Establishment and identification of MIMO fractional Hammerstein model with colored noise for PEMFC system

In order to solve the problems of nonlinearity, strong coupling and fractional order characteristics of multiple physical and chemical processes in the proton exchange membrane fuel cell (PEMFC) system modeling process, this paper proposes a multiple-input multiple-output (MIMO) fractional-order Hammerstein model with colored noise based on a data-driven method to describe the PEMFC system. First, in order to reduce the modeling complexity and improve the calculation efficiency, the canonical correlation analysis (CCA) and the correlation analysis (CA) are combined to select the controllable variables with the greatest correlation with the system output as the model input variables; Secondly, the fractional order theory is combined with the Hammerstein model, and the MIMO fractional order Hammerstein model with colored noise is derived by taking into account the complexity of the actual noise of the PEMFC system; Then, on this basis, it is proposed to combine the multi-innovation identification principle with the Levenberg–Marquardt algorithm, make full use of current data and historical data to improve the identification accuracy, and thereby estimate the unknown parameters of the system and the fractional order of the system. Finally, experiments based on actual data verified the accuracy and effectiveness of the proposed modeling method and identification algorithm. The method proposed in this paper can significantly improve the identification accuracy, and the established identification model of the PEMFC system can accurately describe its true dynamic process.