Markov chain Monte Carlo-based Bayesian method for structural model updating and damage detection

This paper proposes a Bayesian method for structural model updating and damage detection using modal data. A recently developed Markov chain Monte Carlo algorithm is adopted to handle the model updating problem. The proposed Bayesian method focuses on calculation of the posterior probability distribution function of uncertain model parameters. In addition to the most probable values of the uncertain parameters, the associated uncertainties can be calculated with consideration of the effects of both the modeling error and the measurement noise. An experimental case study was carried out with a shear building model under laboratory conditions to study the identifiability of the model-updating problem following the proposed Bayesian method. The results demonstrate the change in the posterior probability distribution function of the uncertain parameters with the amount of measured information. It also demonstrates the ability of the proposed method to handle unidentifiable problems. The proposed Bayesian method is then applied for structural damage detection by calculating the probability distribution of the extent of damage to various structural components. To demonstrate the proposed Bayesian damage-detection method, ambient vibration tests were carried out on a 2-story steel frame with bolted connections. Joint damage was simulated by loosening some bolts at the target beam-column connection. The model-updating results show that the uncertainty associated with the rotational stiffness of the steel joints was very high, rendering the problem almost unidentifiable. Although the problem is almost unidentifiable, the calculated probability distribution of the damage extent can still locate the damaged joint and estimate the damage extent (i.e., the percentage reduction in rotational stiffness) together with the associated uncertainty.