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Conventional Volterra series model is hardly applied to engineering practice due to its parametric complexity and estimation difficulty. To solve this problem, nonlinear system identification using reduced complexity Volterra models is proposed. Since the nonlinear components often play a secondary role compared to the dominant, linear component of the system, they spend the most of identification cost. So it is worth establishing a balance between identification cost and model accuracy by reducing the complexity of nonlinear components. Refer to the idea of nonlinear output frequency response function, conventional Volterra model is simplified. And then a minimum mean square error criterion based method to identify the simplified model is proposed. The distinguishing feature of this method is high accuracy, good robustness, and significant reduction in the computational requirements compare to the identification of conventional Volterra models. The simulation show that the proposed method is effective, and the reduced complexity Volterra model is of good generalization ability in general. So this nonlinear system identification approach is quite applicable to engineering practice.

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Abstract. In this paper, modeling a weakly nonlinear system whose nonlinearity is up to the second order is studied. During this task a second order Hammerstein series model is used because it can lead to a trade-off between computational cost and generalization ability. To extract such model form measured input-output data, a nonparametric algorithm based on the minimum mean square error criterion is proposed. The polyspectrum up to order 4 is used to determine the Hammerstein kernels, while the input is a random multi-sine signal. Finally the proposed modeling method is validated on simulated system.