  Block-oriented models are often used to model nonlinear systems. These models
consist of linear dynamic (L) and nonlinear static (N) sub-blocks. This paper
addresses the generation of initial estimates for a Wiener-Hammerstein model
(LNL cascade). While it is easy to measure the product of the two linear blocks
using a Gaussian excitation and linear identification methods, it is difficult
to split the global dynamics over the individual blocks. This paper first
proposes a well-designed multisine excitation with pairwise coupled random
phases. Next, a modified best linear approximation is estimated on a shifted
frequency grid. It is shown that this procedure creates a shift of the input
dynamics with a known frequency offset, while the output dynamics do not shift.
The resulting transfer function, which has complex coefficients due to the
frequency shift, is estimated with a modified frequency domain estimation
method. The identified poles and zeros can be assigned to either the input or
output dynamics. Once this is done, it is shown in the literature that the
remaining initialization problem can be solved much easier than the original
one. The method is illustrated on experimental data obtained from the
Wiener-Hammerstein benchmark system.
