Bootstrapping Regression Support Tool for Energy Management in Induction Melting Processes: a Multi-Plant Case Study
DOI:
https://doi.org/10.24425/afe.2026.158018Abstract
Efficient energy management is a basis of operational quality in the foundry industry, where induction melting accounts for 70–80% of total electricity costs. This study proposes a decision-support model for predicting energy consumption, developed using data from 11 industrial plants. Facing the challenge of a small dataset, a bootstrap regression approach was employed to ensure robust estimation of Energy Performance Indicators (EnPIs). The resulting model shows high explanatory power and yields statistically significant coefficients for all variables. The model identifies key managerial and technical drivers, such as charge contamination, packing density, and organisational heat loss (furnace temperature). Unlike purely technical models, this approach utilises semi-annual aggregated data, making it a strategic tool for energy budgeting and benchmarking. The model’s predictive power was externally validated against a 12th foundry, yielding a precision of 98,4%, thus proving its reliability for managerial forecasting and carbon footprint auditing in the framework of ISO 50001 standards.
References
[1] Bänsch, K., Busse, J., Meisel, F., Rieck, J., Scholz, S., Volling, T. & Wichmann, M. G. (2021). Energy-aware decision support models in production environments: A systematic literature review. Computers & Industrial Engineering. 159, 107456, 1-27. https://doi.org/10.1016/j.cie.2021.107456.
[2] Pechmann, A. & Zarte, M. (2017). Procedure for generating a basis for PPC systems to schedule the production considering energy demand and available renewable energy. Procedia CIRP. 64, 393-398. https://doi.org/10.1016/j.procir.2017.03.033.
[3] Abhilash, E. & Joseph, M.A. (2008). Studies on energy consumption of melting furnaces and energy conservation options in foundries. In Proceedings of the Conference ENERGY, January 2008 (pp. 307–314). Calicut, Kerala, India: NIT.
[4] Donsbach, F., Rodriguez, M.M., Nordt, U., Hansen, P.K. (2024). Saving energy when melting metals in induction furnaces through practical measures and by analyzing digital melting process data. Retrieved October 13, 2025, from https://www.foundry-planet.com
[5] Naro, R., Williams, D.C., Satre, P. (2019). Economic consequences of insoluble buildup on coreless melting efficiency. Retrieved October 13, 2025, from https://www.foundrymag.com
[6] AFS Institute. (2023). Back to Basics: Induction furnace daily maintenance. Retrieved October 13, 2025, from https://www.moderncasting.com
[7] Holtzer, M., Bagińska, E., Baliński, A., Borla, K., Bydałek, A., Dańko, J., Kowalski, K., Latała-Holtzer, M., Młyński, M., Podrzucki, Cz., Rożek, J., Żmudzińska, M. (2005). Guide to best available techniques (BAT). Guidance for the foundry industry. Warsaw: Ministry of the Environment. (in Polish).
[8] Aries, E., Chronopoulos, G., Schorcht, F., Roudier, S. (2024). European Commission: Best Available Techniques (BAT) Reference Document for the Smitheries and Foundries Industry (SF BREF). Retrieved September 10, 2025, from https://bureau-industrial-transformation.jrc.ec.europa.eu/ reference/smitheries-and-foundries-industry.
[9] Noro, M. & Lazzarin, R.M. (2016). Energy audit experiences in foundries. International Journal of Energy and Environmental Engineering. 7(4), 409-423. https://doi.org/10.1007/s40095-014-0152-y.
[10] Stefana, E., Cocca, P., Marciano, F., Rossi, D. & Tomasoni, G. (2019). A review of energy and environmental management practices in cast iron foundries to increase sustainability. Sustainability. 11(24), 7245, 1-18. DOI: 10.3390/su11247245.
[11] Adetunji, O., Ojo, S.S., Oyetunji, A. & Itua, N. (2021). Melting time prediction model for induction furnace melting using specific thermal consumption from material charge approach. Journal of Minerals and Materials Characterization and Engineering. 9, 61-74. DOI: https://doi.org/10.4236/jmmce.2021.91005.
[12] Abdelshafy, A., Franzen, D., Mohaupt, A., Schüssler, J., Bührig-Polaczek, A. & Walther, G. (2022). A feasibility study to minimize the carbon footprint of cast iron production while maintaining the technical requirements. Journal of Sustainable Metallurgy. 9, 249-265. DOI: https://doi.org/10.1007/s40831 -022-00642-5.
[13] Howard, D.A., Jørgensen, B.N. & Ma, Z. (2024). Identifying best practice melting patterns in induction furnaces: A data-driven approach using time series k-means clustering and multi-criteria decision making. In: Third Energy Informatics Academy Conference, 6-8 December 2023 (pp. 271-288). Springer, Cham. https://doi.org/10.1007/978-3-031-48649-4_16.
[14] Efron, B. (1979). Bootstrap methods: another look at the jackknife. The Annals of Statistics. 7(1), 1-26.
[15] Bollen, K.A. & Stine, R. (1990). Direct and indirect effects: classical and bootstrap estimates of variability. Sociological Methodology. 20, 115-140. DOI: https://doi.org/10.2307/271084.
[16] Stevens, J. (1996). Applied multivariate statistics for social sciences. Mahwah, NJ: Lawrence Erlbaum Associates.
[17] Wu, M-J., Zhao, K., Fils-Aime, F. (2022). Response rates of online surveys in published research: A meta-analysis. Computers in Human Behavior Reports. 7, 100206, 1-11. https://doi.org/10.1016/j.chbr.2022.100206.
[18] Smith, G. (2018). Step away from stepwise. Journal of Big Data. 5(32), 1-12. https://doi.org/10.1186/s40537-018-0143-6
[19] Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research. 64(2), 278-285. https://doi.org/10.1016/0377-2217(93)90182-M.
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