The Bayesian model updating approach (BMUA) has been widely used to update structural parameters using modal measurements because of its powerful ability to handle uncertainties and incomplete data. However, a conventional BMUA is mainly used to update stiffness with the assumption that structural mass is known. Because simultaneously updating stiffness and mass leads to unidentifiable case or coupling effect of stiffness and mass, this assumption in conventional BMUA is questionable to update stiffness when the mass has significantly changed. This study proposes a new updating framework based on two structural systems: original and modified systems. A modified system is created by adding known mass to the original system. Different from the conventional Bayesian approach, two sets of measured vibration data in the proposed Bayesian approach are obtainable to address the coupling effect existing in the conventional Bayesian approach. To this end, a new approach reformulates the prior probability distribution function and the objective function. Two numerical simulations are considered to demonstrate the performance of the proposed approach, including (1) parameter identification, (2) posterior uncertainties, (3) probabilistic damage detections. The proposed BMUA outperforms a conventional BMUA in identifying both stiffness and mass.

中文翻译：

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使用已知附加质量的贝叶斯模型更新方法识别结构刚度和质量：数值研究

贝叶斯模型更新方法（BMUA）因其强大的处理不确定性和不完整数据的能力而被广泛用于使用模态测量更新结构参数。然而，传统的 BMUA 主要用于在结构质量已知的假设下更新刚度。因为同时更新刚度和质量会导致无法识别的情况或刚度和质量的耦合效应，因此传统 BMUA 中的这种假设在质量发生显着变化时更新刚度是有问题的。本研究提出了一个基于两个结构系统的新更新框架：原始系统和修改系统。通过将已知质量添加到原始系统来创建修改后的系统。不同于传统的贝叶斯方法，可以得到所提出的贝叶斯方法中的两组测量振动数据，以解决传统贝叶斯方法中存在的耦合效应。为此，一种新方法重新制定了先验概率分布函数和目标函数。两个数值模拟被认为是证明所提出方法的性能，包括（1）参数识别，（2）后验不确定性，（3）概率损伤检测。所提出的 BMUA 在识别刚度和质量方面优于传统的 BMUA。两个数值模拟被认为是证明所提出方法的性能，包括（1）参数识别，（2）后验不确定性，（3）概率损伤检测。所提出的 BMUA 在识别刚度和质量方面优于传统的 BMUA。两个数值模拟被认为是证明所提出方法的性能，包括（1）参数识别，（2）后验不确定性，（3）概率损伤检测。所提出的 BMUA 在识别刚度和质量方面优于传统的 BMUA。