Ultrasonic nonlinear behaviour of the bolt end in a half-grouted splice sleeve: comparison of phase-space and frequency domains

The insufficient torque value of the threaded end of a half-grouted splice sleeve (HGSS) rebar may cause slippage between the rebar and sleeve, leading to brittle failure in high-rise and underground structures. Therefore, accurate torque monitoring is essential. Traditional nonlinear ultrasonic detection methods analyse the system in the frequency domain, which may lose part of the system information. By contrast, phase-space-domain analysis can preserve more complete dynamic characteristics. This study proposes a novel nonlinear ultrasonic detection method based on the phase space domain for measuring the torque value of HGSS threaded end rebar. A torque evaluation index is established using recursive quantification analysis. The proposed method is compared with high-order nonlinear parameters derived from fast Fourier transform and wavelet packet transform analyses. Results demonstrate that the proposed method achieves higher accuracy, with R2 reaching above 0.86 under different excitation amplitudes, indicating robustness to excitation conditions. In addition, this study verifies the applicability of the method to different HGSS sizes. An increase in HGSS size, i.e. an increase in weak bond layer size, strengthens the nonlinear effect of ultrasound. The findings provide a basis for developing mathematical models describing the interaction between the HGSS threaded end and nonlinear ultrasonic wave.