Unified Probabilistic Approach for Model Updating and Damage Detection

A probabilistic approach for model updating and damage detection of structural systems is presented using noisy incomplete input and incomplete response measurements. The situation of incomplete input measurements may be encountered, for example, during low-level ambient vibrations when a structure is instrumented with accelerometers that measure the input ground motion and the structural response at a few instrumented locations but where other excitations, e.g., due to wind, are not measured. The method is an extension of a Bayesian system identification approach developed by the authors. A substructuring approach is used for the parameterization of the mass, damping and stiffness distributions. Damage in a substructure is defined as stiffness reduction established through the observation of a reduction in the values of the various substructure stiffness parameters compared with their initial values corresponding to the undamaged structure. By using the proposed probabilistic methodology, the probability of various damage levels in each substructure can be calculated based on the available dynamic data. Examples using a single-degree-of-freedom oscillator and a 15-story building are considered to demonstrate the proposed approach.