Fast enhanced MVDR for time-frequency analysis of blade tip timing

Variable-speed blade tip timing signals are inherently non-uniformly undersampled, which makes the identification of weak high-frequency modes particularly challenging and also limits the applicability of conventional high-resolution spectral methods due to their heavy computational burden. To address these issues, this paper proposes a Fast Enhanced Minimum Variance Distortionless Response (FE-MVDR) time-frequency analysis method for rotating blade vibration parameter identification. The proposed method preserves the high-resolution and interference-suppression advantages of MVDR, while improving its efficiency and robustness under variable-speed conditions. Specifically, the overlap structure between adjacent sliding windows is exploited to derive a low-rank recursive update of the inverse covariance matrix, thereby avoiding repeated full-dimensional matrix inversion in sliding-window analysis. In addition, a Gaussian-weighted reference-delay steering vector is introduced to mitigate steering vector mismatch caused by local sampling-structure variation under variable-speed operation. The proposed method is validated through numerical simulations, rotational experiments on a five-blade integrally bladed disk, and compressor blade experiments on a turbofan engine. The results show that FE-MVDR effectively suppresses spectral peak broadening in low-speed and rapid speed-transition regions, and significantly improves the extraction of weak high-frequency modes. Compared with traditional methods, the proposed method produces clearer and more concentrated modal ridges without requiring a predefined signal subspace dimension. Comparisons with strain-gauge measurements further confirm the accuracy and physical credibility of the identified dominant modal frequencies and their temporal evolution. In addition, FE-MVDR achieves an approximately fivefold improvement in computational efficiency under the same data scale and parameter settings. Engine experiments further show that axial measurement location has a significant influence on the observability of different modal orders. These results demonstrate that FE-MVDR provides an effective solution for high-resolution blade vibration identification under complex variable-speed operating conditions.