Abstract
There have been increasing economic and societal demands to ensure the safety of structures against both long-term and short-term damage, and adequate performance during the life span of structures. In this work, a statistical FE model updating using the modal flexibility residual error, which is defined as the difference between the measured modal flexibility and the theoretical one from the FE model, is proposed for the probabilistic damage assessment. On the basis that the structural parameters in the FE model and the measured modal parameters exhibit uncertainties, it is of considerable importance to analyze the influences from both the FE model and the measured modal parameters on the damage identification results. Therefore, the proposed method are formulated on the basis of integrating the conventional FE model updating method with the perturbation statistical framework, and thus employ the probability algorithms, aiming at evaluating the effect of uncertainties in the damage identification results. The idea is that by expanding each term in the conventional FE model updating equations with second-order Taylor series expansion, two recursive systems of equations are derived for estimating the first two moments (mean and covariance) of random structural parameters. The derived means and covariance of random structural parameters are second-order accuracy, as approximating the non linear function between the structural parameters and the modal flexibility. The numerical studies of a cantilever beam are presented to illustrate the proposed method from not only detecting damages but also assessing damages in terms of probability under different level of uncertainties in the FE model and the measured modal flexibility. The results are verified by the Monte Carlo Simulation (MCS) method, and the distribution of structural parameters of the FE model is accepted as normal distribution with a confidence level of 95%. After simulations, it is found that the proposed method is more vulnerable to the random errors in the measured modal flexibility than in structural parameters of the FE model. The effects of modally and spatially incomplete information of modal parameters, and multiple and different level of damage are also investigated. Numerical simulations of a four-storey building are employed to compare the proposed method with another probabilistic damage assessment method, namely Bayesian probabilistic method. The results showed that the accuracy and robustness of the damage assessment using the proposed method are slightly lower than Bayesian probabilistic method, when there exist huge damages at multiple locations. However, when there exist small damages in the structure, accuracy and robustness of the damage detection using the proposed method are slightly higher than Bayesian probabilistic method. Lastly, experimental applications using the adhesively bonded GFRP beams are conducted in order to verify the proposed method. For comparison, three Non-FE model based damage assessment methods are also employed. The results showed that when the damage is severe, i. e. three GFRP plates are removed, both the proposed method and the considered three Non-Model based methods are able to identify the location and severity of the damage. However, when the damage is mild or insignificant the considered Nonmodel based methods are not clearly identify the location and severity of the damage, but the proposed method approximately assess the location and severity of the damage.