Bayesian methodology for structural damage identification and reliability assessment.

A Bayesian framework is presented for structural model selection and damage identification utilizing measured vibration data. The framework consists of a two-level approach. At the first level the problem of estimating the free parameters of a model class given the measured data is addressed. At the second level the problem of selecting the best model class from a set of competing model classes is addressed. The application of the framework in structural damage detection problems is then presented. The structural damage detection is accomplished by associating each model class to a damage location pattern in the structure, indicative of the location of damage. Using the Bayesian model selection framework, the probable damage locations are ranked according to the posterior probabilities of the corresponding model classes. The severity of damage is then inferred from the posterior probability of the model parameters corresponding to the most probable model class. Computational issues are addressed related to the estimation of the optimal model within a class of models and the optimal class of models among the alternative classes. Asymptotic approximations as well as Monte Carlo simulations are used for estimating the probability integrals arising in the formulation. The framework can be used for assessing the reliability of structures based on the measured vibration data. The proposed methodology is illustrated by applying it to the identification of the location and severity of damage of a laboratory small-scaled bridge using measured vibration data.