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Time-Vertex Machine Learning for Optimal Sensor Placement in Temporal Graph Signals: Applications in Structural Health Monitoring

Keivan Faghih Niresi, Jun Qing, Mengjie Zhao, Olga Fink

TL;DR

This work tackles optimal sensor placement for time-varying structural health monitoring by introducing TVML, a data-driven framework that fuses graph signal processing, temporal analysis, and machine learning. TVML extracts statistical and spectral features, clusters sensors to reduce redundancy, and uses a graph-centrality–based TopoScore to select representative sensors within each cluster, with STGNNs evaluating downstream damage detection and signal reconstruction. The approach is validated on two bridge datasets, showing TVML outperforms baselines in both detection accuracy and reconstruction fidelity, especially under sparse sensing. The study also demonstrates robustness to centrality-weight choices and highlights avenues for future enhancements like learnable weights and task-adaptive sensor selection. This framework offers a practical, interpretable path to cost-effective SHM with strong performance guarantees across time-varying graph signals.

Abstract

Structural Health Monitoring (SHM) plays a crucial role in maintaining the safety and resilience of infrastructure. As sensor networks grow in scale and complexity, identifying the most informative sensors becomes essential to reduce deployment costs without compromising monitoring quality. While Graph Signal Processing (GSP) has shown promise by leveraging spatial correlations among sensor nodes, conventional approaches often overlook the temporal dynamics of structural behavior. To overcome this limitation, we propose Time-Vertex Machine Learning (TVML), a novel framework that integrates GSP, time-domain analysis, and machine learning to enable interpretable and efficient sensor placement by identifying representative nodes that minimize redundancy while preserving critical information. We evaluate the proposed approach on two bridge datasets for damage detection and time-varying graph signal reconstruction tasks. The results demonstrate the effectiveness of our approach in enhancing SHM systems by providing a robust, adaptive, and efficient solution for sensor placement.

Time-Vertex Machine Learning for Optimal Sensor Placement in Temporal Graph Signals: Applications in Structural Health Monitoring

TL;DR

This work tackles optimal sensor placement for time-varying structural health monitoring by introducing TVML, a data-driven framework that fuses graph signal processing, temporal analysis, and machine learning. TVML extracts statistical and spectral features, clusters sensors to reduce redundancy, and uses a graph-centrality–based TopoScore to select representative sensors within each cluster, with STGNNs evaluating downstream damage detection and signal reconstruction. The approach is validated on two bridge datasets, showing TVML outperforms baselines in both detection accuracy and reconstruction fidelity, especially under sparse sensing. The study also demonstrates robustness to centrality-weight choices and highlights avenues for future enhancements like learnable weights and task-adaptive sensor selection. This framework offers a practical, interpretable path to cost-effective SHM with strong performance guarantees across time-varying graph signals.

Abstract

Structural Health Monitoring (SHM) plays a crucial role in maintaining the safety and resilience of infrastructure. As sensor networks grow in scale and complexity, identifying the most informative sensors becomes essential to reduce deployment costs without compromising monitoring quality. While Graph Signal Processing (GSP) has shown promise by leveraging spatial correlations among sensor nodes, conventional approaches often overlook the temporal dynamics of structural behavior. To overcome this limitation, we propose Time-Vertex Machine Learning (TVML), a novel framework that integrates GSP, time-domain analysis, and machine learning to enable interpretable and efficient sensor placement by identifying representative nodes that minimize redundancy while preserving critical information. We evaluate the proposed approach on two bridge datasets for damage detection and time-varying graph signal reconstruction tasks. The results demonstrate the effectiveness of our approach in enhancing SHM systems by providing a robust, adaptive, and efficient solution for sensor placement.
Paper Structure (29 sections, 39 equations, 14 figures, 3 tables, 3 algorithms)

This paper contains 29 sections, 39 equations, 14 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graph Signal Processing
  4. Learning Graph from Data
  5. Graph Signal Sampling
  6. Methodology
  7. Problem Definition
  8. Proposed Method
  9. Feature Extraction for Sensor Signals
  10. Clustering via $K$-Means
  11. Graph-Based Representative Selection within Clusters
  12. Spatial-Temporal Graph Neural Networks for Downstream Tasks
  13. Distinction from Existing Methods
  14. Experimental Results
  15. Case Studies
  16. ...and 14 more sections

Figures (14)

  • Figure 1: Block Diagram of the Proposed TVML Framework for Sensor Selection. The framework combines time series and graph-based analysis to select informative and non-redundant sensors. Statistical and spectral features guide clustering, while graph centrality measures help identify representative sensors within each cluster.
  • Figure 2: Visualization of Various Node Centrality Measures in Network Graphs.
  • Figure 3: STGNN Architecture for Evaluation on Damage Detection and Graph Signal Reconstruction Task
  • Figure 4: Comprehensive visualization of the Train-Track-Bridge dataset. (a) Train-Track-Bridge physical structure. (b) The graph representation aligns all nodes in a straight line, resembling the physical structure of the bridge. (c) The colormap of the adjacency matrix visualizes connectivity strengths among nodes.
  • Figure 5: ROC curves for the compared methods
  • ...and 9 more figures