Damage detection using piezoelectric transducers and the Lamb wave approach: II. Robust and quantitative decision making

The propagation of Lamb waves generated by piezoelectric transducers in a one-dimensional structure has been studied comprehensively in part I of this two-paper series. Using the information embedded in the propagating waveforms, we expect to make a decision on whether damage has occurred; however, environmental and operational variances inevitably complicate the problem. To better detect the damage under these variances, we present in this paper a robust and quantitative decision-making methodology involving advanced signal processing and statistical analysis. In order to statistically evaluate the features in Lamb wave propagation in the presence of noise, we collect multiple time series ( baseline signals) from the undamaged beam. A combination of the improved adaptive harmonic wavelet transform (AHWT) and the principal component analysis (PCA) is performed on the baseline signals to highlight the critical features of Lamb wave propagation in the undamaged structure. The detection of damage is facilitated by comparing the features of the test signal collected from the test structure ( damaged or undamaged) with the features of the baseline signals. In this process, we employ Hotelling's T-2 statistical analysis to first purify the baseline dataset and then to quantify the deviation of the test data vector from the baseline dataset. Through experimental and numerical studies, we systematically investigate the proposed methodology in terms of the detectability ( capability of detecting damage), the sensitivity ( with respect to damage severity and excitation frequency) and the robustness against noises. The parametric studies also validate, from the signal processing standpoint, the guidelines of Lamb-wave-based damage detection developed in part I.