Sparse-VMD coupled model for signal recovery and strain field prediction in blade tip timing

Real-time measurement of rotor blade dynamic stress is crucial for accurately predicting the operational status of blades and ensuring the service safety of aero-engines. However, sensing the blade vibration state under multi-mode vibration in real-time poses significant challenges with existing monitoring methods. First, a sparse reconstruction model based on L₀ regularization is applied to the undersampled Blade Tip Timing (BTT) signal for signal recovery. A coupled Sparse-VMD model is then introduced, where the recovered signal is decomposed using adaptive modal selection Variational Mode Decomposition (VMD). This model dynamically selects the optimal number of modes based on the signal characteristics, enabling the decoupling of modal frequencies from rotational frequency and its harmonics. Finally, a transfer matrix is constructed using the blade's modal shapes to predict the dynamic strain responses based on the decoupled modal components obtained from the coupled Sparse-VMD framework. The effectiveness of the proposed method is confirmed through both numerical simulations and experimental testing. Simulation results indicate that the relative error in the blade's dynamic strain predicted by the proposed method remains below 5 % when compared to the theoretical value. In the spinning tests, the relative error of multi-mode dynamic strain prediction of the blade does not exceed 14 %. The proposed method offers robust support for the online monitoring of multi-mode dynamic strain in rotor blades.