Multivariate sparse Bayesian learning for guided wave-based multidamage localization in plate-like structures

This study proposes a new method for guided wave-based multidamage localization employing the multivariate sparse Bayesian learning (SBL) method. It is well accepted that the time-of-flight (ToF) of a guided wave packet is an essential feature for damage localization; however, this feature has uncertainties due to measurement noise and signal processing models, making it difficult to localize multiple defects simultaneously. The multivariate SBL approach has the capability to infer the most plausible atoms of the preset dictionary matrix and thus reduces the uncertainty effectively. In this study, an updated version of SBL is developed based on a multivariable input–output model, and the multivariate SBL shares the error precision parameter while inferring the weight vectors of multiple ToF inputs because the sources of uncertainty of each ToF are almost the same. In addition, for multidamage detection, the correspondence between defects and ToFs is unknown; thus, this study proposes a grouping scheme to address this challenge. In particular, ToFs from all transducers are randomly grouped into multiple vectors as input to this multivariable input–output model. Then, the fitting error of each optional grouping scheme is used to determine the most plausible scheme among all candidates. Consequently, the identified results of this scheme can be considered as the final damage localization results. The effectiveness and robustness of the proposed approach are validated by uncertain ToF data obtained through numerical simulations and an experimental study on a plate structure.