Bolt tension estimation through closed-loop model updating

The task of detecting and quantifying bolt loosening in structural joints has proven amenable to
a solution in a vibration-based model updating framework. In this setting, a model parameterization characterizing the bolt tension is formulated and updated to minimize the discrepancy between experimentally obtained modal data and the corresponding model predictions. A limitation that detracts notably from the practicability of the approach is that the identifiable modal data will often be insufficient to render the model updating problem well-posed. The present paper proposes a technique that enables a remediation of the noted issue through output feedback, which is implemented offline by processing of measured open-loop (OL) excitation input and vibration output. The offline implementation allows computation of multiple closed-loop (CL) eigenstructures based on a single OL input-output realization, thus the modal data to be used for model updating can be readily augmented. The paper outlines the methodological concept behind the CL bolt tension estimation technique and examines its merit in the context of analytical and numerical examples.