient for humidity, nebulosity and sunshine duration
sunshineduration
humidity
nebulosity
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 10/12
Results and discussion
The use of exogenous data generates a decrease of nRMSE between 0.5% and 1% for the both studied locations – On the site of Bastia, the use of the
exogenous data on PMC inputs increases a little the prediction quality : only 0.5%
– At Ajaccio, the nRMSE is improved by 1% The RMSE is decreased by 20
Wh/m²/day (Bastia) and 52 Wh/m²/day (Ajaccio)
9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 11/12
Conclusion and perspectives
We have proposed in this paper to study the contribution of exogenous meteorological data to an optimized MLP neural network
The next step of our work will be to study the hourly time step
Verify that the adding of exogenous data can increase the accuracy when the time step of time series decreases
Thank you for your attention.
Questions?