CRLB-based optimal sensor layout for blade tip timing measurement

Rotating blades are critical but highly damage-prone components of aero-engines, whose vibration characteristics are directly related to the operational safety and stability of the entire system. Owing to its non-contact nature and long service life, the blade tip timing technique has become an important means for monitoring blade vibration in harsh operating environments. However, the limited number of sensors in practical applications leads to severe undersampling of blade tip timing signal, significantly constraining the accuracy of vibration parameter identification. To improve the parameter identification accuracy under limited measurement conditions, this paper proposes a blade tip timing sensor layout optimization method based on a statistical lower bound theory. By linking sensor placement to the theoretical limit of parameter estimation accuracy, the method achieves an optimal layout design that minimizes achievable estimation error. Furthermore, by introducing a weighted optimal design criterion, the layout optimization problem is reformulated as a solvable convex optimization model. In addition, numerical validation using both deterministic and random signals were performed under various noise levels and mode combinations. The proposed method was quantitatively compared against contemporary benchmarks, including the minimization of condition number array and random arrays. Results demonstrate that the sensor layout optimized using the Cramér-Rao lower bound consistently achieves the smallest estimation error and superior noise robustness. Finally, multi-mode vibration frequency identification and amplitude reconstruction experiments were conducted on the high-speed blade rotor test rig. The proposed strategy significantly outperformed the minimization of condition number benchmark by reducing the peak relative error of frequency identification from 6.01 % to within 1 %, and lowering the amplitude reconstruction error from 21.23 % to below 12 %.