Bayesian uncertainty quantification for guided-wave-based multidamage localization in plate-like structures using Gibbs sampling

In this article, a new Bayesian approach for guided-wave-based multidamage localization by employing Gibbs sampling is proposed. By using the information of time-of-flight (ToF) embedded in guided wave signals, the posterior probability distributions of three parameter groups, that is, the horizontal and vertical coordinates of the multidamage locations (x, y) and wave velocity v, are characterized using Gibbs sampling samples. To obtain the analytical form of the conditional posterior probability density function of each parameter group conditional on the other two and the available ToF data, a first_order Taylor expansion of the nonlinear ToF-based damage localization model with respect to each parameter group is performed. Two Gibbs sampling algorithms are proposed, which differ in their strategies to address the posterior uncertainty of the prediction error parameter; however, both algorithms iteratively sample from conditional posterior probability density functions of three parameter groups. Therefore, the effective number of dimensions for Gibbs sampling is always three, regardless of the number of defects. The final damage localization results are obtained by grouping all ToFs and then comparing the posterior uncertainty of localization results of each grouping scheme to obtain the most reliable sampling results among all candidates. The proposed method not only identifies the group velocity but also localizes multiple defects by sharing the same characteristics of damage localization. Furthermore, this method can quantify the uncertainty of multidamage localization to automatically find the most reliable damage locations. The effectiveness and robustness of the proposed algorithms are validated by both numerical and experimental examples.