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Beam damage uncertainty quantification using guided Lamb wave responses

In this article, a Bayesian inference approach is applied to conduct uncertainty quantification on notch damage in a beam structure using guided Lamb wave responses. The proposed methodology not only determines the notch damage characteristics but also quantifies associated uncertainties of these inferred values. The correlation between crack location and extent is investigated as well, because such information is essential for decision-making in the structural health monitoring applications. First, a spectral finite element model is used to characterize Lamb wave propagation responses in a beam under lead-zirconate-titanate actuation and sensing. Very few elements are required to accurately capture the wave propagation. The lead-zirconate-titanate sensor can pick up the reflected wave responses from both boundaries and damages. Total 18 simulation cases were generated by varying notch damage extent, damage location, and noise level. Second, the Markov Chain Monte Carlo techniques are employed to estimate the notch damage location and extent from guided Lamb wave responses, in which the random walk metropolis algorithm is used. Finally, both crack size/location and associated uncertainties are characterized. In summary, the proposed probabilistic damage detection is successfully demonstrated in beam structures using guided wave responses, which can be extended to other structural health monitoring applications.