Iteratively Learning Reconstruction of Blade Tip-Timing Signals and Cointegration-Based Damage Detection Under Variable Conditions

Blade tip-timing (BTT) is a direct blade vibration monitoring technique and how to use under-sampled BTT signals for blade damage detection is still challenging under variable conditions. Compressed sensing (CS) has been introduced for reconstructing BTT vibration signals, but classical CS reconstruction algorithms are limited by the sparsity and slow optimization process. In order to overcome this issue, this paper presents an iteratively learning reconstruction method by introducing the vector approximate message passing (VAMP) algorithm, called VampNet. Firstly, a discrete Multi-coset sampling (MCS)-based CS model is built for BTT vibration signals in order domain and an improved Hanning-Possion window is integrated to reduce the order spectrum leakage in discretization. Then the VampNet model is proposed to reconstruct blade vibration engine orders (EOs) and the sensing matrix is discussed. Based on reconstructed vibration EOs, a cointegration-based method is proposed for blade damage detection, so that the influences of variable conditions can be reduced. Finally, the feasibility of the proposed method is testified by Matlab simulations and experimental dataset. The results show that blade vibration EOs can be accurately reconstructed by the VampNet and then small cracks can be detected by using the cointegrating residual.