Load state identification of rock bolts based on energy and multiscale permutation entropy of ultrasonic signals

Monitoring the load state of rock bolts is of great importance for ensuring the safe operation of geotechnical and underground structures. In view of the pronounced stage-dependent variation of ultrasonic response characteristics under complex contact interface conditions at the anchorage end, this study proposes a stage-wise identification method for rock bolt load states based on wave energy and multiscale permutation entropy (MPE). Starting from the mechanical evolution of the anchorage interface, wavelet packet energy is employed in the low-load stage to characterize the global response dominated by the average contact stiffness, while MPE is introduced in the high-load stage to capture the enhanced interface nonlinearity and the evolution of signal complexity. In this way, stable identification of the rock bolt load state over the entire loading range is achieved. To validate the proposed method, a multi-path piezoelectric (PZT) excitation-reception experimental system was established, and ultrasonic reflection signals were collected under different working conditions and loading levels. The experimental results indicate that wavelet packet energy exhibits high sensitivity to variations in bolt load during the low-load stage, whereas MPE shows a stable and monotonic evolution with increasing load in the high-load range. Owing to the complementary characteristics of the two features across different loading stages, the proposed stage-wise identification strategy enables full-range characterization of the rock bolt load state. The findings provide a physically interpretable ultrasonic monitoring approach for assessing the load state of rock bolts under complex contact interface conditions.