Global analysis and model validation in nonlinear system identification

Abstract

The analysis of parameterised nonlinear models is considered. In particular the emphasis is placed on models produced as a result of applying nonlinear system identification techniques. A qualitative approach is taken, calling upon ideas from bifurcation theory. When combined with an existing numerical method this approach enables the analysis of a variety of nonlinear model forms to be carried out. The combination of qualitative and numerical aspects provides a flexible framework for analysis and in addition adds a global perspective that is difficult to achieve using analytical methods alone. When combined with the well tried methods of system identification, the approach allows the validation of nonlinear models from a qualitative viewpoint to be carried out. The method contrasts well with the statistical model validation techniques traditionally used. The technique is applied to a number of examples.