Sensing limit in blade tip timing measurement and underlying theory

Blade Tip Timing (BTT) is a promising non-contact technique for measuring blade vibrations in rotating machinery due to its minimal hardware intrusion and long service life. However, the inherent mismatch between the high vibration frequencies of the blades and the relatively low sampling rates achievable in practice leads to severe undersampling, thereby hindering accurate parameter identification—an essential task for blade health monitoring. Although numerous advanced parameter identification methods have been proposed, their performance strongly depends on the probe layout, and a unified, intuitive theory for evaluating and optimizing layouts remains lacking. In this paper, we develop a sensing limit theory based on the Delay Sampling Theorem (DST), providing fundamental insights into the capabilities and limitations of BTT measurement. Furthermore, recognizing that sampling jitter arising from tip vibration and rotational speed fluctuations is inevitable in practice, we extend the theory to account for such uncertainties and introduce the concept of a robust sensing limit. For practical applications, we derive a straightforward formula to compute the robust sensing limit for any given layout and present guidelines for layout evaluation and optimization. The strong agreement between theoretical predictions and experimental results validates the correctness and applicability of the proposed theory. Overall, the robust sensing limit theory offers a foundational framework for advancing BTT-based vibration measurement.