Machine learning models trained with structural health monitoring data have become a powerful tool for system identification. This paper presents a physics-informed Gaussian process (GP) model for Timoshenko beam elements. The model is constructed as a multi-output GP with covariance and cross-covariance kernels analytically derived based on the differential equations for deflections, rotations, strains, bending moments, shear forces and applied loads. Stiffness identification is performed in a Bayesian format by maximising a posterior model through a Markov chain Monte Carlo method, yielding a stochastic model for the structural parameters. The optimised GP model is further employed for probabilistic predictions of unobserved responses. Additionally, an entropy-based method for physics-informed sensor placement optimisation is presented, exploiting heterogeneous sensor position information and structural boundary conditions built into the GP model. Results demonstrate that the proposed approach is effective at identifying structural parameters and is capable of fusing data from heterogeneous and multi-fidelity sensors. Probabilistic predictions of structural responses and internal forces are in closer agreement with measured data. We validate our model with an experimental setup and discuss the quality and uncertainty of the obtained results. The proposed approach has potential applications in the field of structural health monitoring (SHM) for both mechanical and structural systems.

翻译：利用结构健康监测数据训练的机器学习模型已成为系统识别的强大工具。本文提出了一种面向Timoshenko梁单元的物理信息高斯过程模型。该模型被构建为多输出高斯过程，其协方差和互协方差核函数基于挠度、转角、应变、弯矩、剪力和外载荷的微分方程解析推导得出。通过马尔可夫链蒙特卡洛方法最大化后验模型，以贝叶斯格式实现刚度识别，从而得到结构参数的随机模型。优化后的高斯过程模型进一步用于未观测响应的概率预测。此外，本文提出了一种基于熵的物理信息传感器布设优化方法，利用嵌入GP模型中的异构传感器位置信息和结构边界条件。结果表明，所提方法能有效识别结构参数，并具备融合异构及多保真度传感器数据的能力。结构响应和内力的概率预测与实测数据吻合度更高。我们通过实验装置对模型进行了验证，并讨论了所得结果的质量与不确定性。该方法在机械与结构系统的结构健康监测领域具有潜在应用价值。