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An analytical perspective on Bayesian uncertainty quantification and propagation in mode shape assembly

机译：贝叶斯不确定性量化和模式形状组装中的传播的分析观点

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摘要

Assembling local mode shapes identified from multiple setups to form global mode shapes is of practical importance when the degrees of freedom (dofs) of interest are measured separately in individual setups or when one expects to exploit the computational autonomous capabilities of different setups in full-scale operational modal test. The Bayesian mode assembly methodology was able to obtain the optimal global mode shape as well as the associated uncertainties by taking the inverse of the analytically derived Hessian matrix of the negative log-likelihood function (NLLF) (Yan and Katafygiotis, 2015) [1]. In this study, we investigate how the posterior uncertainties existing in the local mode shapes obtained from different setups propagate into the global mode shapes in an explicit manner by borrowing a novel approximate analysis strategy. The explicit closed-form approximation expressions are derived to investigate the effects of various data parameters on the posterior covariance matrix of the global mode shapes. Such quantitative relationships, connecting the posterior uncertainties with global mode shapes and the data information, offer a better understanding of uncertainty propagation over the process of mode shape assembly. The posterior uncertainty of the global mode shapes is inversely proportional to 'normalized data length' and the 'frequency bandwidth factor', and propositional to 'noise-to-environment' ratio and damping ratio. Validation studies using field test data measured from the Metsovo bridge located in Greece provide a practical verification of the rationality of the theoretical findings of uncertainty quantification and propagation analysis in Bayesian mode shape assembly.
机译：当在单个设置中分别测量感兴趣的自由度（dofs）或希望充分利用不同设置的计算自主功能时，组装从多个设置中识别出的局部模式形状以形成全局模式形状非常重要。操作模态测试。贝叶斯模式组装方法能够通过取负对数似然函数（NLLF）的解析得出的黑森州矩阵的逆来获得最佳的全局模式形状以及相关的不确定性（Yan和Katafygiotis，2015）[1] 。在这项研究中，我们通过借鉴一种新颖的近似分析策略，研究了从不同设置获得的局部模式形状中存在的后验不确定性如何以显式方式传播到全局模式形状中。推导了显式的闭式近似表达式，以研究各种数据参数对全局模式形状的后协方差矩阵的影响。这种将后验不确定性与全局模式形状和数据信息联系起来的定量关系，可以更好地理解模式形状组装过程中不确定性的传播。整体模态形状的后验不确定性与“归一化数据长度”和“频率带宽因子”成反比，与“噪声与环境”比和阻尼比成正比。使用从位于希腊的Metsovo桥测得的现场测试数据进行的验证研究，对贝叶斯模式形状组装中不确定性量化和传播分析的理论发现的合理性进行了实际验证。

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