Mathematical modelling and parameter identification of a stainless steel annealing furnace

A new, comprehensive mathematical model of continuous annealing furnaces is developed, under consideration of both the radiative and convective heat transfer of the furnace components. Based on measured normal operating data from an industrial stainless steel plant, parameter identification is basically carried out using a nonlinear least-squares optimization algorithm for the whole annealing furnace, to estimate optimal values of uncertain parameters, such as emissivities. Due to the complexity of the model, a sequential approach for parameter identification is proposed and implemented, i.e. the parameter set is divided into different subsets, and the parameter estimation is carried out sequentially in several steps and iterations. The performance of the model with the estimated parameters is then evaluated on a different test data set. It is shown that the obtained model can predict temperature evolutions along the furnace in good agreement to measured data, under both steady-state and transient conditions. The presented model is suitable for controller design and process optimization.