用机器学习修正结构模型误差，提升数字孪生预测精度。
Machine learning assisted state prediction of misspecified linear dynamical system via modal reduction
- 在模态空间中用高斯过程建模未建模动力学，非参数化捕捉误差
- 联合估计状态与误差，降低位移和转角预测误差超70%
- 跨不同网格可迁移，无需重新训练，适合工程实际应用
精确预测结构动力学对维持数字孪生在服役期内的保真度至关重要。基于有限元的参数化模型常因几何、材料行为、阻尼或边界条件简化而忽略关键物理效应，导致模型形式误差（MFE），影响预测准确性。本文提出一种针对高维有限元结构动力系统的完整MFE估计与修正框架。通过高斯过程隐力模型（GPLFM）在降阶模态域非参数化表征偏差，实现对未建模动力学的灵活数据驱动刻画。采用线性贝叶斯滤波方法联合估计系统状态与偏差，同时考虑认知不确定性和随机不确定性。为保证计算可行性，将有限元系统投影至降阶模态基，并引入网格无关的神经网络，将模态状态映射为偏差估计，实现不同有限元离散化下的模型修正而无需重训。在五种典型MFE场景下验证：错误梁理论、阻尼误设、边界条件错配、未建模材料非线性及局部损伤，均在未见激励下显著降低位移与转角预测误差。该方法为应对建模固有不确定性提供了保障数字孪生准确性的可行路径。
原文摘要 · Abstract (English)
Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in geometry, material behavior, damping, or boundary conditions, resulting in model form errors (MFEs) that impair predictive accuracy. This work introduces a comprehensive framework for MFE estimation and correction in high-dimensional finite element (FE) based structural dynamical systems. The Gaussian Process Latent Force Model (GPLFM) represents discrepancies non-parametrically in the reduced modal domain, allowing a flexible data-driven characterization of unmodeled dynamics. A linear Bayesian filtering approach jointly estimates system states and discrepancies, incorporating epistemic and aleatoric uncertainties. To ensure computational tractability, the FE system is projected onto a reduced modal basis, and a mesh-invariant neural network maps modal states to discrepancy estimates, permitting model rectification across different FE discretizations without retraining. Validation is undertaken across five MFE scenarios-including incorrect beam theory, damping misspecification, misspecified boundary condition, unmodeled material nonlinearity, and local damage demonstrating the surrogate model's substantial reduction of displacement and rotation prediction errors under unseen excitations. The proposed methodology offers a potential means to uphold digital twin accuracy amid inherent modeling uncertainties.
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