Nonlinear Structural Model Updating Based On The Instantaneous Characteristics Of Decomposed Dynamic Responses

Civil structures subjected to complex natural environment and the extreme loads show the complex nonlinear properties. However, the existing finite element model updating methods are usually based on the hypothesis of the linear model. The updated model cannot represent the actual state and performance of the real structures. Thus, this thesis 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. Finally, the parameters of the nonlinear model are obtained by optimizing the objective function using the simulated annealing global optimization method.To validate the effectiveness of the proposed nonlinear structural model updating method, a three-story nonlinear shear type structure is simulated as a numerical example. In this thesis, 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. In the numerical simulation, the nonlinear structural model is updated for the nonlinear structure subjected to earthquake and harmonic loads. The noise effect is also considered. The simulation results show that, the time-varying filter can be designed based on the discrete analytical mode decomposition, and the principle component can be extracted; the instantaneous amplitude and frequency can then be extracted based on the Hilbert transform and analytical signal; the Bouc-Wen model parameters can be finally updated based on the proposed nonlinear model updating method.Finally, the proposed method is verified by two shake table tests. The first shake table test is a seven-story shear type structure under earthquake loads, and the second one is a switch-type structure under harmonic load. The nonlinear models of the two structures are also assumed as Bouc-Wen model. The nonlinear models of the two real structures are further updated based on the instantaneous features of measured dynamic responses. The experimental results have also 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.