Sparse Reconstruction for Blade Tip Timing Based on Projective Minimax Concave Penalty

Monitoring the vibration state of rotor blades is essential for ensuring the operational safety of turbomachinery. However, existing vibration measurement techniques are insufficient to fully meet the online monitoring requirements for rotor blades. Blade Tip Timing (BTT) is a promising technique for blade vibration monitoring, offering the ability to capture vibration data across the entire rotor blade stage without contact. However, due to the nature of BTT measurement, the resulting signals are often highly undersampled. To address this challenge, researchers have introduced sparse reconstruction methods for parameter identification in BTT signals, but the L1 regularization method frequently underestimates the amplitude of blade vibrations. In response, this paper proposes a new nonconvex sparse regularization model designed to accurately recover blade vibration parameters from undersampled BTT signals. Simulated blade resonance signals were used to evaluate the model, with undersampled signals reconstructed using both L1 and PMC regularization terms. The results demonstrate that the proposed method not only accurately estimates blade vibration frequency and amplitude but also provides superior amplitude estimation accuracy compared to the L1 regularization method.