Structural health monitoring by bayesian updating

For any structure the problems of damage detection and reliability assessment are closely related, and should be dealt with in a unified approach. In fact, the health monitoring of a damaged construction requires both damage detection (that is, identification, quantification, and localization of damages) and the assessment of the effects of damages on the life-cycle reliability. Actually, structural reliability theory provides the tools to assess, in a rational way, the effects of damages on the lifetime performance of a structure, taking into account the various sources of uncertainty. In this paper, a complete procedure for structural health monitoring, that is, for both damage detection and reliability assessment of a structure subject to seismic excitation, is briefly illustrated and applied to an example case. The problem of damage detection is dealt with by an identification technique with unknown input; a Bayesian model updating procedure is adopted to quantify the damage to the structure based on the data from monitoring. Bayesian updating is based on an adaptive Markov Chain Monte Carlo method: the knowledge of the modal quantities of the undamaged and damaged structure is used to update the stiffness parameters that are chosen as the damage indicators. An advanced simulation technique, Subset Simulation, is then used to assess the probability of exceeding any structural response level, that is, the risk for the damaged structure. The procedure is formulated in a unified probabilistic framework that takes into account any kind of uncertainty involved in the various phases of the analysis. It is observed that the Bayesian approach is really efficient in characterizing the structural damage and its effects in probabilistic terms: the main reason is that this approach gives as final result the probability density functions of the identified parameters, which in turn can be used in any structural reliability assessment. Moreover, Subset Simulation requires a much smaller number of samples than Monte Carlo simulation; this advantage is essential, especially for structures which exhibit a strongly nonlinear behaviour when subject to seismic excitation.