Modeling of Hammerstein-Wiener processes with special input test signals

Blocks in Hammerstein-Wiener nonlinear processes, in which an input static nonlinear block, a linear dynamic block, and an output static nonlinear block are connected in a series, have numbers of parameters, and their parametric identifications usually require solving multidimensional nonlinear optimization problems. Unless the initial values are appropriately determined, multidimensional nonlinear optimization methods suffer from poor convergence and heavy computational loads. To reduce such problems, three special test signals of two binary input signals and a multistep signal are proposed. Combining responses of these test inputs, the model parameters of each block in the Hammerstein-Wiener process can be identified sequentially without solving a multidimensional nonlinear optimization problem. From responses of two binary test inputs with different sizes, the model parameters of the output nonlinear static function are estimated by solving a one-dimensional nonlinear optimization problem and the linear dynamic block is identified using well-established linear system identification methods. Finally, the model parameters of the input nonlinear static function are analytically identified from the response of the multistep test signal.