Bayesian finite element model updating techniques have found widespread application in the structural health monitoring. The conventional Bayesian modeling framework (CBMF) identifies the posterior distribution of structural parameters using data from a single experiment. However, structural parameters exhibit variability due to changes in environmental or experimental conditions, an aspect overlooked by CBMF. In recent years, the hierarchical Bayesian modeling framework (HBMF) has gradually attracted attention. This framework incorporates an additional layer of hyperparameters and utilizes multiple sets of experimental data to describe the variability in structural parameters caused by changes in experimental conditions. Unfortunately, the increase in hyperparameters and data size leads the HBMF to face the dilemma of exceedingly high computational costs. To address this issue, this study proposes an improved hierarchical Bayesian modeling framework (IHBMF). To enhance the computational efficiency of IHBMF, the importance sampling method is employed to simplify the computation of the likelihood function for hyperparameters. Subsequently, a surrogate model based on arbitrary polynomial chaos expansion is introduced to further reduce the computational cost of IHBMF. The framework's accuracy and efficiency were validated through analysis of a simply supported beam and a steel pedestrian bridge. The results demonstrate that IHBMF not only delivers a more accurate quantification of structural parameter uncertainty than CBMF but also exhibits higher computational efficiency compared to HBMF, showcasing its superior capability in structural health monitoring applications.

中文翻译：

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改进的具有任意多项式混沌的分层贝叶斯建模框架，用于概率模型更新

贝叶斯有限元模型更新技术在结构健康监测中得到了广泛的应用。传统的贝叶斯建模框架（CBMF）使用来自单个实验的数据来识别结构参数的后验分布。然而，由于环境或实验条件的变化，结构参数表现出可变性，这是 CBMF 忽视的一个方面。近年来，分层贝叶斯建模框架（HBMF）逐渐引起人们的关注。该框架包含额外的超参数层，并利用多组实验数据来描述由实验条件变化引起的结构参数的变化。不幸的是，超参数和数据量的增加导致HBMF面临计算成本极高的困境。为了解决这个问题，本研究提出了一种改进的分层贝叶斯建模框架（IHBMF）。为了提高IHBMF的计算效率，采用重要性采样方法来简化超参数似然函数的计算。随后，引入基于任意多项式混沌展开的代理模型，进一步降低IHBMF的计算成本。通过对简支梁和钢制人行桥的分析，验证了该框架的准确性和效率。结果表明，IHBMF 不仅能够比 CBMF 更准确地量化结构参数不确定性，而且比 HBMF 具有更高的计算效率，展示了其在结构健康监测应用中的卓越能力。