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

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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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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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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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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

)

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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.

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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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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.

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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

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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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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?