Generally, the system modelling and parameter identification can be divided in to three categories. First is a physical or analytical model which is based on physical structure and geometry of the system and is also known as white box model because every process inside the system is known and can be modelled mathematically. The model parameters have physical meaning and needs to be determined from experimental testing of individual components of the system. The model is valid for large range of test conditions.
Second is a black box model, in which the input and the output relationship is obtained by fitting the response data to the known input regardless of internal structure of the system. The model is strongly correlated with the measurements but is valid only for a specific range of test conditions.
Third is a grey box model, in which the model structure is obtained from the physical principles and then test data is used to obtain the model parameters. Both black box and grey box models are known as parametric models, in which the model parameters may or may not have any physical meaning, but are strongly correlated with measurements.