A modified virtual time reversal method for enhancing monitoring sensitivity of bolt preloads based on ultrasonic guided waves

Bolted joints are prone to loosening due to inaccurate initial preloads and time-varying service conditions. Real-time monitoring of bolt preloads is therefore an important means to warrant the reliability and safety of a bolted structure, though it remains a daunting task to implement precise monitoring of early bolt loosening. A modified virtual time reversal (MVTR) method is developed in this study, aimed at enhanced sensitivity of bolt preload monitoring. To begin with, the frequency response function (FRF) of an intact bolted structure is ascertained using the excitation wave and the received wave signal through the bolt. Then a received wave signal captured from the bolted structure under monitoring is time-reversed, and a refocused signal is calculated in virtue of the time-reversed signal and the FRF in the intact state. Bolt tightness indices are established by the peak amplitude or energy of the refocused wave packet. To facilitate interpretation of the principle of the proposed MVTR, a semi-analytic model is developed, which combines the waveform superposition method and finite element method. With the model, the effects of interface contact length, wave mode and signal frequency on the tightness indices are investigated. The effectiveness of the proposed MVTR is experimentally verified using three representative bolted lap structures featuring single bolt or multiple bolts. The results confirm the findings from the semi-analytic model, demonstrating that the MVTR enhances monitoring sensitivity compared to prevailing approaches using linear or nonlinear guided wave features.