Structural Health Monitoring (SHM) is increasingly shaped by the adoption of low-power and distributed sensing technologies, which make long-standing challenges — such as limited data transmission, energy efficiency, and computational scalability — more critical than ever. In vibration-based monitoring, these constraints motivate the use of highly compressed measurements, where traditional frequency identification methods often rely on computationally expensive signal reconstruction and problem-specific tuning, limiting their applicability at high compression ratios. This study introduces a novel general method, named approximate Bayesian Frequency Identification ( Bay-Fi ), which enables direct identification of the main modal frequency without requiring signal reconstruction and any prior tuning. The proposed approach adopts Bayesian principles to update prior information on the main frequency using an approximate likelihood derived from compressed measurements, enabling robust estimation under severe data sparsity. The effectiveness of Bay-Fi is first validated through experimental tests on a laboratory-scale, simply-supported beam, demonstrating superior frequency identification performance compared to conventional techniques. Subsequently, the methodology is applied to real-world data collected from an operational composite steel–concrete bridge. Results confirm the robustness of the approach, showcasing its ability to accurately identify structural vibration frequencies even under extreme data sparsity, without requiring prior training. These findings highlight the potential of Bay-Fi for real-time, low-power SHM applications in large-scale infrastructure monitoring.
Nardin et al. (2026) studied this question.