A methodology for probabilistic damage detection in Bayesian framework without any requirement of mode matching is presented with detailed formulations on finite element model updating using incomplete modal data measured using limited number of sensors. Multiple modal measurement/data sets from multiple different sensor set-ups can be used in the proposed methodology with further scope for using repeated measurements from any single sensor set-up. Combined normal–lognormal multivariate distribution is considered in the Bayesian framework. Strictly positive random parameters are assigned with lognormal distribution, while the remaining random parameters are assigned with normal distribution. In this work, the normal distribution is incorporated for the likelihood function, which consists of the eigen-system equation error and the error between the system mode shapes and experimental mode shapes. On the other hand, mass and stiffness parameters are assigned with the lognormal distribution. Detailed formulations for probabilistic identification of changes/damages are also developed. The proposed approach is validated using a three-dimensional building structure considering multiple simulated damage cases. Performance in updating and damage detection is evaluated based on multi-set-up and multi-dataset considerations. Besides, the proposed technique is compared with the similar Bayesian updating solely based on normal distribution and the Gibbs sampling.

提出了一种贝叶斯框架中概率损失检测的方法，该方法无需模式匹配，并使用有限数量的传感器测量的不完整模态数据，对有限元模型更新进行了详细阐述。来自多个不同传感器设置的多个模态测量/数据集可用于建议的方法中，并具有使用来自任何单个传感器设置的重复测量的进一步范围。贝叶斯框架考虑了正态-对数正态组合多元分布。严格的正随机参数分配为对数正态分布，而其余的随机参数分配为正态分布。在这项工作中，似然函数包含了正态分布，它由本征系统方程误差和系统模式形状与实验模式形状之间的误差组成。另一方面，质量和刚度参数分配为对数正态分布。还开发了用于概率识别更改/损坏的详细公式。考虑到多个模拟损坏案例，使用三维建筑结构对提出的方法进行了验证。基于多设置和多数据集的考虑，评估更新和损坏检测的性能。此外，将所提出的技术与仅基于正态分布和吉布斯采样的相似贝叶斯更新进行了比较。还开发了用于概率识别更改/损坏的详细公式。考虑到多个模拟损坏案例，使用三维建筑结构对提出的方法进行了验证。基于多设置和多数据集的考虑，评估更新和损坏检测的性能。此外，将所提出的技术与仅基于正态分布和吉布斯采样的相似贝叶斯更新进行了比较。还开发了用于概率识别更改/损坏的详细公式。考虑到多个模拟损坏情况，使用三维建筑结构对提出的方法进行了验证。基于多设置和多数据集的考虑，评估更新和损坏检测的性能。此外，将所提出的技术与仅基于正态分布和吉布斯采样的相似贝叶斯更新进行了比较。