Abstract
Thermal models of buildings are helpful to forecast their energy use and to enhance the control of their mechanical systems. However, these models are building-specific and require a tedious, error-prone and time-consuming development effort relying on skilled building energy modelers. Compared to white-box and gray-box models, data-driven (black-box) models require less development time and a minimal amount of information about the building characteristics. In this paper, autoregressive neural network models are compared to gray-box and black-box linear models to simulate indoor temperatures. These models are trained, validated and compared to actual experimental data obtained for an existing commercial building in Montreal (QC, Canada) equipped with roof top units for air conditioning. Results show that neural networks mimic more accurately the thermal behavior of the building when limited information is available, compared to gray-box and black-box linear models. The gray-box model does not perform adequately due to its under-parameterized nature, while the linear models cannot capture non-linear phenomena such as radiative heat transfer and occupancy. Therefore, the neural network models outperform the alternative models in the presented application, reaching a coefficient of determination R2 up to 0.824 and a root mean square error down to 1.11 °C, including the error propagation over time for a 1-week period with a 5-minute time-step. When considering a 50-hour time horizon, the best neural networks reach a much lower root mean square error of around 0.6 °C, which is suitable for applications such as model predictive control.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Afram A, Janabi-Sharifi F (2014). Theory and applications of HVAC control systems-A review of model predictive control (MPC). Building and Environment, 72: 343–355.
Amasyali K, El-Gohary NM (2018). A review of data-driven building energy consumption prediction studies. Renewable and Sustainable Energy Reviews, 81: 1192–1205.
ASHRAE (2009). Heat balance method. In: ASHRAE Handbook: Fundamentals (SI Edition). Atlanta, GA, USA: American Society of Heating, Refrigerating and Air-Conditioning Engineers.
Beckman WA, Broman L, Fiksel A, Klein SA, Lindberg E, Schuler M, Thornton J (1994). TRNSYS The most complete solar energy system modeling and simulation software. Renewable Energy, 5: 486–488.
Bennett C, Stewart RA, Lu J (2014). Autoregressive with exogenous variables and neural network short-term load forecast models for residential low voltage distribution networks. Energies, 7: 2938–2960.
Braun JE, Chaturvedi N (2002). An inverse gray-box model for transient building load prediction. HVAC&R Research, 8: 73–99.
Bueno B, Norford L, Pigeon G, Britter R (2012). A resistance-capacitance network model for the analysis of the interactions between the energy performance of buildings and the urban climate. Building and Environment, 54: 116–125.
Caruana R, Lawrence S, Giles CL (2001). Overfitting in neural nets: Backpropagation, conjugate gradient, and early stopping. In: Proceedings of the 13th International Conference on Neural Information Processing Systems.
Castilla M, Álvarez JD, Normey-Rico JE, Rodríguez F (2014). Thermal comfort control using a non-linear MPC strategy: A real case of study in a bioclimatic building. Journal of Process Control, 24: 703–713.
Coakley D, Raftery P, Keane M (2014). A review of methods to match building energy simulation models to measured data. Renewable and Sustainable Energy Reviews, 37: 123–141.
Crawley DB, Lawrie LK, Winkelmann FC, Buhl WF, Huang Y, Pedersen CO, Strand RK, Liesen RJ, Fisher DE, Witte MJ, Glazer J (2001). EnergyPlus: creating a new-generation building energy simulation program. Energy and Buildings, 33: 319–331.
Crawley DB, Hand JW, Kummert M, Griffith BT (2008). Contrasting the capabilities of building energy performance simulation programs. Building and Environment, 43: 661–673.
Davalo E, Naïm P (1991). Neural Networks. Paris: Macmillan Education.
Djunaedy E, van den Wymelenberg K, Acker B, Thimmana H (2011). Oversizing of HVAC system: Signatures and penalties. Energy and Buildings, 43: 468–475.
