Prediction error identification of Hammerstein models in the presence of ARIMA disturbances

In this paper, an algorithm is developed for the identification of a Hammerstein system in the presence of non-stationary measurement noise in the form of an Auto Regressive Integral Moving Average (ARIMA) model. Many systems used in the chemical process control industry can be modelled with the Hammerstein structure, a block oriented model consisting of a memoryless non-linearity followed by a linear filter. However, these systems are often subject to random step disturbances which violate the stationarity assumptions required by most system identification algorithms. Stationarity can be restored by differencing the measured output. As a result, parametric identification methods are applied to approximate the elements of the modified plant, and noise models, as well as the non-linearity simultaneously using prediction error minimization based approaches. Instrumental Variable methods are employed to generate good initial estimates of these systems, and so to decrease the chances of the optimization getting caught in suboptimal local minima. Estimates of the original system components are then recovered from the identified model. Monte-Carlo simulation and high-order correlation-based validation tests are used to demonstrate the performance of the algorithm.