Coupling error correction method for bolt stress ultrasonic measurement based on echo compensation of thread transition zone

To address the problem that fluctuations in coupling-layer thickness in contact ultrasonic measurement of bolt axial stress can easily induce time-of-flight (TOF) drift and consequently significantly reduce the measurement accuracy in the low-stress region, this paper proposes a coupling-error compensation method based on thread transition echo (TTE). In this method, the scattered echo generated by the geometric discontinuity in the thread transition zone is used as an internal reference echo. An coupling-error compensation is established, and the linear relationship between the compensated TOF and the axial stress is derived. Because the TTE is weak and susceptible to structural scattering and random noise, a joint denoising method based on successive variational mode decomposition (SVMD) and an improved wavelet threshold is proposed. In combination with Gabor time–frequency energy peak-cluster localisation, stable extraction of the TTE-TOF is achieved. Experiments using a contact ultrasonic pulse-echo system and axial tensile loading show that the proposed method exhibits better linear fitting accuracy and limits the average measurement error to within 4%, compared with approximately 8% for the conventional method. Moreover, the proposed method requires no bolt modification or complex sensing devices, demonstrating low implementation cost and potential for engineering applications.