Pregled modela sive kutije za modelovanje i optimizaciju HVAC&R sistema
##plugins.themes.bootstrap3.article.sidebar##
Objavljeno
Feb 16, 2026
##plugins.themes.bootstrap3.article.main##
Danijela Srećković
Mina Mirović
Aleksandra Sretenović-Dobrić
http://orcid.org/0000-0003-1152-6377
http://orcid.org/0000-0003-1152-6377
Apstrakt
Model „sive kutije“ kombinuje pristupe zasnovane na fundamentalnim fizičkim principima, poznate kao modeli „bele kutije“, sa modelima zasnovanim na eksperimentalnim podacima, odnosno modelima „crne kutije“, sa ciljem kreiranja modela koji predstavlja kompromis i omogućava precizno opisivanje složene dinamike sistema. Ovaj hibridni pristup posebno je pogodan u domenu KGH sistema, gde izražene termodinamičke nelinearnosti, nepredvidivi radni uslovi i nepotpuno poznavanje karakteristika procesa ograničavaju primenljivost analitičkih modela, dok primena empirijskih pristupa u promenjenim uslovima zahteva veliku količinu, najčešće merenih podataka. Tokom protekle decenije, modeli ‘sive kutije’ uspešno su primenjeni na širok spektar izazova u KGH sistemima, uključujući dinamičko modelovanje i predikciju termičkog ponašanja posmatranog objekta, optimizaciju potrošnje energije, detekciju i dijagnostiku grešaka, kao i razvoj upravljačkih modela koji integrišu veštačke neuronske mreže sa diferencijalnim jednačinama. U radu će biti razmatrane osnovne karakteristike kombinovanog modela sive kutije, kao i aktuelne inženjerske primene relevantne za modelovanje, kontrolu i optimizaciju savremenih KGH sistema, uz pružanje preporuka za buduće istraživačke pravce.
##plugins.themes.bootstrap3.article.details##
Kako citirati
SREĆKOVIĆ, Danijela; MIROVIĆ, Mina; SRETENOVIĆ-DOBRIĆ, Aleksandra.
Pregled modela sive kutije za modelovanje i optimizaciju HVAC&R sistema.
Zbornik Međunarodnog kongresa i izložbe o KGH, [S.l.], v. 56, n. 1, p. 219-231, feb. 2026.
Dostupno na: <https://izdanja.smeits.rs/index.php/kghk/article/view/8289>. Datum pristupa: 12 mar. 2026
Broj časopisa
Sekcija
Rashladne mašine i sistemi
Reference
[1] Sretenović, A. A., Prediction of Energy Use for HVAC Systems Using Artificial Intelligence Methods, Ph.D. thesis, University of Belgrade, Faculty of Mechanical Engineering, Belgrade, Serbia, 2016.
[2] Palaić, D., I. Štajduhar, S. Ljubić, I. Wolf, Development, Calibration, and Validation of a Simulation Model for Indoor Temperature Prediction and HVAC System Fault Detection, Build-ings, 13 (2023), 1388.
[3] Haves, P., B. Ravache, M. Yazdanian, Accuracy of HVAC Load Predictions: Validation of En-ergyPlus and DOE-2 Using FLEXLAB Measurements, Lawrence Berkeley National Laboratory, Energy Technologies Area, Berkeley, CA, USA, 2020.
[4] Mörth, M., A. Heinz, R. Heimrath, V. Kaisermayer, M. Gölles, H. Edtmayer, T. Mach, C. Hochenauer, Grey-Box Model for Efficient Building Simulations: A Case Study of an Integrat-ed Water-Based Heating and Cooling System, Buildings, 15 (2025), 1959.
[5] Leerbeck, K., P. Bacher, C. Heerup, H. Madsen, Grey-Box Modeling of Supermarket Refrig-eration Cabinets, Energy and AI, 10 (2022), 100211.
[6] Dawood, S. M., A. Hatami, R. Z. Homod, HVAC system modeling and control methods: a review and case study, Journal of Energy Management and Technology (JEMT), 6 (2021), 4, pp. 218–220.
[7] https://smart-cities-centre.org/wp-content/uploads/grey_box_intro.pdf
[8] Bohlin, T. P., Practical Grey-Box Process Identification: Theory and Applications, Springer, 2006.
[9] Schweidtmann, A. M., D. Zhang, M. von Stosch, A Review and Perspective on Hybrid Model-ing Methodologies, Digital Chemical Engineering, 10 (2024), 100136.
[10] Duarte, B. P., P. M. Saraiva, Hybrid Models Combining Mechanistic Models with Adaptive Regression Splines and Local Stepwise Regression, Industrial & Engineering Chemistry Re-search, 42 (2003), 1, pp. 99–107.
