Minimal parameterizations in diagnosis-oriented multivariable identification

Dynamical systems can be described by several classes of models and it is also possible to define, inside most of these classes, equivalence relations that have no influence on the input–output behaviour of the system. For most applications it is thus possible to use any model inside an equivalence class and, in fact, this possibility is widely used in the solution of analysis and synthesis problems (e.g. changes of basis in the state space for state space models). When the models are used for identification purposes, however, the use of non minimally parameterized models leads to a larger dispersion of the parameter estimates with obvious negative effects on fault detection and localization procedures based on the values of the parameters of identified models. This paper defines the minimal number of parameters that can describe a dynamical system on the basis of the invariance properties of equivalence relations defined inside the considered class of models and shows, by means of Monte Carlo simulations, that also modest overparameterizations can lead to remarkable increases in the dispersion of the parameter estimates.