Likelihood-based testing of wavelet coefficients for damage detection in beam structures

Early detection of damage has emerged as an important concern for engineers involved in structural condition assessments. This paper presents a damage detection approach that combines different techniques to improve detection and localization of small increments of damage using mode shapes derived from vibration tests on a structure. An experimental study is carried out on a beam with two joints that can simulate incremental damage with a system of plates and bolts. The initial condition is defined as the state when the plates are fully assembled. In this state, the beam comprises two weaker zones at the location of each joint assembly due to a 12% reduction in stiffness in comparison to an intact beam. The test setup is used to simulate incremental damage by modifying the mass and stiffness of the beam at each joint. The proposed method of detection is shown to outperform current alternative methods in detecting small increments of damage and to result in fewer false alarms. The detection procedure comprises four steps: (1) a continuous wavelet transform to detect local anomalies in the first mode shape; (2) a principal component analysis of wavelet coefficients to extract dominant patterns that are most highly correlated with incremental damage and to reduce noise; (3) statistical tests of hypothesis on the scores of principal components to detect statistically significant incremental damage, and (4) a likelihood ratio test to determine the most likely location of incremental damage along the beam.