  Block-oriented nonlinear models are popular in nonlinear modeling because of
their advantages to be quite simple to understand and easy to use. To increase
the flexibility of single branch block-oriented models, such as Hammerstein,
Wiener, and Wiener-Hammerstein models, parallel block-oriented models can be
considered. This paper presents a method to identify parallel
Wiener-Hammerstein systems starting from input-output data only. In the first
step, the best linear approximation is estimated for different input excitation
levels. In the second step, the dynamics are decomposed over a number of
parallel orthogonal branches. Next, the dynamics of each branch are partitioned
into a linear time invariant subsystem at the input and a linear time invariant
subsystem at the output. This is repeated for each branch of the model. The
static nonlinear part of the model is also estimated during this step. The
consistency of the proposed initialization procedure is proven. The method is
validated on real-world measurements using a custom built parallel
Wiener-Hammerstein test system.
