Identification of nonlinear Hammerstein system using mixed integer-real coded particle swarm optimization: application to the electric daily peak-load forecasting

This paper investigates the modeling of a class of dynamic systems using nonlinear Hammerstein (NLH) model composed of a memory-less polynomial block cascaded to an autoregressive with exogenous input (ARX) time-series block. The model thus defined is known as NLHARX. Both the integer orders and the real coefficients of the model are identified simultaneously in a unified framework using a new algorithm based on a mixed coded integer-real particle swarm optimization. Unlike classical identification methods which assume the orders to be known in advance, the proposed approach is new since it estimates both the real and integer design parameters while minimizing the error between the outputs of the system and the model. The usefulness and the effectiveness of the proposed approach have been demonstrated through extensive simulations. Two illustrative examples are included in this paper: an empirical example and an application to the forecasting of the daily peak-load of Hail region, Saudi Arabia. Future works will be devoted to the identification of more complex dynamic systems, such as Hammerstein–Wiener and the application to the prediction of time-series related to water and energy.