| Author: | Yuan, Lei |
| Title: | Physics informed machine learning for structural response prediction and health monitoring |
| Advisors: | Ni, Yiqing (CEE) |
| Degree: | Ph.D. |
| Year: | 2025 |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xxi, 251 pages : color illustrations |
| Language: | English |
| Abstract: | The rapid development of machine learning methods in recent years has provided researchers with alternative approaches to explain the physical world solely through data. These advanced data-driven methods offer great flexibility in handling various physical problems and have demonstrated superiority over traditional model-based methods in many fields. As a result, there is now a growing tendency to utilize these machine learning methods to tackle difficult problems in science and engineering, especially in physical problems involving uncertain systems. However, existing data-driven methods still face some limitations. Machine learning models trained from data are often hobbled by noise, imbalance, and sparsity in the training data, posing challenges to the generalization of the models. Additionally, since the intrinsic laws of physical systems are only represented at a shallow level from the training data, the trained machine learning models may produce physically implausible result predictions that violate the governing laws of physical systems. Given the challenges existing in these data-driven methods, this study delves deeply into the application of physics-informed machine learning (PIML) in engineering physical systems. PIML is an emerging machine learning concept that aims to couple various prior physical constraints into the training of machine learning models, thereby enhancing the physical feasibility of the models and improving their generalization and robustness. The focus of this thesis is on the application of PIML in structural dynamic response and structural damage monitoring. Several PIML frameworks are proposed to integrate machine learning models and physical knowledge to address the difficulties encountered by current data-driven and traditional physics-driven methods. First, a framework named structural dynamics learner (SDL) is proposed to solve the forward problem of structural dynamics by integrating physical information with neural network models. In SDL, a novel recurrent convolutional neural network framework that integrates physical information described as the implicit Crank-Nicolson form of the system's motion equations is established to predict the dynamic response of linear/nonlinear structural systems. Afterward, the focus of this thesis shifted to the research of inverse problems in structural dynamics. The first inverse problem investigated is the reconstruction of external forces and dynamic responses of structures, where a physics-informed Markov parameters (PI-MP) framework is proposed to accurately reconstruct the external excitations and dynamic responses from partial vibration measurement data. Here, the neural network with strong characterization ability for reconstructing unknown external force input is coordinated with the Markov parameter for describing the motion equation of the structure in the state space to predict the acceleration response of the structure. By minimizing the deviation between the predicted structural acceleration response and the measured vibration response, PI-MP can locate and reconstruct the external excitation input of the structure and predict the vibration response of all nodes of the structure. Then, the application of PIML for structural damage identification with unknown external forces from vibration measurements is further investigated. A physics-informed Fourier feature neural networks (PI-FFNN) framework integrates Fourier neural networks with excellent multi-frequency characterization capabilities and the Newmark-beta scheme of the motion equation as physical information is presented to achieve this research goal. The integration of physical information makes this method unsupervised learning, which can be trained to accurately detect structural damage from vibration measurements without relying on any damage-related data labels. Finally, based on the physics-informed neural networks framework, we propose a PIML framework that can simultaneously identify the structural mechanical parameters, reconstruct the unknown external excitation on the structure, and establish a surrogate model for nonlinear systems. In this framework, two neural network models are employed to represent the structure's unknown external excitation and nonlinear internal restoring forces respectively, and the mechanical parameters of the structure are also updated together with the neural network model as trainable parameters. The physical information of the structural vibration equations is seamlessly integrated into the proposed machine learning framework through a set of mathematical equations that describe the Newmark-beta relations of the dynamic system. By minimizing the difference between the predicted structural response and the structural vibration observation, both the external excitation and the internal nonlinear restoring force of the structure can be reconstructed simultaneously and the exact values of the structural parameters can be discovered. This thesis presents several innovative PIML frameworks for solving forward and inverse problems in structural dynamics. Under the constraints of physical information, these frameworks demonstrate the independence of complex and large training data and achieve efficient and accurate model training in a physically constrained search space. The embedding of physical information also gives the predictions of the proposed PIML frameworks with physical interpretation, outstanding noise robustness, and excellent generalization for physical systems in a variety of environments. The results of simulation analysis and real physical experiments show that the proposed PIML frameworks have outstanding ability and performance to accurately model real physical systems. Looking ahead, more in-depth research is still needed to apply the promising PIML method to more complex physical systems, involving large structural degrees of freedom and complex nonlinearities. |
| Rights: | All rights reserved |
| Access: | open access |
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