Simulation error minimization methods for NARX model identification

In non-linear model identification the problem of model structure selection is critical for the success of the identification process. This paper discusses this problem with reference to the class of polynomial NARX models. First it is shown that classical identification approaches based on (one-step-ahead) Prediction Error Minimisation (PEM) may lead to an incorrect or redundant model structure selection, especially in non-ideal identification conditions where the identification data are not adequately exciting or over-sampled. Then a more effective approach is introduced, based on the minimisation of the simulation (or model prediction) error. Finally, to reduce the computational load required for the evaluation of the simulation error, a two-stage identification algorithm, that exploits the effect of the choice of the sampling time on structure selection is proposed. A coarse identification of the model structure is initially performed using over-sampled input-output data, and then the structure is refined considering a decimated version of the data. Some simulation and experimental examples are also discussed.