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.