Imputation of missing data for use in district heating networks modeling
DOI:
https://doi.org/10.17512/INSTAL.2026.08.02Keywords:
district heating network, hydraulic modeling, imputation, missing dataAbstract
This study addresses the issue of imputing missing data relating to the operation of district heating substations when accurate telemetry data is unavailable. A complete set of input data is required to inform a mathematical model of a district heating network. Three imputation methods were characterized and compared: mean imputation; the hot-deck method; and imputation using linear regression. The methods were evaluated using actual telemetry data in which missing values were randomly induced. Linear regression proved to be the most effective method for filling the gaps, achieving R² scores of up to 0.95 for substation heat power and up to 0.86 for volumetric flow rate. The article identifies sources of potentially valuable auxiliary knowledge that could be used to fill in missing data.
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References
1. Niemyjski, O. Kalibracja modelu hydraulicznego sieci ciepłowniczej. INSTAL 2020, 415, 12–16, https://doi.org/10.36119/15.2020.3.1.
2. Dhungana, H.; Bellotti, F.; Berta, R.; De Gloria, A. Performance Comparison of Imputation Methods in Building Energy Data Sets. In Applications in Electronics Pervading Industry, Environment and Society; Saponara, S., De Gloria, A., Eds.; Lecture Notes in Electrical Engineering; Springer International Publishing: Cham, 2021; Vol. 738, pp. 144–151 ISBN 978-3-030-66728-3.
3. Pokropek, A. Wybrane statystyczne metody radzenia sobie z brakami danych. Polskie Forum Psychologiczne 2018, 291–310, https://doi.org/10.14656/PFP20180205.
4. Młodak, A. Imputacja Danych w Spisach Powszechnych. WS 2010, 2010, 7–22, https://doi.org/10.59139/ws.2010.08.2.
5. Enders, C.K.; Little, T.D. Applied Missing Data Analysis; Methodology in the social sciences; Second Edition.; The Guilford Press: New York London, 2022; ISBN 978-1-4625-4986-3.
6. Wesołowski, J.; Tarczyński, J. Podstawy matematyczne technik imputacyjnych. Wiadomości Statystyczne 2016, 7–54.
7. Misztal, M. Próba Oceny Wpływu Wybranych Metod Imputacji Danych Na Wyniki Klasyfikacji Obiektów z Wykorzystaniem Drzew Klasyfikacyjnych. Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu. Taksonomia 2011, 18, 246--253.
8. Horton, N.J.; Kleinman, K.P. Much Ado About Nothing: A Comparison of Missing Data Methods and Software to Fit Incomplete Data Regression Models. The American Statistician 2007, 61, 79–90, https://doi.org/10.1198/000313007X172556.
9. Luo, Z.; Lin, X.; Zhong, W.; Feng, E. Research on Coarse Granularity Data Sample Completion Method for District Heating System. In Proceedings of the 2023 26th International Conference on Computer Supported Cooperative Work in Design (CSCWD); IEEE: Rio de Janeiro, Brazil, May 24 2023; pp. 249–254.
10. Zhou, Y.; Aryal, S.; Bouadjenek, M.R. Review for Handling Missing Data with special missing mechanism, https://doi.org/10.48550/arXiv.2404.04905.
11. Alwateer, M.; Atlam, E.-S.; El-Raouf, M.M.A.; Ghoneim, O.A.; Gad, I. Missing Data Imputation: A Comprehensive Review. JCC 2024, 12, 53–75, https://doi.org/10.4236/jcc.2024.1211004.
12. Schaffer, M.; Tvedebrink, T.; Marszal Pomianowska, A. Three Years of Hourly Data from 3021 Smart Heat Meters Installed in Danish Residential Buildings. Sci Data 2022, 9, 420, https://doi.org/10.1038/s41597-022-01502-3.
13. Johra, H.; Leiria, D.; Heiselberg, P.; Marszal-Pomianowska, A.; Tvedebrink, T. Treatment and Analysis of Smart Energy Meter Data from a Cluster of Buildings Connected to District Heating: A Danish Case. E3S Web Conf. 2020, 172, 12004, https://doi.org/10.1051/e3sconf/202017212004.
14. Leiria, D.; Johra, H.; Marszal-Pomianowska, A.; Pomianowski, M.Z.; Kvols Heiselberg, P. Using Data from Smart Energy Meters to Gain Knowledge about Households Connected to the District Heating Network: A Danish Case. Smart Energy 2021, 3, 100035, https://doi.org/10.1016/j.segy.2021.100035.
15. Inman, D.; Elmore, R.; Bush, B. A Case Study to Examine the Imputation of Missing Data to Improve Clustering Analysis of Building Electrical Demand. Building Services Engineering Research and Technology 2015, 36, 628–637, https://doi.org/10.1177/0143624415573215.
16. Lee, G.; Choi, S.; Choi, Y.; Koo, J.; Kim, D.-W.; Yoon, S. A Two-Stage Imputation Method for Enhancing Urban Building Energy Data Resilience Using Bayesian Inference. Energy and Buildings 2025, 349, 116515, https://doi.org/10.1016/j.enbuild.2025.116515.
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Copyright (c) 2026 Jakub Kuś, Michał Żurawski, Łukasz Mika (Autor)

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