Parameter identification for damaged condition investigation on masonry arch bridges using a Bayesian approach

In this work, an inverse analysis procedure adopting a Bayesian approach is proposed as a numerical tool to investigate the causes that have led a masonry arch bridge to be in a certain pathological condition. Within this framework, the damaged condition investigation is formulated as a parameter estimation problem. A nonlinear finite element model is developed, and the implementation of plausible loading scenarios together with possible initial undamaged configurations of the bridge is then carried out. Computer model predictions are subsequently compared against real, measured geometrical data. The aim of the identification problem is to obtain the distribution of the most likely values of the parameters of the mechanical model so that the numerical predictions reproduce with the highest accuracy the existing damage pattern. The posterior probability distributions of the unknown parameters are estimated via the use of simulation techniques, namely, the Markov chain Monte Carlo (MCMC) method. The computational burden associated with both the MCMC sampling procedure and the time-consuming numerical model is alleviated by the adoption of a Gaussian process emulator. The feasibility of the practical implementation of the method is tested on a real case study located in Kakodiki village on the island of Crete (Greece). The results indicate that reasonable inferences about the original geometry of the bridge, as well as possible damage loading scenarios, can be made, resulting in a nearly identical crack pattern with respect to the present damaged state. The possibility of exploiting the posterior distributions of the model updating parameters for subsequent structural assessment tasks is also shown, allowing probabilistic simulation outcomes from which a more reliable judgement of the actual bridge safety condition can be established. The application of the proposed methodology would result in a better understanding of the underlying mechanisms triggering damage while also providing useful guidelines for decision making, such as those related to the planning of adequate maintenance actions and the selection of optimal strengthening measures.