NARMAX model based pseudo-Hammerstein identification for rate-dependent hysteresis

In this paper, a nonlinear auto-regressive moving average model with exogenous inputs (NARMAX) based pseudo-Hammerstein model is proposed for the identification of rate-dependent hysteresis. The presented model has the cascade structure comprised of a NARMAX model in series with an auto-regressive moving average (ARMA) model. In view of the multivalued mapping of hysteresis, a hysteretic operator is introduced to establish an expanded input space for the NARMAX model where the change tendency of the rate-dependent hysteresis can be extracted. To avoid the tedious dynamic back-propagation optimization for the auto-regressive (AR) parameters of the NARMAX model within the pseudo-Hammerstein model, a NARMAX model with the introduced hysteretic operator is applied to implement a preliminary identification for the rate-dependent hysteresis. Both the modified Akaike information criterion (MAIC) and the recursive least squares (RLS) algorithm are employed to estimate an appropriate structure and the AR parameters of the NARMAX model. Subsequently, the Levenberg-Ma-rquardt (L-M) algorithm of the pseudo-Hammerstein model is developed to acquire an appropriate structure and the parameters of the ARMA model as well as the remaining parameters of the NARMAX model. Finally, numerical simulation results on a Duhem model of the piezoelectric actuators have demonstrated the effectiveness of the proposed model.