Probabilistic machine learning for detection of tightening torque in bolted joints

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.