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.

在本文中，提出了一种新的贝叶斯方法，该方法采用Gibbs采样进行基于波的多损伤定位。利用嵌入在导波信号中的飞行时间（ToF）信息，可以确定三个参数组的后验概率分布，即多损伤位置（x，y）的水平和垂直坐标以及波速v使用Gibbs采样样本进行特征化。为了获得以其他两个为条件的每个参数组的条件后验概率密度函数的解析形式以及可用的ToF数据，对每个参数组执行基于非线性ToF的损伤定位模型的一阶泰勒展开。提出了两种吉布斯采样算法，它们的策略不同，以解决预测误差参数的后验不确定性。但是，这两种算法都从三个参数组的条件后验概率密度函数中迭代采样。因此，与缺陷数量无关，用于Gibbs采样的有效维数始终为3。通过将所有ToF分组，然后比较每个分组方案的本地化结果的后验不确定性，可以获得最终的损伤定位结果，从而在所有候选样本中获得最可靠的采样结果。该方法不仅可以识别群速度，而且可以通过共享相同的损伤定位特征来定位多个缺陷。此外，该方法可以量化多损伤定位的不确定性，以自动找到最可靠的损伤位置。数值和实验实例验证了所提算法的有效性和鲁棒性。该方法不仅可以识别群速度，而且可以通过共享相同的损伤定位特征来定位多个缺陷。此外，该方法可以量化多损伤定位的不确定性，以自动找到最可靠的损伤位置。数值和实验实例验证了所提算法的有效性和鲁棒性。该方法不仅可以识别群速度，而且可以通过共享相同的损伤定位特征来定位多个缺陷。此外，该方法可以量化多损伤定位的不确定性，以自动找到最可靠的损伤位置。数值和实验实例验证了所提算法的有效性和鲁棒性。