The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based principles and can be derived from corresponding governing equations, often of differential equation form. However, complex system characteristics, such as nonlinearities and energy dissipation mechanisms, often imply that such models are approximative and often imprecise. This challenge is further compounded in SHM, where sensor data is often sparse, making it difficult to fully observe the system's states. To address these issues, this paper explores the use of Physics-Informed Neural Networks (PINNs), a class of physics-enhanced machine learning (PEML) techniques, for the identification and estimation of dynamical systems. PINNs offer a unique advantage by embedding known physical laws directly into the neural network's loss function, allowing for simple embedding of complex phenomena, even in the presence of uncertainties. This study specifically investigates three key applications of PINNs: state estimation in systems with sparse sensing, joint state-parameter estimation, when both system response and parameters are unknown, and parameter estimation within a Bayesian framework to quantify uncertainties. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in presence of modelling errors. However, these errors tend to have a more significant impact on parameter estimation, as the optimization process must reconcile discrepancies between the prescribed model and the true system behavior. Despite these challenges, PINNs show promise in dynamical system modeling, offering a robust approach to handling uncertainties.

该研究解决了传统动力系统建模中的不准确性和传感器数据稀疏问题。通过采用物理启发神经网络（PINNs），研究首次将已知物理法则嵌入到神经网络的损失函数中，显著提高了对动态系统的状态和参数的估计。研究结果表明，PINNs在动态系统建模中展现出强大的潜力，特别是在面对不确定性和建模误差时。

通过物理启发神经网络进行动力系统响应估计和系统识别