COMBINING SEMI-PHYSICAL AND NEURAL NETWORK MODELING: AN EXAMPLE OF ITS USEFULNESS U. FORSSELL AND P. LINDSKOG

We illustrate the power of combining semi-physical and neural network modeling in an application example. It is argued that some of the problems related to the use of neural networks, such as high dimensionality of the parameter space and problems with local minima, can be alleviated using this approach. 1. INTRODUCTION System identiication as described by, e.g., Ljung (1987) is a well established methodology for designing mathematical models of dynamical systems using input-output data. After experiment design, the problem can be split into two parts: model structure selection followed by parameter estimation. While various least-squares type of algorithms are predominant for parameter estimation , one has a large spectrum of model structure approaches to choose between. Physically parameterized modeling (where all physical insight about the system is condensed into the model) is a quite time-consuming procedure that normally requires a lot of prior, which can be more or less hard to acquire. However, such an approach often leads to models that are parsimonious with parameters to estimate, a property that is highly desired in identiication. On the other extreme we have the black box approach , where the models are searched for in a suuciently exible model family. Instead of incorporating prior system knowledge, such a procedure uses \size" as the basic structure option, i.e., the models typically involve a large number of parameters so that the unknown function can be approximated without too large a bias (at least in theory). This approach requires much less engineering time but depends heavily on the data quality. For nonlinear systems, neural networks (NNs) is one out of many possible and reasonable choices within this category. Between these modeling extremes there is a large zone where important physical knowledge as well