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2010 05-15-cpaoli-prague-eeeic final

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Ministry for Europe and Foreign Affairs
Ministry for Europe and Foreign Affairs

Use of exogenous data to improve an artificial neural network dedicated to daily global radiation forecasting

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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
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 2/12
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 3/12
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 4/12
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) 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 5/12
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. 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 6/12
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 7/12
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 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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 8/12
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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 9/12
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 10/12
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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 11/12
Thank you for your attention. Questions?

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2010 05-15-cpaoli-prague-eeeic final

  • 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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 2/12
  • 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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 3/12
  • 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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 4/12
  • 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) 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 5/12
  • 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. 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 6/12
  • 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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 7/12
  • 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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 8/12
  • 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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 9/12
  • 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) 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 10/12
  • 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 9th EEEIC Conference, 16-19 May 2010, Prague, Czech Republic 11/12
  • 12. Thank you for your attention. Questions?

Editor's Notes

  1. 1 hidden layer, the activation function are hyperbolic tangent (hidden) and linear (output), the learning algorithm is the Levenberg-Marquardt model (with max fail parameter equal to 5, μ decreases and increases respectively to 0.1 and 0.001, and goals equal to zero), the normalization is done between 0 and 1; the ratio of train, validation and test periods represent respectively 80%, 10% and 10%. We have learned the ANN during the 8 first years and we have computed the global solar radiation during the 2 last years.