Study on an auto-correlation-function-based damage index: Sensitivity analysis and structural damage detection

The damage index based on the auto correlation function to detect the damage of the structure under white noise excitation is studied in detail in this paper. The maximum values of the auto correlation function of the vibration response signals (displacement, velocity and acceleration) from different measurement points of the structure are collected and formulated as a vector called Auto Correlation Function at Maximum Point Value Vector (AMV), which is expressed as a weighted combination of the Hadamard product of two mode shapes. AMV is normalized by its root mean square value so that the influence of the excitation can be eliminated. Sensitivity analysis for the different parts of the normalized AMV shows that the sensitivity of the normalized AMV to the local stiffness is dependent most on the sensitivity of the Hadamard product of the two lower order mode shapes to the local stiffness, which has a sudden change of the value around the local stiffness change position. The sensitivity of the normalized AMV has the similar shape and same trend that shows it is a very good damage indicator even for the very small damage. The relative change of the normalized AMV before and after damage occurs in the structure is adopted as the damage index to show the damage location. Several examples of the stiffness reduction detection of a 12-story shear frame structure are utilized to validate the results in sensitivity analysis, illustrate the effectiveness and anti-noise ability of the AMV-based damage detection method and compare the effect of the response type on the detectability of the normalized AMV.