Identification of the Hammerstein nonlinear system with noisy output measurements

In this research, we present a methodology to identify the Hammerstein nonlinear system with noisy output measurements. The Hammerstein system presented is comprised of neural fuzzy model (NFM) as its static nonlinear block and auto-regressive with extra input (ARX) model as its dynamic linear block, and a two-step procedure is accomplished using signal combination. In the first step, in the case of input–output of Gaussian signals, the correlation function-based least squares (CF-LS) technique is utilized to identify the linear block, solving the problem that the intermediate variable connecting nonlinear and linear blocks cannot be measured. In the second step, to improve the identification accuracy of the nonlinear block parameters, an improved particle swarm optimization technique is developed under input–output of random signals. The validity and accuracy of the presented scheme are verified by a numerical simulation and a practical nonlinear process, and the results illustrate that the proposed methodology can identify well the Hammerstein nonlinear system with noisy output measurements.