Gray-box modeling for prediction and control of molten steel temperature in tundish

Iftikhar Ahmad, Manabu Kano*, Shinji Hasebe, Hiroshi Kitada, Noboru Murata

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


To realize stable production in the steel industry, it is important to control molten steel temperature in a continuous casting process. The present work aims to provide a general framework of gray-box modeling and to develop a gray-box model that predicts and controls molten steel temperature in a tundish (TD temp) with high accuracy. Since the adopted first-principle model (physical model) cannot accurately describe uncertainties such as degradation of ladles, their overall heat transfer coefficient, which is a parameter in the first-principle model, is optimized for each past batch separately, then the parameter is modeled as a function of process variables through a statistical modeling method, random forests. Such a model is termed as a serial gray-box model. Prediction errors of the first-principle model or the serial gray-box model can be compensated by using another statistical model; this approach derives a parallel gray-box model or a combined gray-box model. In addition, the developed gray-box models are used to determine the optimal molten steel temperature in the Ruhrstahl-Heraeus degassing process from the target TD temp, since the continuous casting process has no manipulated variable to directly control TD temp. The proposed modeling and control strategy is validated through its application to real operation data at a steel work. The results show that the combined gray-box model achieves the best performance in prediction and control of TD temp and satisfies the requirement for its industrial application.

Original languageEnglish
Pages (from-to)375-382
Number of pages8
JournalJournal of Process Control
Issue number4
Publication statusPublished - 2014 Apr


  • Gray-box modeling
  • Model-based control
  • Soft-sensor
  • Steel making process
  • Virtual sensing

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modelling and Simulation
  • Computer Science Applications
  • Industrial and Manufacturing Engineering


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