Foucquier A, Robert S, Suard F, Stéphan L, Jay A (2013). State of the art in building modelling and energy performances prediction: A review. Renewable and Sustainable Energy Reviews, 23: 272–288.
Frausto HU, Pieters JG, Deltour JM (2003). Modelling greenhouse temperature by means of auto regressive models. Biosystems Engineering, 84: 147–157.
Frausto HU, Pieters JG (2004). Modelling greenhouse temperature using system identification by means of neural networks. Neurocomputing, 56: 423–428.
GitHub (2019). Populartimes. Available at: https://github.com/m-wrzr/populartimes. Accessed 8 Feb 2019.
Google (2019). Popular times, wait times, and visit duration. Available at https://support.google.com/business/answer/6263531?hl=en. Accessed 8 Feb 2019.
Hagan MT, Demuth HB, Beale MH, De Jesús O (1996). Neural Network Design. Boston, MA: PWS Publishing Company.
Hand JW (2011). The ESP-r cookbook. University of Strathclyde, Glasgow, UK.
Hernandez A (2019). A Python wrapper for the forecast.10 API. Available at: https://github.com/bitpixdigital/forecastiopy3. Accessed 8 Feb 2019.
Horne BG, Giles CL (1995). An experimental comparison of recurrent neural networks. In: Proceedings of the 8th International Conference on Neural Information Processing Systems, pp. 697-704.
Hu J, Karava P (2014). A state-space modeling approach and multilevel optimization algorithm for predictive control of multi-zone buildings with mixed-mode cooling. Building and Environment, 80: 259–273.
International Energy Agency (2019). Energy Efficiency: Buildings. Available at https://www.iea.org/topics/energyefficiency/buildings/. Accessed 13 Feb 2019.
Katipamula S, Brambley MR (2005a). Review article: methods for fault detection, diagnostics, and prognostics for building systems-A review, part I. HVAC&R Research, 11: 3–25.
Katipamula S, Brambley MR (2005b). Review article: methods for fault detection, diagnostics, and prognostics for building systems-A review, part II. HVAC&R Research, 11: 169–187.
Katipamula S, Kim W, Lutes RG, Underhill RM (2015). Rooftop unit embedded diagnostics: Automated fault detection and diagnostics (AFDD) development, field testing and validation. Richland, WA, USA: Pacific Northwest National Lab.
Kim W, Katipamula S (2018). A review of fault detection and diagnostics methods for building systems. Science and Technology for the Built Environment, 24: 3–21.
Klein SA, Beckman WA, Mitchell JW, et al. (2017). TRNSYS 18: A Transient System Simulation Program. Madison, WI, USA: Solar Energy Laboratory, University of Wisconsin.
Kramer R, van Schijndel J, Schellen H (2012). Simplified thermal and hygric building models: A literature review. Frontiers of Architectural Research, 1: 318–325.
Kutner MH, Nachtsheim CJ, Neter J, Li W (2005). Applied Linear Statistical Models. Boston, MA, USA: McGraw-Hill Irwin.
Li DHW, Yang L, Lam JC (2013). Zero energy buildings and sustainable development implications-A review. Energy, 54: 1–10.
Lin T, Horne BG, Tino P, Giles CL (1996). Learning long-term dependencies in NARX recurrent neural networks. IEEE Transactions on Neural Networks, 7: 1329–1338.
Mechaqrane A, Zouak M (2004). A comparison of linear and neural network ARX models applied to a prediction of the indoor temperature of a building. Neural Computing & Applications, 13: 32–37.
Mustafaraj G, Lowry G, Chen J (2011). Prediction of room temperature and relative humidity by autoregressive linear and nonlinear neural network models for an open office. Energy and Buildings, 43: 1452–1460.
Myers GE (1971). Analytical Methods in Conduction Heat Transfer. New-York: McGraw-Hil.
Nakamura G, Potthast R (2015). Inverse Modeling: An Introduction to the Theory and Methods of Inverse Problems and Data Assimilation. Bristol, UK: IOP Publishing.
