Detection Method for Rail Bottom Cracks Based on Frequency Response Function Curvature Differential Correlation Analysis

［Objective］ Detection methods based on vibration characteristics are widely applied for structural damage monitoring in urban rail transit systems. However, in practical applications, it is challenging to obtain the modal shapes of structures, necessitating the exploration of more effective methods for detecting rail bottom cracks. ［Method］ A new rail bottom crack detection method based on frequency response function (FRF) variation is proposed. First, a SDOF (single degree of freedom) system is used to illustrate the dynamic characteristic change induced by cracks. The Pearson Correlation Coefficient is employed to analyze the correlation between the FRF (frequency response function), FRFC (frequency response function curvature) and FRFCD (frequency response function curvature differentiation) of undamaged and damaged systems. Taking a cracked rail as the research subject, a combination of finite element simulation and frequency response experiments is used to investigate the relationship between crack size and the correlation coefficients of FRF, FRFC, and FRFCD. ［Result & Conclusion］ When the rail structure is intact, the correlation coefficients of FRF, FRFC, and FRFCD are close to 1. When a rail crack occurs, as the crack depth increases, the absolute values of the correlation coefficients between the intact and the cracked rail progressively decrease from 1 toward 0. Moreover, the FRFCD correlation coefficient exhibits significantly higher sensitivity to cracks compared to FRF and FRFC correlation coefficients. The crack identification method based on the FRFCD correlation coefficient effectively distinguishes cracked structures from intact ones, reducing false positives in crack structure.