Correlation analysis-based parameter learning of Hammerstein nonlinear systems with output noise

Abstract

In this paper, a novel correlation analysis-based parameter learning scheme for Hammerstein nonlinear systems with output noise is presented. The developed Hammerstein system contains a static nonlinear block approximated by neural fuzzy network and a linear dynamic block modeled by transfer function, and parameter separation learning of the nonlinear block and linear block are realized by using combined signals. Firstly, based on the input and output of the separable signal, the correlation analysis algorithm is applied to estimate linear block parameters, thereby the interference of moving average noise is dramatically handled. Moreover, to improve parameter estimation precision of the learned Hammerstein system, multi-innovation theory and data filtering technology are introduced, and a data filtering-based multi-innovation stochastic gradient learning scheme is implemented for jointly estimating nonlinear block parameters and noise model using random signals. Studies with a numerical simulation and a practical nonlinear process demonstrate the efficiency. In the numerical simulation, when the noise to signal ratio is less than 33.37%, estimate error of the linear block parameters using least squares method is less than 0.0796. In contrast, estimate error of the proposed method is less than 0.0338. For the modeling ability of the nonlinear block, the proposed method has an improvement of 67.07% than the MI-ESG method with innovation length of six. With regard to practical nonlinear process, when the concentration set value is 0.1, the rise time of the proposed method is 0.021 h, while the rise time of MPC and traditional PI controller and is 0.055 h and 0.143 h, respectively.