LAUSR

Observing the loss of tightening torque using modal parameters is challenging due to the variability and nonlinear effects in bolted joints. Thus, this paper proposes a combined application of two probabilistic machine learning methods. First, a Gaussian mixture model (GMM) is learned using estimated natural frequencies, assuming the tightening torque in a safe situation. This probabilistic model can assuredly detect the lack of torque using indirect vibration measures in other unknown states by computing a damage index. A Gaussian process regression (GPR) is also learned considering a set of torque and damage index pairs in several conditions. The GPR model interpolates a curve to supply an estimative of the tightening torque for other conditions not used in this learning. An illustrative application is performed considering the Orion beam, an academic-scale specimen composed of a lap-joint configuration that retains the friction surface in contact patches. The structure is subjected to a random vibration with a controlled RMS level and several tightening torque conditions to identify the modal parameters. The probabilistic model learning via the GMM and GPR can detect adequately, with a low number of false diagnoses, the actual state of torque using an indirect measure of vibration, that is, without the need for a torque sensor on each bolt.