[11] Von Krannichfeldt, L., K. Orehounig, O. Fink, Combining Physics-Based and Data-Driven Modeling for Building Energy Systems, Applied Energy, 391 (2025), 125853.
[12] Hauth, J., Grey-Box Modelling for Nonlinear Systems, Ph.D. dissertation, Fachbereich Mathe-matik, Technische Universität Kaiserslautern, Kaiserslautern, Germany, 2008.
[13] Reynders, G., J. Diriken, D. Saelens, Quality of Grey-Box Models and Identified Parameters as a Function of the Accuracy of Input and Observation Signals, Energy and Buildings, 82 (2014), pp. 263–274.
[14] Zaaoumi, A., A. Sempey, Z. Aketouane, P. Sebastian, Development and Experimental Vali-dation of a RC Model to Predict Indoor Air Temperature of a Room Assigned for Extreme Warm Climate: Case Study of Baitykool Prototype in Dubai, Proceedings of the 18th IBPSA Conference, Shanghai, China, Sept. 4–6, 2023, pp. 3326.
[15] Murphy, M. D., P. D. O’Sullivan, G. Carrilho da Graça, A. O’Donovan, Development, Cal-ibration and Validation of an Internal Air Temperature Model for a Naturally Ventilated Nearly Zero Energy Building: Comparison of Model Types and Calibration Methods, Energies 14, 2021.
[16] Afram, A., F. Janabi-Sharifi, Gray-box modeling and validation of residential HVAC system for control system design, Applied Energy, 137 (2015), pp. 134–150.
[17] Hu, J., P. Karava, A state-space modeling approach and multi-level optimization algorithm for predictive control of multi-zone buildings with mixed-mode cooling, Building and Environment, 80 (2014), pp. 259–273.
[18] Li, Y., Z. O’Neill, L. Zhang, J. Chen, P. Im, J. DeGraw, Grey-box modeling and application for building energy simulations—A critical review, Renewable and Sustainable Energy Reviews, 146 (2021), 111174.
[19] Thilker, C. A., P. Bacher, H. G. Bergsteinsson, R. G. Junker, D. Cali, H. Madsen, Non-linear grey-box modelling for heat dynamics of buildings, Energy and Buildings, 252 (2021), 111457.
[20] Harb, H., N. Boyanov, L. Hernandez, R. Streblow, D. Müller, Development and validation of grey-box models for forecasting the thermal response of occupied buildings, Energy and Buildings, 117 (2016), pp. 199–207.
[21] Berthou, T., P. Stabat, R. Salvazet, D. Marchio, Development and validation of a gray box model to predict thermal behavior of occupied office buildings, Energy and Buildings, 74 (2014), pp. 91–100.
[22] Kim, H., Daisuke, S., & Choi, Y. Development of a Gray-box Modeling Method for HVAC&R Systems in Commercial Buildings with an Automatic Calibration Process. Proceedings of the 17th IBPSA Conference, Bruges, Belgium, September 1–3, 2021.
[23] Estrada-Flores, S., Merts, I., De Ketelaere, B., and Lammertyn, J. Development and valida-tion of grey-box models for refrigeration applications: a review of key concepts. International Journal of Refrigeration, vol. 29, pp. 931–946, 2006.
[24] Ji, Y., and Xu, P. Model based indirect submetering method of HVAC end-use in existing office building. Procedia Engineering., vol. 121, no. 114, pp. 1705–1712, 2015.
[25] Amara, F., Agbossou, K., Cardenas, A., Dubé, Y., and Kelouwani, S. Comparison and simulation of building thermal models for effective energy management. Smart Grid and Renew-able Energy, vol. 6, pp. 95–112, 2015.
[26] Coninck, R. D., Magnusson, F., Åkesson, J., and Helsen, L. Toolbox for development and validation of grey-box building models for forecasting and control. Journal of Building Perfor-mance Simulation, vol. 9, no. 3, pp. 288–303, 2016.
[27] Saurav, K. Gray-box approach for thermal modelling of buildings for applications in district heating and cooling networks. Proceedings of the Eighth International Conference on Future En-ergy Systems, pp. 347–352, 2017
[28] Xiong, W., and Wang, J. A semi-physical static model for optimizing power consumption of HVAC systems. Control Engineering Practice., vol. 96, p. 104312, 2020
[29] Ahamed, S., Zmeureanu, R., Cortrufo, N., and Candanedo, J. Gray-box virtual sensor of the supply air temperature of air handling units. Science and Technology for the Built Environ-ment., pp. 1–12, 2020.
