Global Analysis and Model Validation in Nonlinear System Identification

The analysis of parameterised nonlinear models is considered. In particular the emphasis is on models produced as a result of applying nonlinear system identification techniques. A qualitative approach is taken which calls upon ideas from bifurcation theory, which when combined with an existing numerical method enables the analysis of a wide variety of nonlinear model forms. The combination of qualitative and numerical aspects provides a flexible framework for analysis at the same time as providing a global perspective that is difficult to achieve using analytical methods alone. When combined with the well tried methods of system identification, the approach enables the validation of nonlinear models from a qualitative viewpoint. This contrasts well with the statistical model validation techniques used in identification. The technique is applied to a number of examples to illustrate the effect of input design and signal to noise ratio on the modelling process.