Physics-Informed Machine Learning for Beam-Type Structures: Multiple Incipient Crack Assessment in Metal Beams and Time-Dependent Behavior Prediction of Prestressed Concrete Beams = 보형 구조물을 위한 물리 정보 기반 기계학습: 금속보의 다중 초기 균열 진단 및 프리스트레스트 콘크리트 보의 시간의존적 거동 예측

다국어 초록 (Multilingual Abstract)

Although machine learning has been increasingly adopted in structural engineering as a flexible alternative to conventional numerical methods, its performance remains highly dependent on the availability of large, high-quality datasets, a condition rarely met in practice. To overcome this limitation, physics-informed machine learning （PIML）, which integrates governing physical knowledge into the learning process, has emerged as a promising approach capable of enabling reliable predictions even under data-scarce conditions. This study presents a unified PIML framework for addressing two fundamental machine learning problem categories, classification and regression, through their representative applications in structural engineering, under conditions where measurement data are scarce and the available physical models are necessarily simplified and cannot fully represent the actual structural behavior, with physical knowledge incorporated into the learning process to compensate for data scarcity in both cases. In the first application, a PIML-assisted framework is proposed for assessing multiple incipient cracks in beam-type structures as a representative classification problem in structural health monitoring. A closed-form frequency equation derived from the phase-closure principle is employed as a physics-based surrogate model to efficiently generate large-scale training datasets of broadband modal frequencies at minimal computational cost. The augmented data are refined and used to train a classifier capable of identifying the number of cracks. Based on the identified crack count, grid optimization is subsequently applied to assess crack locations and depths. The proposed framework is validated through blind tests using both finite element-based and experimentally measured data, demonstrating reliable crack assessment performance even without prior knowledge of the crack count. In the second application, a physics-informed neural network （PINN） is introduced for predicting the early-age time-dependent behavior of prestressed concrete girders and reconstructing their camber profiles as a representative regression problem in structural performance prediction. Integro-differential governing equations accounting for concrete creep, shrinkage, tendon relaxation, and the variation of elastic modulus are embedded directly into the neural network loss function in dimensionless form to predict the time- dependent prestress loss. Based on the predicted prestress force, a second PINN model incorporating the curvature–deflection relationship is subsequently employed to reconstruct the camber profile along the girder span. The prestress loss prediction is validated against reference solutions obtained from the finite difference method, while the camber reconstruction is further validated against experimental measurements from an actual prestressed concrete girder, demonstrating accurate prediction of prestress loss and physically consistent camber reconstruction under limited data conditions. The two applications collectively establish physics-informed learning as a practical and unified approach for data-scarce structural engineering problems, demonstrating consistent effectiveness across these two distinct problem types.

목차 (Table of Contents)

• Ⅰ. Introduction 1
• 1.1 Research Background 1
• 1.2 Research Motivations 3
• 1.2.1 Physics-Informed Machine Learning (PIML) 3
• 1.2.2 Research Trends and Literature Review 5
• 1.3 Problem Categories in PIML 12
• 1.3.1 Problem Categorization in ML and Conceptual Reformulation in PIML 12
• 1.3.2 Classification Problem 15
• 1.3.3 Regression Problem 19
• 1.4 Objectives and Scope 24
• 1.5 Notations 28
• 1.5.1 Nomenclature Used in ChapterⅡ 28
• 1.5.2 Nomenclature Used in ChapterⅢ 29
• Ⅱ. PIML-Based Classification for Multiple Incipient Crack Assessment in Beams 32
• 2.1 Assessment of Multiple Incipient Cracks in Beams 32
• 2.1.1 Limitations of Previous Studies 32
• 2.1.2 Challenges in Applying PIML 37
• 2.2 Broadband Modal Frequency Measurement 44
• 2.3 Surrogate Model for PIML 52
• 2.3.1 Closed-Form Solution Based on the Phase-Closure Principle 52
• 2.3.2 Finite Element Analysis for Validation 54
• 2.4 PIML for Crack-count Identification 57
• 2.4.1 Data Augmentation 57
• 2.4.2 Data Refinement 59
• 2.4.3 Implementation of PIML 60
• 2.4.4 Blind-Test Data Generation for Numerical and Experimental Validation 61
• 2.5 Crack Location and Depth Assessment 66
• 2.5.1 Grid Optimization 66
• 2.5.2 Determining Optimal Resolution 67
• 2.6 Validation Results 71
• 2.7 Additional Validation: Fixed-Free Beam 76
• 2.8 Chapter Summary 84
• Ⅲ. PINN-Based Regression for Time-Dependent Behaviors Prediction and Camber Reconstruction of PSC Girders 89
• 3.1 Time-Dependent Behaviors of PSC Girder 89
• 3.1.1 Early-Age Behavior and Limitations of Previous Approaches 89
• 3.1.2 Challenges in Applying PINN to PSC Girders 92
• 3.2 Governing Equations of PSC Girder 95
• 3.2.1 Prestress Loss 95
• 3.2.2 Camber Reconstruction 103
• 3.3 PINN Configuration 104
• 3.3.1 Prestress Loss 104
• 3.3.2 Camber Reconstruction 106
• 3.4 Optimal Hyperparameters 108
• 3.5 Numerical Verification and Results 111
• 3.5.1 Rectangular Cross Section 111
• 3.5.2 Conventional PSC I-Beam Section 120
• 3.5.3 Camber Reconstruction (TY7) 123
• 3.6 Chapter Summary 128
• Ⅳ. Conclusion 131
• Appendices 135
• References 152
• 국문초록 178