Natural Resources Canada (2018). Energy management software for new buildings. Available at: https://www.nrcan.gc.ca/energy/efficiency/buildings/20701. Accessed 25 Feb 2019.
Oldewurtel F, Parisio A, Jones CN, Morari M, Gyalistras D, Gwerder M, Stauch V, Lehmann B, Wirth K (2010). Energy efficient building climate control using Stochastic Model Predictive Control and weather predictions. In: Proceedings of the 2010 American Control Conference, pp. 5100–5105.
Pedregosa F, Varoquaux G, Gramfort A, et al. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12: 2825–2830.
Prechelt L (1998). Early stopping-but when? In: Orr GB, Müller K-R (eds), Neural Networks: Tricks of the Trade. Berlin: Springer, pp. 55–69.
Ramallo-González AP, Eames ME, Coley DA (2013). Lumped parameter models for building thermal modelling: An analytic approach to simplifying complex multi-layered constructions. Energy and Buildings, 60: 174–184.
Ruiz GL, Cuéllar PM, Calvo-Flores DM, Jiménez DM (2016). An application of non-linear autoregressive neural networks to predict energy consumption in public buildings. Energies, 9: 684.
Scikit-learn (2019a). Generalized linear models. Available at https://scikitlearn.org/dev/modules/linear_model.html. Accessed 16 Apr 2019.
Scikit-learn (2019b). Neural network models (supervised). Available at https://scikitlearn.org/dev/modules/neural_networks_supervised.html. Accessed 17 Apr 2019.
Scikit-learn (2019c). MLPRegressor class. Available at https://scikitlearn.org/dev/modules/generated/sklearn.neural_network.MLPRegressor.html#sklearn.neural_network.MLPRegressor. Accessed 17 Apr 2019.
Sheela KG, Deepa SN (2013). Review on methods to fix number of hidden neurons in neural networks. Mathematical Problems in Engineering, 2013: 425740.
Siegelmann HT, Horne BG, Giles CL (1997). Computational capabilities of recurrent NARX neural networks. IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 27: 208–215.
The Dark Sky Company (2019). Dark Sky API. Available at https://darksky.net/dev. Accessed 8 Feb 2019.
The SciPy community (2019). Signal processing. Available at https://docs.scipy.org/doc/scipy/reference/tutorial/signal.html. Accessed 18 Apr 2019.
TRANSSOLAR Energietechnik (2017). Multizone Building modeling with Type56 and TRNBuild. Stuttgart, Germany: TRANSSOLAR Energietechnik GmbH.
Xu X, Wang S (2008). A simplified dynamic model for existing buildings using CTF and thermal network models. International Journal of Thermal Sciences, 47: 1249–1262.
Zhang G, Patuwo BE, Hu MY (1998). Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting, 14: 35–62.
Zhang A, Lipton ZC, Li M, Smola AJ (2019a). Recurrent neural networks. In: Dive into deep learning. Available at https://www.d2l.ai/.
Zhang A, Lipton ZC, Li M, Smola AJ (2019b). Multilayer Perceptron. In: Dive into deep learning. Available at https://www.d2l.ai/.
Zhang A, Lipton ZC, Li M, Smola AJ (2019c). Optimization algorithms. In: Dive into deep learning. Available at https://www.d2l.ai/.
Zhao H, Magoulès F (2012). A review on the prediction of building energy consumption. Renewable and Sustainable Energy Reviews, 16: 3586–3592.
Acknowledgments
The research work presented in this paper is financially supported by the Institute for Data Valorization (IVADO).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Delcroix, B., Ny, J.L., Bernier, M. et al. Autoregressive neural networks with exogenous variables for indoor temperature prediction in buildings. Build. Simul. 14, 165–178 (2021). https://doi.org/10.1007/s12273-019-0597-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12273-019-0597-2