One could build a so-called white-box model based on first principles, eg. a model for a physical process from the Newton equations, but in many cases such models will be overly complex and possibly even impossible to obtain in reasonable time due to the complex nature of many systems and processes.
A much more common approach is therefore to start from measurements of the behavior of the system and the external influences (inputs to the system) and try to determine a mathematical relation between them without going into the details of what is actually happening inside the system. This approach is called system identification. Two types of models are common in the field of system identification:
In the context of non-linear model identification Jin et.al. describe greybox modeling as assuming a model structure a priori and then estimating the model parameters. This model structure can be specialized or more general so that it is applicable to a larger range of systems or devices. The parameter estimation is the tricky part and Jin et.al point out that the search for a good fit to experimental data tend to lead to an increasingly complex model. Jin et.al. then define a black-box model as a model which is very general and thus containing little a priori information on the problem at hand and at the same time being combined with an efficient method for parameter estimation. But as Nielsen and Madsen points out, the choice of parameter estimation can itself be problem-dependent.
Aircraft and rotorcraft system identification; engineering methods with flight-test examples.(Brief article)(Book review)
Dec 01, 2006; 1563478374 Aircraft and rotorcraft system identification; engineering methods with flight-test examples. Tischler, Mark B. and...