A method for multi-frequency guided wave response characterization and tightness assessment of bolted joint structures

Bolted joints, as vital connecting components, significantly influence structural safety and performance through their fastening conditions. To address limitations of existing methods—including strong frequency dependence, the Greenwood–Williamson microcontact theory is employed to establish a physical mapping between preload and guided wave leakage energy. Finite element simulations verify the non-monotonic response characteristics of single-frequency guided wave energy indicators under different excitation frequencies, highlighting the influence of frequency selection on identification results. Based on this, a Chirp-excited frequency-domain reconstruction method is used to extract multiple narrowband responses in the range of 50–180 kHz, and a weight optimization strategy is applied to achieve multi-frequency energy fusion, yielding the bolt tightness index ( T I ). Results from three repeated loading tests demonstrate good linear correlation between the fused indicator and preload, with fitting performance superior to any single-frequency damage index, mutually validating the simulation findings. To enhance environmental robustness, a bivariate energy-temperature regression model compensates for temperature drift. Validation in 25–60 °C confirms compensated model R 2 >0.98 under typical preloads, with R M S E as low as 1 . 2 × 1 0 − 5 , highlighting precision and generalizability. Finite element simulations further verify that increased preload enhances contact area and wave transmission efficiency, corroborating the model’s physical validity. In summary, this method delivers exceptional accuracy, stability, and engineering applicability, providing theoretical and technical foundations for high-reliability health monitoring of bolted structures.