Considering the measurement noise for a nonlinear system identification with evolutionary algorithms

This paper deals with the identification of a nonlinear system modelled by a nonlinear output error (NOE) model when the system output is disturbed by an additive zero-mean white Gaussian noise. In that case, standard on-line or off-line least squares methods may lead to poor results. Here, our approach is based on evolutionary algorithms. Although their computational cost can be higher than the above methods, these algorithms present some advantages, which often lead to an “effortless” optimisation. Indeed, they do not need an elaborate formalisation of the problem. When their parameters are correctly tuned, they avoid to get stuck at a local optimum. To take into account the influence of the additive noise, we investigate different approaches and we suggest a whole protocol including the selection of a fitness function and a stop rule. Without loss of generality, simulations are provided for two nonlinear systems and various signal-to-noise ratios.