[30] Kathirgamanathan, A., De Rosa, M., Mangina, E., & Finn, D. P. Data-driven predictive control for unlocking building energy flexibility: A review. Renewable and Sustainable Energy Reviews, 135, 11012., 2021
[31] Kim, D., Lee, J., Do, S., Mago, P. J., Lee, K. H., and Cho, H. Energy modeling and model predictive control for HVAC in buildings: A review of current research trends, Energies, vol. 15, p. 7231, 2022.
[32] Klanatsky, P., Veynandt, F., and Heschl, C. Grey-box model for model predictive control of buildings. Energy & Buildings, vol. 300, p. 113624, 2023.
[33] Seiler, V., Huber, G., and Kepplinger, P. Systematic model selection for grey box modeling of HVAC systems In Heat Powered Cycle Conference, The University of Edinburgh, Scotland, 6th September 2023
[34] Lin, X., Tian, Z., Song, W., Lu, Y., Niu, J., Sun, Q., & Wang, Y. Grey-box modeling for thermal dynamics of buildings under the presence of unmeasured internal heat gains, Energy and Buildings, 314 (2024), 114229.
[35] Tugores, J., Macarulla, M., & Gangolells, M. Hybrid grey box modelling of indoor air quality and thermal dynamics in indoor environments. Energy and Buildings, 334, 115528, 2025.
[2] Palaić, D., I. Štajduhar, S. Ljubić, I. Wolf, Development, Calibration, and Validation of a Simulation Model for Indoor Temperature Prediction and HVAC System Fault Detection, Build-ings, 13 (2023), 1388.
[3] Haves, P., B. Ravache, M. Yazdanian, Accuracy of HVAC Load Predictions: Validation of En-ergyPlus and DOE-2 Using FLEXLAB Measurements, Lawrence Berkeley National Laboratory, Energy Technologies Area, Berkeley, CA, USA, 2020.
[4] Mörth, M., A. Heinz, R. Heimrath, V. Kaisermayer, M. Gölles, H. Edtmayer, T. Mach, C. Hochenauer, Grey-Box Model for Efficient Building Simulations: A Case Study of an Integrat-ed Water-Based Heating and Cooling System, Buildings, 15 (2025), 1959.
[5] Leerbeck, K., P. Bacher, C. Heerup, H. Madsen, Grey-Box Modeling of Supermarket Refrig-eration Cabinets, Energy and AI, 10 (2022), 100211.
[6] Dawood, S. M., A. Hatami, R. Z. Homod, HVAC system modeling and control methods: a review and case study, Journal of Energy Management and Technology (JEMT), 6 (2021), 4, pp. 218–220.
[7] https://smart-cities-centre.org/wp-content/uploads/grey_box_intro.pdf
[8] Bohlin, T. P., Practical Grey-Box Process Identification: Theory and Applications, Springer, 2006.
[9] Schweidtmann, A. M., D. Zhang, M. von Stosch, A Review and Perspective on Hybrid Model-ing Methodologies, Digital Chemical Engineering, 10 (2024), 100136.
[10] Duarte, B. P., P. M. Saraiva, Hybrid Models Combining Mechanistic Models with Adaptive Regression Splines and Local Stepwise Regression, Industrial & Engineering Chemistry Re-search, 42 (2003), 1, pp. 99–107.
[11] Von Krannichfeldt, L., K. Orehounig, O. Fink, Combining Physics-Based and Data-Driven Modeling for Building Energy Systems, Applied Energy, 391 (2025), 125853.
[12] Hauth, J., Grey-Box Modelling for Nonlinear Systems, Ph.D. dissertation, Fachbereich Mathe-matik, Technische Universität Kaiserslautern, Kaiserslautern, Germany, 2008.
[13] Reynders, G., J. Diriken, D. Saelens, Quality of Grey-Box Models and Identified Parameters as a Function of the Accuracy of Input and Observation Signals, Energy and Buildings, 82 (2014), pp. 263–274.
[14] Zaaoumi, A., A. Sempey, Z. Aketouane, P. Sebastian, Development and Experimental Vali-dation of a RC Model to Predict Indoor Air Temperature of a Room Assigned for Extreme Warm Climate: Case Study of Baitykool Prototype in Dubai, Proceedings of the 18th IBPSA Conference, Shanghai, China, Sept. 4–6, 2023, pp. 3326.
[15] Murphy, M. D., P. D. O’Sullivan, G. Carrilho da Graça, A. O’Donovan, Development, Cal-ibration and Validation of an Internal Air Temperature Model for a Naturally Ventilated Nearly Zero Energy Building: Comparison of Model Types and Calibration Methods, Energies 14, 2021.
