Asymptotic identification uncertainty of close modes in Bayesian operational modal analysis
Asymptotic identification uncertainty of close modes in Bayesian operational modal analysis
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DOI：
10.1016/j.ymssp.2019.106273
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发表时间：
2019-11-01
影响因子：
8.4
通讯作者：
Brownjohn, James M. W.
中科院分区：
文献类型：
--
作者：
Au, Siu-Kui;Brownjohn, James M. W.
闭合模态不是运行模态分析（OMA）中的典型对象，但它们确实发生在具有相似动力特性的模态的结构中，例如高层建筑和塔楼。与分离良好的模式相比，它们的识别更具挑战性，结果可能具有更高的不确定性，特别是在模态形状方面。有识别（ID）和不确定度计算的算法，但值本身并不提供任何ID不确定度的见解，这是必要的环境测试规划中的管理。贝叶斯方法之后，这项工作研究分析的ID不确定性的接近模式下的渐近条件下的长数据和高信噪比，这仍然是典型的应用。Fisher信息矩阵（Fisher Information Matrix）的渐近表达式，其逆矩阵给出渐近“后验”（即，给定的数据）的模态参数的协方差矩阵，推导出明确的控制动力学特性。通过分析研究的本征值特性的的，我们表明，模式形状的不确定性发生在两个特征类型的相互不相关的主方向，一个垂直（类型1）和一个内的“模式形状子空间”跨越的模式形状（类型2）。先前在分离良好的模式中发现了类型1的不确定性。它与其他模态参数不相关（例如，频率和阻尼）随着数据质量的提高而减小，并且在应用中可以忽略。第二类不确定性是封闭模式特有的新发现。它可能与所有模态参数相关，即使对于无噪声数据也不会消失。它揭示了固有的复杂性，并管理可实现的精度限制OMA与关闭模式。理论研究结果进行了数值验证，并与现场数据应用。这项工作还没有达到“测不准定律”的最终目标，即，明确地将ID不确定性与测试配置相关联，以便于理解和测试规划，但对ID不确定性的分析表达式及其特征值属性的理解揭示了可能性，并提供了实现可能性的途径。（C）2019作者。爱思唯尔有限公司出版
Close modes are not typical subjects in operational modal analysis (OMA) but they do occur in structures with modes of similar dynamic properties such as tall buildings and towers. Compared to well-separated modes they are much more challenging to identify and results can have significantly higher uncertainty especially in the mode shapes. There are algorithms for identification (ID) and uncertainty calculation but the value itself does not offer any insight on ID uncertainty, which is necessary for its management in ambient test planning. Following a Bayesian approach, this work investigates analytically the ID uncertainty of close modes under asymptotic conditions of long data and high signal-to-noise ratio, which are nevertheless typical in applications. Asymptotic expressions for the Fisher Information Matrix (FIM), whose inverse gives the asymptotic 'posterior' (i.e., given data) covariance matrix of modal parameters, are derived explicitly in terms of governing dynamic properties. By investigating analytically the eigenvalue properties of FIM, we show that mode shape uncertainty occurs in two characteristic types of mutually uncorrelated principal directions, one perpendicular (Type 1) and one within the 'mode shape subspace' spanned by the mode shapes (Type 2). Uncertainty of Type 1 was found previously in well-separated modes. It is uncorrelated from other modal parameters (e.g., frequency and damping), diminishes with increased data quality and is negligible in applications. Uncertainty of Type 2 is a new discovery unique to close modes. It is potentially correlated with all modal parameters and does not vanish even for noiseless data. It reveals the intrinsic complexity and governs the achievable precision limit of OMA with close modes. Theoretical findings are verified numerically and applied with field data. This work has not reached the ultimate goal of 'uncertainty law', i.e., explicitly relating ID uncertainty to test configuration for understanding and test planning, but the analytical expressions of FIM and understanding about its eigenvalue properties shed light on possibility and provide the pathway to it. (C) 2019 The Authors. Published by Elsevier Ltd.