基于模态统计信息的有限元模型不确定性分级贝叶斯量化
Hierarchical Bayesian Uncertainty Quantification of Finite Element Models using Modal Statistical Information
摘要：
提出了一种基于模态信息的有限元模型不确定性量化的层次贝叶斯建模框架。该框架使用现有的快速傅立叶变换（FFT）的方法来识别实验模态参数的时间历史数据，并采用一类最大熵概率分布占模态参数之间的不匹配。它还考虑了一个参数化的概率分布，用于捕获多个数据集的结构参数的变异性。在这个框架中，计算是通过期望最大化（EM）的战略，授权的拉普拉斯近似。其结果是，一个新的理由被引入时，更新结构参数的模态特性分配最佳的权重。根据这一框架，模态特征的权重等于总不确定性的倒数，包括识别和预测的不确定性。所提出的框架是一致的，在建模的整个过程中推断结构参数的响应只测量，是全面的不确定性的不同来源，包括多个数据集的模态和结构参数的变异性，以及他们的识别不确定性。数值和实验的例子来证明HBM框架，其中的环境和操作条件几乎是恒定的。据观察，跨数据集的参数的可变性仍然是不确定性的主要来源，而远大于识别的不确定性。
英文摘要：
This paper develops a Hierarchical Bayesian Modeling (HBM) framework for uncertainty quantification of Finite Element (FE) models based on modal information. This framework uses an existing Fast Fourier Transform (FFT) approach to identify experimental modal parameters from time-history data and employs a class of maximum-entropy probability distributions to account for the mismatch between the modal parameters. It also considers a parameterized probability distribution for capturing the variability of structural parameters across multiple data sets. In this framework, the computation is addressed through Expectation-Maximization (EM) strategies, empowered by Laplace approximations. As a result, a new rationale is introduced for assigning optimal weights to the modal properties when updating structural parameters. According to this framework, the modal features weights are equal to the inverse of the aggregate uncertainty, comprised of the identification and prediction uncertainties. The proposed framework is coherent in modeling the entire process of inferring structural parameters from response-only measurements and is comprehensive in accounting for different sources of uncertainty, including the variability of both modal and structural parameters over multiple data sets, as well as their identification uncertainties. Numerical and experimental examples are employed to demonstrate the HBM framework, wherein the environmental and operational conditions are almost constant. It is observed that the variability of parameters across data sets remains the dominant source of uncertainty while being much larger than the identification uncertainties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
