Haywood-Alexander Marcus, Arcieri Giacomo, Kamariotis Antonios, Chatzi Eleni
Department of Civil, Environmental and Geomatic Engineering, ETH Zürich, Wolfgang-Pauli Strasse, 8049 Zürich, Switzerland.
Future Resilient Systems, Singapore-ETH Centre, Singapore, Singapore.
Adv Model Simul Eng Sci. 2025;12(1):8. doi: 10.1186/s40323-025-00291-9. Epub 2025 Apr 23.
The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), structural design optimisation, 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. Or in an additional context, in inverse modelling from noisy full-field data, modelling assumptions are compounded in to the observation uncertainty approximation. 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 from full-field observation, within a Bayesian framework to quantify uncertainties. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in the 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 model uncertainties.
结构动力学的精确建模在众多工程应用中至关重要，如结构健康监测（SHM）、结构设计优化和振动控制。通常，这些模型源于基于物理的原理，可从相应的控制方程推导得出，这些方程往往是微分方程形式。然而，复杂的系统特性，如非线性和能量耗散机制，往往意味着此类模型是近似的，且常常不精确。在结构健康监测中，这一挑战进一步加剧，因为传感器数据往往很稀疏，难以全面观测系统状态。或者在另一种情况下，从有噪声的全场数据进行逆建模时，建模假设会与观测不确定性近似相结合。为解决这些问题，本文探讨了使用物理信息神经网络（PINNs），这是一类物理增强机器学习（PEML）技术，用于动态系统的识别和估计。PINNs通过将已知物理定律直接嵌入神经网络的损失函数，提供了独特的优势，即使存在不确定性，也能简单地嵌入复杂现象。本研究具体调查了PINNs的三个关键应用：在稀疏传感系统中的状态估计、当系统响应和参数均未知时的联合状态 - 参数估计，以及在贝叶斯框架内从全场观测进行参数估计以量化不确定性。结果表明，即使存在建模误差，PINNs在上述所有任务中都提供了一种有效的工具。然而，这些误差往往对参数估计有更显著的影响，因为优化过程必须协调规定模型与真实系统行为之间的差异。尽管存在这些挑战，PINNs在动态系统建模中显示出前景，为处理模型不确定性提供了一种稳健的方法。
