Structural modeling of Wiener-Hammestein system in the presence of the process noise

The identification of Wiener-Hammerstein (WH) systems has received intensive attention without the presence of the process noise, see the Special Section in Control Engineering Practice [1] and the algorithms reported therein. The WH model identification with the process noise preceding the static nonlinearity is recently considered with a cost function of totally different formulation [2]. So it is primary to determine the location where the process noise enters into the WH model prior to implementing any algorithm for consistent identification. The goal of this paper is to propose a simple protocol to differentiate Case I and Case II (see Fig. 1), providing a good block-oriented model structure for the WH model identification.