Enhanced time-frequency representation of blade tip timing signals via group sparse modelling

High-speed rotating blades in aero-engines operate under extreme mechanical and thermal conditions, where high-cycle fatigue caused by low-amplitude, high-frequency vibrations is a primary source of structural failure. Reliable and accurate vibration monitoring is therefore essential for maintaining blade integrity and preventing catastrophic incidents. Blade Tip Timing (BTT) provides a non-intrusive alternative to strain measurement. Achieving a precise time–frequency representation of BTT signals is crucial for non-contact blade vibration monitoring and for the early detection of structural degradation, such as fatigue cracks. However, BTT measurements are non-uniform and undersampled, resulting in poor time–frequency concentration, susceptibility to noise, and frequency coupling among adjacent blades. To address these challenges, this paper introduces an enhanced time–frequency reconstruction framework based on group sparse modelling, which leverages the inherent continuity of blade dynamic frequencies. The framework explicitly encodes the intrinsic group sparse structure of blade vibration time–frequency characteristics. It formulates the reconstruction problem as a row-LASSO optimization model, which enforces group sparsity in the coefficient matrix. This approach simultaneously enhances time–frequency concentration, suppresses noise and spurious frequency components, and preserves the continuity of modal frequency trajectories. An efficient Alternating Direction Method (ADM) is further developed to solve the resulting convex optimization problem. Extensive numerical simulations and high-speed rotor experiments demonstrate that the proposed method achieves substantially improved time–frequency concentration and reconstruction accuracy compared with standard LASSO and Orthogonal Matching Pursuit (OMP). When applied to blades containing fatigue cracks, the method accurately tracks dynamic frequency shifts caused by crack initiation and clearly distinguishes crack-related signatures from coupled components. These results confirm that the proposed group sparse encoding framework provides an effective method for blade vibration monitoring and early crack diagnosis.