The document discusses the use of exogenous meteorological data to enhance an artificial neural network (ANN) designed for daily global radiation forecasting. It details the methodology involving time series preprocessing, multi-layer perceptron configuration, and the incorporation of various meteorological inputs, resulting in improved prediction accuracy. The findings indicate a notable decrease in error metrics, suggesting that external data significantly contributes to enhancing the model's predictive performance.

1. 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

2. 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
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3. 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
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4. 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
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5. measured data ; VC=0,539
9000
Methodology
Global Radiation (W.h/m²)
8000
7000
6000
5000
4000
3000
2000
1000
0
 Time series
1 48 95 142 189 236 283 330 377 424 471 518 565 612 659 706
Time (Days)
preprocessing clearness index ; VC=0,326
– Prediction of the solar 0,9
0,8
energy time series
0,7
clearness index
0,6
perturbed by the non-
0,5
0,4
0,3
stationarity of the signal
0,2
0,1
0
and the periodicity of 1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691
Time (Days)
the phenomena
– Use of a stationary
clearness index, with mobil average and periodic
coefficients ; VC=0,323
method to increase the detrended data (no unit)
1,2
1
prediction quality, based 0,8
0,6
on the clear sky model 0,4
0,2
0
1 47 93 139 185 231 277 323 369 415 461 507 553 599 645 691
Time (Days)
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6. Input windows
xt
Methodology
 MLP configuration t
– Choice of the hidden layer Sliding window technique
number and activation function
– Choice of the time lag numbers Xt-1
Xt
for the endogenous input Xt-2
Error
– Choice of the time lag numbers
Xt-3
for the exogenous
meteorological inputs ˆ
Xt
• Daily Pressure Variation
• Wind Direction, Humidity,
Xt-p
• Insulation, Nebulosity,
• Precipitation, Mean Pressure
• Min-Max-Mean Temperatures 1 hidden layer, hyperbolic tangent
• Night Temperature, Wind Speed (hidden) and linear
(output), Levenberg-Marquardt.
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7. 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
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8. 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 On figure, we can see the
– We have used PACF to need to use St, St-1, St-2
determine the best time and St-3 as input of the
lags for the endogenous MLP to predict St+1.
input of the MLP
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9. Methodology humidity
 Pearson correlation
– Determines the extent to
nebulosity
which values of two
variables are "proportional"
to each other
– Choice of a threshold sunshine
R = 20% duration
On figure, we can see that a threshold R =
20% implies that the time lag 1 is sufficient for
humidity, nebulosity and sunshine duration
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10. 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)
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11. 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
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12. Thank you for your attention.
Questions?