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An innovative Bayesian system identification method using autoregressive model

机译：一种使用自回归模型的贝叶斯系统识别方法

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摘要

This paper proposes an innovative Bayesian method for system identification based on autoregressive (AR) model. The dynamics of a structure is first modeled by an AR model. Due to measurement noise and modeling errors in practical problems, it is important to quantify uncertainties of the model. The posterior PDF of the parameters of the AR model is then formulated following Bayes' theorem. New formulations of the most probable values (MPVs) and the posterior uncertainties of the AR model parameters are derived in closed form. It is shown that the model of a vibrating structure can be transformed to an AR model, so the modal parameters of the structure can be extracted from the parameter matrices of the AR model. For assessing the posterior uncertainties of the modal parameters, original analytical formulations are derived to propagate the uncertainties of AR model parameters to the modal parameters. The proposed method is verified by measured ambient vibration data of a 20-story building. Working directly on the measured accelerations, the proposed method can make use of the original information in the data to identify all modal parameters of interest together with corresponding uncertainties in a few minutes. The contribution of this paper is that the algebraically involved derivation is resolved to develop new formulations for the MPVs and associated uncertainties, reveal the complicated relationship between the uncertainties of modal parameters and those of AR model parameters, and provide a mathematically manageable algorithm for efficient practical applications.
机译：本文提出了一种基于自回归（AR）模型的系统识别的创新贝叶斯方法。结构的动态由AR模型建模。由于测量噪声和建模误差在实际问题中，重要的是量化模型的不确定性。然后在贝叶斯定理后制定AR模型参数的后部PDF。最可能值（MPV）的新配方和AR模型参数的后部不确定性以封闭形式推导出来。结果表明，可以将振动结构的模型转换为AR模型，因此可以从AR模型的参数矩阵中提取结构的模态参数。为了评估模态参数的后部不确定性，导出原始分析制剂以将AR模型参数的不确定性传播到模态参数。通过20层建筑的测量的环境振动数据来验证所提出的方法。直接在测量的加速下工作，所提出的方法可以利用数据中的原始信息，以将所有Modal参数识别在几分钟内相应的不确定性。本文的贡献是，解决代数涉及的推导，以开发用于MPV和相关的不确定性的新配方，揭示了模型参数的不确定因素与AR模型参数之间的复杂关系，并提供了一种有效的实用算法应用程序。

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