Modeling of Hammerstein−Wiener Processes with Special Input Test Signals

Abstract

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.

Improved system identification method for Hammerstein-Wiener processes

“…Remarks 1. The proposed activation method requires only one experiment, while the previous method [8] using two binary signals and one multi-step signal requires two experiments.…”

“…We can determine appropriately the scale of the minimum switching time for the binary signal and the multi-step signal on the basis of the period of the relay feedback signal. Meanwhile, the previous approach [8] has no a priori information to set the minimum switching time.…”

“…The corresponding upper value and the lower value of the output of the input nonlinear static function will be v u =f(u u ) and v l =f(u l ). Then, the first two terms in the Fourier series of the output of the input nonlinear static function are (8) The higher-order harmonic terms of the symmetric output are relatively small compared with the first two terms. Also, the process dynamics attenuates much more the higher-order harmonic terms than the first two terms.…”

“…However, none of the previous approaches could separate the identification problem of the linear dynamic subsystem from that of the output nonlinear static function. Recently, a new identification method [8] has been proposed to separate the three identification problems of the input nonlinear static function, the linear dynamic subsystem, and the output nonlinear static function using three special test signals of two binary input signals with different sizes and a multi-step signal. From two binary input tests, it estimates the model parameters of the output nonlinear static function by solving a one-dimensional nonlinear optimization problem.…”

“…In this research, we improve the previous strategy [8] to identify Hammerstein-Wiener processes by applying the recently proposed relay feedback method [27]. The proposed method activates the process using a relay feedback signal followed by a binary signal and a multi-step signal to separates the three identification problems of the input nonlinear static function, the linear dynamic subsystem, and the output nonlinear static function, which significantly simplifies the system identification procedure.…”