| Author: | Zhang, Weijia |
| Title: | Development of physics-informed machine learning methods for structural analysis and parameter identification |
| Advisors: | Ni, Yi-qing (CEE) Zou, Fangxin (AAE) |
| Degree: | Ph.D. |
| Year: | 2025 |
| Department: | Department of Civil and Environmental Engineering |
| Pages: | xxiv, 232 pages : color illustrations |
| Language: | English |
| Abstract: | This research aims to advance the field of physics-informed machine learning (PIML) in four critical aspects and to apply PIML methods to solve forward and inverse problems in structural engineering. The research begins with a detailed introduction to the basic knowledge of PIML including two powerful frameworks, namely physics-informed neural network (PINN) and physics-informed graph neural network (PIGNN), by reviewing extensive relevant literature. The core idea of PIML is to integrate the physical laws described by governing equations into neural network (NN) architectures by incorporating these equations, along with boundary and initial conditions and other essential constraints, as penalty terms in the loss function. Then, the applications of PINN and PIGNN in the field of structural engineering are comprehensively reviewed, and the current limitations of PIML are also discussed and summarized. To address the existing research gaps, several solutions are proposed in this research to enhance the performance of PIML methods. Automatic differentiation (AD) is a key function of PINN, as it computes the derivatives of the NN output based on the chain rule to form the physics-informed loss function. Vanilla PINN often struggles with high-order governing equations because the AD function should be applied multiple times to compute the high-order derivatives, which inevitably accumulates computational errors. Therefore, the first improvement lies in the introduction of auxiliary outputs of PINN for reducing the highest order of the governing equation. By defining auxiliary outputs representing the lower-order derivatives of the original NN output, the governing equation can be reformulated in a downscaled form. The effectiveness of the proposed approach is validated through numerical examples involving high-order differential equations, demonstrating significant improvements in both training efficiency and prediction accuracy. In addition to high-order governing equations, the large number of boundary conditions and their treatment in vanilla PINN also pose computational challenges. Boundary conditions are embedded by defining a penalty term in the total loss function and are satisfied by enforcing this penalty term to approach zero, which is called the "soft" manner. However, this soft enforcement cannot guarantee zero residuals of the boundary after training. Thus, a series of modulating functions are derived as the second improvement for "hard" enforcement of all boundary conditions, thereby converting the original output of NN to automatically satisfy the boundary conditions without the need for a penalty term. The performance of this method is validated through both forward problems, i.e. structural response prediction, and inverse problems, i.e. identifying the unknown rotational stiffness of semi-rigid joints. Numerical case studies and experimental validation are carried out, showing that PINN with hard-embedded boundary conditions outperforms vanilla PINN in both forward and inverse cases. Although modulating functions are effective for tackling boundary conditions, this method exhibits limitations when applied to problems involving complex and irregular domains. Deriving analytical forms of modulating functions becomes challenging or even impossible in such cases. To address this issue, a unified framework termed two-phase physics-informed neural network (TP-PINN) is proposed as the third improvement. TP-PINN framework employs pretrained NNs, which can be constructed in arbitrary shapes, to replace modulating functions. TP-PINN is not only suitable for irregular domains but also decouples the enforcement of boundary conditions from the multi-objective loss function by separating the training process into two phases, thereby mitigating the negative impact of multi-objective optimization on computational efficiency. The effectiveness of this novel framework is demonstrated through a forward problem involving the computation of the deformation of an Euler-Bernoulli beam and a Kirchhoff-Love plate, which are governed by high-order ordinary and partial differential equations. In the analysis of structures with graph-like connectivity, such as truss structures and cable-strut systems, the geometry and topology of structures are important structural information that can be learned within the PIML framework. These inherent graph-like properties inspire the integration of graph neural network (GNN) into PIML frameworks. In the last part of this research, PIGNN, where GNN is leveraged to replace the commonly used fully-connected feedforward neural network (FCFNN), is proposed as the fourth aspect to improve vanilla PINN. The prestress design task of tensegrity structures, a type of prestressed cable-strut structure, is performed by both vanilla PINN and PIGNN. Two-dimensional and three-dimensional tensegrity structures with regular and irregular geometries are investigated. Results show that PIGNN outperforms PINN in terms of efficiency and accuracy by effectively capturing the geometry and topology information of structures. |
| Rights: | All rights reserved |
| Access: | open access |
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