[16] Afram, A., F. Janabi-Sharifi, Gray-box modeling and validation of residential HVAC system for control system design, Applied Energy, 137 (2015), pp. 134–150.
[17] Hu, J., P. Karava, A state-space modeling approach and multi-level optimization algorithm for predictive control of multi-zone buildings with mixed-mode cooling, Building and Environment, 80 (2014), pp. 259–273.
[18] Li, Y., Z. O’Neill, L. Zhang, J. Chen, P. Im, J. DeGraw, Grey-box modeling and application for building energy simulations—A critical review, Renewable and Sustainable Energy Reviews, 146 (2021), 111174.
[19] Thilker, C. A., P. Bacher, H. G. Bergsteinsson, R. G. Junker, D. Cali, H. Madsen, Non-linear grey-box modelling for heat dynamics of buildings, Energy and Buildings, 252 (2021), 111457.
[20] Harb, H., N. Boyanov, L. Hernandez, R. Streblow, D. Müller, Development and validation of grey-box models for forecasting the thermal response of occupied buildings, Energy and Buildings, 117 (2016), pp. 199–207.
[21] Berthou, T., P. Stabat, R. Salvazet, D. Marchio, Development and validation of a gray box model to predict thermal behavior of occupied office buildings, Energy and Buildings, 74 (2014), pp. 91–100.
[22] Kim, H., Daisuke, S., & Choi, Y. Development of a Gray-box Modeling Method for HVAC&R Systems in Commercial Buildings with an Automatic Calibration Process. Proceedings of the 17th IBPSA Conference, Bruges, Belgium, September 1–3, 2021.
[23] Estrada-Flores, S., Merts, I., De Ketelaere, B., and Lammertyn, J. Development and valida-tion of grey-box models for refrigeration applications: a review of key concepts. International Journal of Refrigeration, vol. 29, pp. 931–946, 2006.
[24] Ji, Y., and Xu, P. Model based indirect submetering method of HVAC end-use in existing office building. Procedia Engineering., vol. 121, no. 114, pp. 1705–1712, 2015.
[25] Amara, F., Agbossou, K., Cardenas, A., Dubé, Y., and Kelouwani, S. Comparison and simulation of building thermal models for effective energy management. Smart Grid and Renew-able Energy, vol. 6, pp. 95–112, 2015.
[26] Coninck, R. D., Magnusson, F., Åkesson, J., and Helsen, L. Toolbox for development and validation of grey-box building models for forecasting and control. Journal of Building Perfor-mance Simulation, vol. 9, no. 3, pp. 288–303, 2016.
[27] Saurav, K. Gray-box approach for thermal modelling of buildings for applications in district heating and cooling networks. Proceedings of the Eighth International Conference on Future En-ergy Systems, pp. 347–352, 2017
[28] Xiong, W., and Wang, J. A semi-physical static model for optimizing power consumption of HVAC systems. Control Engineering Practice., vol. 96, p. 104312, 2020
[29] Ahamed, S., Zmeureanu, R., Cortrufo, N., and Candanedo, J. Gray-box virtual sensor of the supply air temperature of air handling units. Science and Technology for the Built Environ-ment., pp. 1–12, 2020.
[30] Kathirgamanathan, A., De Rosa, M., Mangina, E., & Finn, D. P. Data-driven predictive control for unlocking building energy flexibility: A review. Renewable and Sustainable Energy Reviews, 135, 11012., 2021
[31] Kim, D., Lee, J., Do, S., Mago, P. J., Lee, K. H., and Cho, H. Energy modeling and model predictive control for HVAC in buildings: A review of current research trends, Energies, vol. 15, p. 7231, 2022.
[32] Klanatsky, P., Veynandt, F., and Heschl, C. Grey-box model for model predictive control of buildings. Energy & Buildings, vol. 300, p. 113624, 2023.
[33] Seiler, V., Huber, G., and Kepplinger, P. Systematic model selection for grey box modeling of HVAC systems In Heat Powered Cycle Conference, The University of Edinburgh, Scotland, 6th September 2023
[34] Lin, X., Tian, Z., Song, W., Lu, Y., Niu, J., Sun, Q., & Wang, Y. Grey-box modeling for thermal dynamics of buildings under the presence of unmeasured internal heat gains, Energy and Buildings, 314 (2024), 114229.
[35] Tugores, J., Macarulla, M., & Gangolells, M. Hybrid grey box modelling of indoor air quality and thermal dynamics in indoor environments. Energy and Buildings, 334, 115528, 2025.