Multi-coset angular sampling-based compressed sensing of blade tip-timing vibration signals under variable speeds

Blade Tip-Timing (BTT) has been regarded as a promising way of on-line blade vibration monitoring. But blind multi-band BTT vibration reconstruction is a big challenge under variable speeds and under-sampling. In order to deal with it, a novel Compressed Sensing (CS) method is proposed based on Multi-Coset Angular Sampling (MCAS) in this paper. First, multi-coset sampling scheme of BTT vibration signals is presented. Then the CS model of BTT vibration signals is derived in order domain. A sufficient condition of the number of BTT sensors is derived for perfect reconstruction and optimal placement of BTT sensors is determined by minimizing the condition number. In the end, numerical simulations are done to validate the proposed method and the performances of four reconstruction algorithms are compared, i.e., Orthogonal Matching Pursuit (OMP), Multiple Signal Classification (MUSIC), Basis Pursuit Denoising (BPDN) and Modified Focal Underdetermined System Solver (MFOCUSS). Influences of the sensor placement, the number of BTT sensors and measurement noises on the reconstruction performances are also testified. The results demonstrate that the proposed method is feasible and the overall performance of the BPDN algorithm is the best among the four algorithms. Also the reconstruction performance decreases with the accelerations of rotating speed.