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Topological Data Analysis for Subsurface Utility Sensing

초록/요약

Data analysis is fundamentally concerned with understanding the structure and patterns embedded in data, rather than relying solely on raw numer- ical values. In many sensing and imaging problems, the shape and geo- metric organization of data carry critical information that is often over- looked by conventional feature representations. Topological Data Analy- sis (TDA) provides a principled framework for capturing such structural characteristics by describing data through topological features that are ro- bust to noise and deformation. In this work, we explore the potential of TDA for subsurface utility sensing, where measurements are indirect and subject to significant uncertainty. Reliable identification of buried utilities is essential for safe excavation and infrastructure management, yet exist- ing nondestructive testing methods face inherent limitations. Subsurface sensing data are highly sensitive to noise, soil heterogeneity, and dielectric contrasts, while electrical resistance measurements yield sparse and spa- tially discontinuous information. Furthermore, the scarcity of labeled field data and the domain gap between simulated and real measurements hin- der robust underground detection. To address these challenges, this thesis proposes a unified, physics-informed framework that integrates topological representations with data-driven learning across multiple sensing modalities. For GPR data, a shape-aware topological representation embeds persistent- homology descriptors into simulated B-scan images, preserving hyperbolic geometry and improving Sim2Real generalization. For electrical resistance data, kriging-based spatial reconstruction transforms sparse inter-electrode measurements into dense spatial fields suitable for convolutional learning. Simulation and Sim2Real validation studies demonstrate improvements in hyperbola detection, pipe-location regression, and multi-pipe classification. Overall, the results indicate that integrating physical structure, topological reasoning, and data-driven learning provides an accurate and interpretable foundation for subsurface utility sensing.

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목차

1 Introduction 1
1.1 Research Background and Motivation 1
1.2 Limitations of Conventional Techniques 2
1.3 Overview of the Proposed Research Framework 4
1.4 Structure of the Thesis 7
Part I: GPR-Based Subsurface Utility Sensing 9
2 Theoretical Background of GPR and Topological Data Analysis 9
2.1 Principles of Ground Penetrating Radar 9
2.2 Signal Formation and B-Scan Characteristics 12
2.3 Topological Data Analysis 15
2.3.1 Persistent Homology 15
2.3.2 Vectorized Topological Descriptors 19
3 Simulation and Dataset Construction for GPR 22
3.1 Numerical Data Generation 22
3.2 Field Data Collection 25
4 Methodology 29
4.1 Step 1: Shape-Aware Topological Representation 30
4.2 Step 2: Sim2Real Training 32
4.3 Model Configurations 33
4.4 Training Setup 35
4.5 Results and Comparison 37
5 Summary of Part I 44
Part II: Electrical-Resistance–Based Subsurface Utility Sensing 47
6 Theoretical Background 47
6.1 Electrical Resistance Survey 47
6.2 Kriging-Based Spatial Interpolation 49
6.3 Convolutional Neural Network Regression 51
7 Simulated Data Generation 53
7.1 Simulated Data Generation 53
8 Methodology and Experiments 56
8.1 Overview of the Proposed Framework 56
8.2 Sparse-to-Dense Spatial Reconstruction 60
8.3 CNN Architecture for Regression 64
8.4 Input data and preprocessing 67
8.5 Experimental Setup 70
8.6 Comparison and Results 71
9 Summary of Part II 75
10 Conclusion and Future Directions 77
References 79
Appendix A: Multi-Pipe Classification from Electrical Resistance Measurements 85
A.1 Simulation of Multi-Pipe Configurations 85
A.2 Feature Representation and Classification Models 87
A.3 Training Setup and Evaluation Metrics 90
A.4 Classification Results 91
A.5 Summary 96

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