Optimization Approach to Estimate Hammerstein–Wiener Nonlinear Blocks in Presence of Noise and Disturbance

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.

Authors:

• Leili Esmaeilani
• Jafar Ghaisari
• Mohsen Ahmadian

Keywords:

• Identification
• Hammerstein-Wiener
• optimization
• quantization.

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