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A comparison of linear and neural network ARX models applied to a prediction of the indoor temperature of a building

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Abstract

A neural network auto regressive with exogenous input (NNARX) model is used to predict the indoor temperature of a residential building. Firstly, the optimal regressor of a linear ARX model is identified by minimising Akaike’s final prediction error (FPE). This regressor is then used as the input vector of a fully connected feedforward neural network with one hidden layer of ten units and one output unit. Results show that the NNARX model outperforms the linear model considerably: the sum of the squared error (SSE) is 15.0479 with the ARX model and 2.0632 with the NNARX model. The optimal network topology is subsequently determined by pruning the fully connected network according to the optimal brain surgeon (OBS) strategy. With this procedure near 73% of connections were removed and, as a result, the performance of the network has been improved: the SSE is equal to 0.9060.

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References

  1. Norlén U, Hammarsten S (1988) Model specification for time series analysis of energy flows in buildings. In: Proceedings of North Sun ‘88, Borlänge, Sweden

  2. Norlén U (1990) Estimating thermal parameters of outdoor test cells. Build Envir 25(1):17–24

    Article  Google Scholar 

  3. Angeby J, Söderström T (1991) Determination of thermal parameters in houses. IFAC identification and system parameter estimation, Budapest, Hungary pp 561–566

  4. Bloem H (ed) (1992) Workshop on parameter identification methods and physical reality. Institute for Systems Engineering and Informatics, Joint Research Centre, Ispra, Italy

  5. Bloem H (ed) (1993) Workshop on the Application of System Identification in Energy Saving in Building. Institute for Systems Engineering and Informatics, Joint Research Centre, Ispra, Italy

  6. Bloem H (ed) (1994) Workshop on System Identification Applied to Building Performance Data. Institute for Systems Engineering and Informatics, Joint Research Centre, Ispra, Italy

  7. Bloem H (ed) (1996) System Identification Competition. Institute for Systems Engineering and Informatics, Joint Research Centre, Ispra, Italy

  8. Andersen KK, Madsen H, Hansen LH (2000) Modelling the heat dynamics of a building using stochastic differential equations. Energ Build 31:13–24

    Article  Google Scholar 

  9. Kalogirou SA, Neocleous CE, Schizas CN. Heating load estimation using artificial neural networks. In: Proceedings of the CLIMA 2000 Conference, Brussels, Belgium, September 1997

  10. Curtiss PS, Brandemuehl MJ, Kreider JF (1995) Energy management in central HVAC plants using neural networks. In: Haberl JS, Nelson RM, Culp CC (eds) The use of artificial intelligence in building systems. ASHRAE, Tampa, FL

  11. Kalogirou SA, Bojic M (2000) An artificial neural network for the prediction of the energy consumption of a passive solar building. Energy 25(5):479–491

    Article  Google Scholar 

  12. Kalogirou SA (2000) Application of artificial neural-networks for energy systems. Appl Energ 67:17–35

    Article  Google Scholar 

  13. Nørgaard M (2000) Neural network based system identification toolbox. Tech. Report. 00-E 891, Department of Automation, Technical University of Denmark

  14. Söderstrom T, Stoica P (1989) System identification. Prentice Hall International, London

  15. Ljung L (1995) System identification toolbox. The MathWorks, Inc. Natick, MA

  16. Akaike H (1969) Fitting autoregressive models for prediction. Ann Inst Stat Math 21:243–347

    MATH  Google Scholar 

  17. Irie B, Miyaki S (1988) Capabilities of three layer perceptrons. In: Proceedings of the IEEE Second International Conference on Neural Networks, San Diego, CA

  18. Hsu KL, Gupta HV, Sorooshian S (1993) Artificial neural network modelling of the rainfall-runoff process. Wat Resour Res 29(4):1185–1194

    Article  Google Scholar 

  19. Demuth H, Beal M (1988) Neural network toolbox user’s guide. Version 3.0. The Math Works, Inc. Natick, MA

  20. Hecht-Nielsen R (1990) Neurocomputing. Addison-Wesley, Reading, MA

  21. Maren AJ, Harston CT, Pap RM (1990) Handbook of neural computing applications. Academic Press, San Diego, CA

  22. Padovese LR (1999) Using acoustical noise for fault classification in gearbox. In: Proceedings of the 15th Brazilian Congress of Mechanical Engineering, Sao Paulo, Brazil, November 1999

  23. Aspeslagh KB (2000) Utilizing a genetic algorithm to search the structure-space of artificial neural networks for optimal architectures. In: A study presented to the faculty of Wheaton College, Departmental Honors in Computer Science, Norton, MA, 15 May 2000

  24. Schiffmann W (2000) Encoding feedforward networks for topology optimization by simulated evolution. In: Proceedings of the Fourth International Conference on Knowledge-Based Intelligent Engineering Systems & Allied Technologies (KES ‘2000), Brighton, UK, 30 August–1 September 2000

  25. Branke J (1995) Evolutionary algorithms for neural network design and training. In: Proceedings of the 1st Nordic Workshop on Genetic Algorithms and its Applications, Vaasa, Finland, January 1995

  26. Hassibi B, Stork DG (1993) Second order derivatives for network pruning: optimal brain surgeon. In: Hanson SJ et al. (eds) NIPS, Morgan Kaufmann, San Mateo, CA

  27. Hansen LK, Pederson MW (1994) Controlled growth of cascade correlation nets. In: Proceedings of ICANN ‘94, Sorrento, Italy, May 1994

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  1. Faculté des Sciences et Techniques Fès Saiss B.P., L.S.S.C., 2202 Fès 30000, Maroc

    A. Mechaqrane & M. Zouak

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  1. A. Mechaqrane
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  2. M. Zouak
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Correspondence to A. Mechaqrane.

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Mechaqrane, A., Zouak, M. A comparison of linear and neural network ARX models applied to a prediction of the indoor temperature of a building. Neural Comput & Applic 13, 32–37 (2004). https://doi.org/10.1007/s00521-004-0401-8

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  • DOI: https://doi.org/10.1007/s00521-004-0401-8

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