Model Mixing for Long-term Extrapolation

Reliable extrapolation – simulation or prediction – of system output is an invaluable departure point for the control system design. For application of model-based techniques, the knowledge of the model structure is essential. It can be based purely on the physical point of view or estimated from process data while the system is considered as a black box. Mixing of both methods results in grey box modelling. Often, modelled systems are governed by several known physical laws and each of these laws implies a model, which should match the data. Nevertheless inevitable uncertainties often make simulated outputs of respective models unreliable. The problem is especially pronounced for systems with a significant time delay. This motivates search for methods, which utilize all available models at once and mix their outputs with the aim to get better results. In the paper, four variants of mixing are considered, discussed and their performance compared on industrial data. Seeming alternative – a simple complex model is discussed as well. Data for experiments came from a cold rolling mill.