Hybrid grey box modelling of a pickling process

This paper deals with grey box modelling of an industrial process, in which known parts are modelled using a priori information and significant unknown parts are described as general continuous nonlinear functions. The modelling procedure follows a structured approach, which includes basic modelling, data acquisition, model calibration, hybrid expanded modelling, stochastic modelling and model appraisal. The general functions are approximated by means of the Taylor series including higher order terms, where the partial derivatives are estimated from measured data by minimising the maximum likelihood function. The Taylor series approach is used to keep the number of estimated parameters low in comparison with other nonlinear black box identification methods. The model is suitable for formulating algorithms to control the process, for example, a model predictive controller. The model can also be used to simulate various different production situations in order to improve the capacity of the total production line. Further, the relevant parts of the Taylor series can be used to explain in what way unknown process parts influence the behaviour of the process and give ideas for further investigation concerning the studied process.