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A new Gibbs sampling based algorithm for Bayesian model updating with incomplete complex modal data

机译：基于Gibbs采样的新算法用于不完整复杂模态数据的贝叶斯模型更新

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摘要

Model updating using measured system dynamic response has a wide range of applications in system response evaluation and control, health monitoring, or reliability and risk assessment. In this paper, we are interested in model updating of a linear dynamic system with non-classical damping based on incomplete modal data including modal frequencies, damping ratios and partial complex mode shapes of some of the dominant modes. In the proposed algorithm, the identification model is based on a linear structural model where the mass and stiffness matrix are represented as a linear sum of contribution of the corresponding mass and stiffness matrices from the individual prescribed substructures, and the damping matrix is represented as a sum of individual substructures in the case of viscous damping, in terms of mass and stiffness matrices in the case of Rayleigh damping or a combination of the former. To quantify the uncertainties and plausibility of the model parameters, a Bayesian approach is developed. A new Gibbs-sampling based algorithm is proposed that allows for an efficient update of the probability distribution of the model parameters. In addition to the model parameters, the probability distribution of complete mode shapes is also updated. Convergence issues and numerical issues arising in the case of high-dimensionality of the problem are addressed and solutions to tackle these problems are proposed. The effectiveness and efficiency of the proposed method are illustrated by numerical examples with complex modes.
机译：使用测得的系统动态响应进行模型更新在系统响应评估和控制，运行状况监视或可靠性和风险评估中具有广泛的应用。在本文中，我们对基于不完整模态数据（包括模态频率，阻尼比和某些主模的部分复模形状）的具有非经典阻尼的线性动力系统的模型更新感兴趣。在提出的算法中，识别模型基于线性结构模型，其中质量和刚度矩阵表示为来自各个指定子结构的相应质量和刚度矩阵的贡献的线性和，阻尼矩阵表示为在粘性阻尼的情况下，单个子结构的总和，在瑞利阻尼的情况下，质量或刚度矩阵或前者的组合。为了量化模型参数的不确定性和合理性，开发了一种贝叶斯方法。提出了一种新的基于吉布斯采样的算法，该算法可以有效更新模型参数的概率分布。除了模型参数外，完整模式形状的概率分布也将更新。解决了在问题的高维情况下出现的收敛性问题和数值问题，并提出了解决这些问题的解决方案。通过具有复杂模式的数值例子说明了该方法的有效性和效率。

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