论文标题
使用模态统计信息对有限元模型进行分层贝叶斯不确定性量化
Hierarchical Bayesian Uncertainty Quantification of Finite Element Models using Modal Statistical Information
论文作者
论文摘要
本文开发了基于模态信息的有限元(Fe)模型的不确定性量化的层次结构贝叶斯建模(HBM)框架。该框架使用现有的快速傅立叶变换(FFT)方法来识别时间历史数据的实验模态参数,并采用一类最大渗透概率分布来说明模态参数之间的不匹配。它还考虑了用于捕获多个数据集结构参数的可变性的参数化概率分布。在此框架中,通过Laplace近似授权的预期最大化(EM)策略来解决计算。结果,在更新结构参数时,引入了新的理由,以将最佳权重分配给模态属性。根据该框架,模态特征权重等于骨料不确定性的倒数,包括识别和预测不确定性。所提出的框架在模拟从仅响应测量的整个过程中建模的整个过程是一致的,并且在考虑到不同的不确定性来源的情况下,包括模态和结构参数在多个数据集上的变异性以及其识别不确定性。使用数值和实验示例来证明HBM框架,其中环境和操作条件几乎是恒定的。可以观察到,跨数据集的参数的可变性仍然是不确定性的主要来源,同时比识别不确定性大得多。
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.