A subspace-based identification of Wiener–Hammerstein benchmark model

• A new method of identifying Wiener–Hammerstein systems is developed.
• The ORT subspace method is used for identifying the best linear model.
• The poles of the best linear model are allocated between two linear subsystems.
• For each allocation, unknown parameters are estimated by separable least-squares.
• The best configuration that yields the minimum mean square error is selected.

This paper develops a subspace-based method of identifying the Wiener–Hammerstein system, where a nonlinearity is sandwiched by two linear subsystems. First, a state space model of the best linear approximation of it is identified by using a subspace identification method and the poles of the best linear model are allocated between two linear subsystems by a state transformation. Unknown system parameters and coefficients of a basis function expansion of the nonlinearity are estimated by using the separable least-squares for all possible allocations of poles, so that there is a possibility that many iterative minimization problems should be solved. Finally, the best Wiener–Hammerstein system that yields the minimum mean square error is selected. Numerical results for a benchmark model show the applicability of the proposed method.