Semi-empirical modeling of non-linear dynamical systems

The author is concerned with modeling problems where there are some empirical data, and some limited system knowledge available. In that case, first principles modeling may lead to an inaccurate model. Using the black-box alternative, not much of the system knowledge can be incorporated a priori. Hence, both these approaches have serious drawbacks in some cases. The proposed approach is based on the observation that for many systems, adequate models of the behavior within small operating regimes can be found without too much difficulty, while global models, covering all possible operating conditions, tend to be very complex and difficult or expensive to build. The author's approach is to construct local models for the various operating regimes, and build a global model by interpolating the local models. Globally, a large number of interacting phenomena can be observed. However, within one operating regime, only a small number of these phenomena will dominate, and the modeling problem be considerably reduced. If some phenomena are not understood, a black-box model representation combined with parameter estimation may be used in operating regimes where non-understood phenomena are significant.