Nonlinear structural model updating based on instantaneous frequencies and amplitudes of the decomposed dynamic responses

• A novel nonlinear model updating method is proposed.
• The objective function based on instantaneous characteristics is developed.
• The proposed method is validated by numerical simulations and shake table tests.
• The accuracy of the proposed method is quantified using the defined error indices.

This paper proposes a new nonlinear structural model updating method based on the instantaneous frequencies and amplitudes of the decomposed dynamic responses under forced vibration. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by analytical mode decomposition (AMD) and Hilbert transform. Then, an objective function based on the residuals of instantaneous frequencies and amplitudes between experimental structure and nonlinear model is created for calibration of the nonlinear model. In this paper, the structural nonlinear properties are simulated by using hysteresis material parameters of Bouc–Wen model, and the optimal values of the hysteresis parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a three-story nonlinear shear type structure under earthquake and harmonic excitations is simulated as a numerical example. Then, the proposed method is verified by the shake table test of a real high voltage switch structure under forced vibration. The updated nonlinear structural model is further evaluated by the shake table test of the switch structure subjected to a new severe excitation. Both numerical and experimental results have shown that the proposed method can effectively update the nonlinear model and the updated model can be further used to predict the nonlinear responses due to new severe excitations.