Bayesian time-frequency sparse representation of blade tip timing signals

Rotor blades are critical components of aircraft engines, operating under extreme conditions of high temperature, pressure, and speed for long periods. These conditions make them prone to various faults. Therefore, rotor blade health monitoring is crucial for ensuring the operational safety of aircraft engines. Blade dynamic frequency is a key indicator for assessing the health status of blades. As a non-contact measurement technique, blade tip timing (BTT) enables simultaneous monitoring of vibration signals from all blades at the same stage. However, due to the unique nature of BTT measurement, the acquired signals are often highly undersampled, making it difficult to satisfy the Nyquist sampling theorem. To address the issue of frequency aliasing caused by non-uniformly undersampled BTT signals within the Fourier analysis framework, this study proposes a Bayesian time-frequency sparse representation method for undersampled BTT signals. The method employs an adaptive sliding window function to segment the non-uniform BTT signals, ensuring consistent time resolution in the time-frequency domain. Within each window, the Student-t distribution is utilized as the Bayesian prior information to exploit the sparsity of blade vibration signals in the frequency domain. Furthermore, the change continuity of the blade dynamic frequency is integrated into the Bayesian prior information to enhance dynamic frequency tracking accuracy. To confirm the effectiveness of the proposed method, ℓ₁-distance error and Rényi entropy are used to evaluate the time-frequency spectrogram, which confirms the effectiveness of the proposed method in the simulation section. A fatigue crack propagation test is conducted on rotor blades, revealing that at 1860s, cracks formed in the failed blade, accompanied by dynamic frequency shifts. The analysis results confirm that the proposed method accurately tracks dynamic frequency and provides an early warning of blade crack propagation.