Modal-based uncertainty quantification for deterministically estimated structural parameters in low-fidelity model updating of complex connections复杂结点低保真模型更新中确定性估计结构参数的模态不确定性量化
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Mehrkash M, Santini-Bell E, 2024. Modal-based uncertainty quantification for deterministically estimated structural parameters in low-fidelity model updating of complex connections. Probabilistic Engineering Mechanics, 77: 103671.DOI: 10.1016/j.probengmech.2024.103671
结构中的复杂结点建模需要大量时间成本，因此必须进行简化。低保真建模的认知不确定性可通过随机模型更新进行量化。然而，采用物理代理模型简化连接构造面临挑战。此外，需建立包含连接结构参数的 Bayes 公式。该研究采用了经验证的参数化简化方法，对基准试验钢网中的复杂半刚性结点进行代理建模。提出了一类模态随机 Bayes 方法，以量化结构结点的不确定性。采用三类基于模态的目标函数进行有限元模型更新。通过冲击测试进行试验模态分析提取结构的模态特性，采用这些特性进行模型更新过程。将确定性和随机结构参数估计结合，以增强 Bayes 技术的鲁棒性。此外，还提供了选取最佳超参数的指导。结果表明，利用确定性估计参数作为先验知识可以促进并改善复杂结点结构的模态概率模型更新。此外，尽管对连接进行了很大简化，但代理模型最大后验估计的结构参数容许度仍然较低。关键词: 不确定性量化, Bayes 模型更新, 结构参数估计, 复杂结点, 低保真建模, 模态分析Modeling complex joints in structures entails significant time and effort, necessitating simplifications. Epistemic uncertainties arising from low-fidelity modeling can be quantified through probabilistic model updating. However, finding a surrogate physical model to represent simplified joint configurations poses challenges. Additionally, establishing a Bayesian formulation capable of incorporating structural parameters of connections is necessary. This study employs a validated simplifying parameterization approach for surrogate modeling of complex semi-rigid connections in a benchmark laboratory steel grid. It proposes a modal probabilistic Bayesian methodology to quantify uncertainties in the structure's joints. Three modal-based objective functions are utilized for finite element model updating. The modal properties of the structure are extracted by experimental modal analysis during an impact test, which will be utilized in the model updating process. Deterministic and probabilistic structural parameter estimations are integrated to enhance the robustness of the Bayesian technique. Furthermore, a guideline for selecting optimal hyperparameters is provided. Results demonstrate that utilizing deterministically estimated parameters as prior knowledge can facilitate and improve modal probabilistic model updating for structures with complex joints. Also, it is found that despite significant simplifications of joints, structural parameter tolerance around the maximum a posteriori estimate in surrogate models remains low.
Keywords: Uncertainty quantification; Bayesian model updating; Structural parameter estimation; Complex connection; Low-fidelity modeling; Modal analysis.![]()
Fig. 1. Experimental setup of the UCF grid
Fig. 2. Low-fidelity model of the structure developed in the SAP2000
Fig. 3. One of the UCF grid connections
Fig. 4. Simplified model of the UCF grid connections
图 5: 工况 I: 基于频率、刚度与柔度误差函数估计的刚度后验概率密度函数Fig. 5. Case I: Posterior PDF of the stiffness estimated by the frequency- (top), Stiffness- (middle), and flexibility-based (bottom) error functions
图 6: 工况 II: 基于频率、刚度与柔度误差函数估计的刚度后验概率密度函数Fig. 6. Case II: Posterior PDF of the mass estimated by the frequency- (top), Stiffness- (middle), and flexibility-based (bottom) error functions
图 7: 工况 III: 基于频率、刚度与柔度误差函数估计的刚度后验概率密度函数Fig. 7. Case III: posterior PDF of the mass estimated by the frequency- (top), Stiffness- (middle), and flexibility-based (bottom) error functions
作者信息 | Authors
美国新罕布什尔大学 (University of New Hampshire) 土木与环境工程系
Erin Santini-Bell, 通讯作者 (Corresp.)美国新罕布什尔大学 (University of New Hampshire) 土木与环境工程系Email: erin.bell@unh.edu
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
