Bayesian based nonlinear model updating using instantaneous characteristics of structural dynamic responses

Abstract This paper proposes a Bayesian based nonlinear model updating approach using the instantaneous amplitudes of the decomposed dynamic responses. Uncertainty quantification of the model updating results due to the measurement noise is conducted. The residual of the instantaneous amplitudes of the decomposed structural dynamic responses between the test structure and the analytical nonlinear model is used to construct the maximum likelihood function. Since nonlinear model parameters and simulated error variances of the instantaneous parameters are all unknown, the extended maximum likelihood estimation method is used to update these parameters. The uncertainty in the updated nonlinear model parameters can be evaluated by using the Cram-Rao lower bound theorem with the exact Fisher Information matrix. A numerical study on a three-storey building structure model under earthquake excitation is performed to verify the accuracy and performance of the proposed approach. An experimental verification on a high voltage switch structure under harmonic excitation is conducted to investigate the accuracy of using the proposed approach for nonlinear model updating. Both numerical and experimental results demonstrate that the proposed approach is reliable and accurate for nonlinear model updating, with the capacity of considering the uncertain noise effect in the measurements.