用概率模型补全错漏的物理方程，让数字孪生更可信。
Probabilistic Digital Twin for Misspecified Structural Dynamical Systems via Latent Force Modeling and Bayesian Neural Networks
- 把物理模型误差当作隐变量力，用高斯过程联合估计状态和误差
- 通过贝叶斯神经网络学习状态到误差的非线性映射，保留不确定性
- 适用于物理模型不准但有传感器数据的系统，适合工程可靠性评估
本文提出一种针对物理模型误设的动力系统响应预测概率数字孪生框架。该方法结合高斯过程隐力模型（GPLFM）与贝叶斯神经网络（BNN），实现端到端的不确定性感知推断与预测。诊断阶段，将模型形式误差（MFE）视为名义线性动力系统的隐输入力，利用GPLFM从传感器数据中联合估计系统状态与误差；随后，基于后验样本训练BNN，学习从系统状态到MFE的非线性概率映射，并捕捉诊断不确定性。在预测阶段，利用该映射生成伪观测，通过卡尔曼滤波实现状态预测。框架支持不确定性从诊断到预测的系统性传播，是可信数字孪生的关键能力。在四个非线性案例中验证：单自由度振子、多自由度系统，以及两个经典基准——Bouc-Wen滞回系统和Silverbox实验数据集，展示了其预测精度与对模型误设的鲁棒性。
原文摘要 · Abstract (English)
This work presents a probabilistic digital twin framework for response prediction in dynamical systems governed by misspecified physics. The approach integrates Gaussian Process Latent Force Models (GPLFM) and Bayesian Neural Networks (BNNs) to enable end-to-end uncertainty-aware inference and prediction. In the diagnosis phase, model-form errors (MFEs) are treated as latent input forces to a nominal linear dynamical system and jointly estimated with system states using GPLFM from sensor measurements. A BNN is then trained on posterior samples to learn a probabilistic nonlinear mapping from system states to MFEs, while capturing diagnostic uncertainty. For prognosis, this mapping is used to generate pseudo-measurements, enabling state prediction via Kalman filtering. The framework allows for systematic propagation of uncertainty from diagnosis to prediction, a key capability for trustworthy digital twins. The framework is demonstrated using four nonlinear examples: a single degree of freedom (DOF) oscillator, a multi-DOF system, and two established benchmarks -- the Bouc-Wen hysteretic system and the Silverbox experimental dataset -- highlighting its predictive accuracy and robustness to model misspecification.
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