Incorporating Risk in Operational Water Resources Management: Probabilistic Forecasting, Scenario Generation, and Optimal Control

Accurate measurement of tension forces in vertical hangers is critical for ensuring the operational safety of arch bridges. To overcome the limitations of traditional contact-based sensors, such as time-consuming deployment and labor-intensive processes, this study introduces a lightweight and -cost-effective millimeter-wave radar system for efficient tension force monitoring. The contributions of this work are twofold: (1) A lightweight radar system is developed, integrating a compact radar unit, embedded data processing modules, and a remote control computer. This system achieves real-time tension force measurement with ultra-high spatial resolution (5 cm), superior to conventional centimeter-wave radar systems, while significantly reducing weight (1 kg) and hardware costs. (2) A theoretical framework is established to correlate vibration displacement (captured by the developed radar) with dynamic tension forces, incorporating the analysis of critical parameters such as measurement alignment (in-plane vs. out-of-plane directions) and sensor positioning effects. Field experiments on an operational arch bridge validate the proposed methodology. Key findings include: (a) measurement direction has negligible influence (<1% relative error) on tension estimation, though in-plane alignment yields marginally higher accuracy; (b) while sensor positioning strongly affects displacement amplitudes, vibration frequencies (and thus derived tension forces) remain position-insensitive; (c) radar-measured tension forces exhibit <3% deviation from reference sensors. These results demonstrate that the developed millimeter-wave radar system has significant potential for tension force measurement and safety evaluation of arch, suspension, and cable-stayed bridges in transportation networks.