Abstract: Hammerstein–Wiener model is a block-oriented model
where a linear dynamic system is surrounded by two static
nonlinearities at its input and output and could be used to model
various processes. This paper contains an optimization approach
method for analysing the problem of Hammerstein–Wiener systems
identification. The method relies on reformulate the identification
problem; solve it as constraint quadratic problem and analysing its
solutions. During the formulation of the problem, effects of adding
noise to both input and output signals of nonlinear blocks and
disturbance to linear block, in the emerged equations are discussed.
Additionally, the possible parametric form of matrix operations
to reduce the equation size is presented. To analyse the possible
solutions to the mentioned system of equations, a method to reduce
the difference between the number of equations and number of
unknown variables by formulate and importing existing knowledge
about nonlinear functions is presented. Obtained equations are applied
to an instance H–W system to validate the results and illustrate the
proposed method.
Abstract: Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.