Quantitative evaluation of bolt pre-load using coda wave interferometry and nonlinear coda wave interferometry: a comparative study

The quantitative evaluation of bolt pre-load is crucial for the maintenance and prevention of accidents in bolt-connected structures. This study introduces the coda wave interferometry (CWI) method and the nonlinear coda wave interferometry (NCWI) method for quantitative evaluation of bolt pre-load. Experimental tests across three different scales of bolt pre-load changes were conducted on a bolt to compare the performances of CWI and NCWI in the quantitative evaluation of bolt pre-load. The results demonstrate that both CWI and NCWI can effectively characterize changes in bolt pre-load. For CWI, the relative velocity change (∆v/v) exhibits a linear relationship with the bolt pre-load. Meanwhile, for NCWI, the effective nonlinear level, denoted as \({\alpha }_{\Delta v/v}\) ${\alpha }_{\mathrm{\Delta }v/v}$ , demonstrates a quadratic dependence on the bolt pre-load. In CWI, the calculation of ∆v/v is dependent on the correlation coefficient between the coda waves of signals before and after bolt pre-load changes. It is prone to failure when there are significant changes in bolt pre-load. Conversely, NCWI demonstrates enhanced robustness in evaluating bolt pre-load changes across a range of magnitudes.