Compressed Sensing-based Blade Tip-timing Vibration Reconstruction under Variable Speeds

Blade tip-timing (BTT) has been regarded as a promising solution of on-line blade vibration monitoring. The rotating speed is often considered to be constant in traditional BTT methods. In practice, this assumption is hardly satisfied, so that BTT vibration monitoring under variable speeds faces is a big problem to be solved. Moreover, BTT vibration signals are always under-sampled due to the limited number of BTT probes and multi-band with less prior knowledge due to system's nonlinearity and complicated aerodynamic excitations. Thus blind multi-band vibration reconstruction under variable speeds is a key challenge by using under-sampled BTT signals. To deal with it, a novel compressed sensing (CS) method in angular domain is proposed to overcome the challenge in this paper. First, angular-domain sampling model of BTT signals is built and its multi-coset sampling scheme is first presented. Then the CS model of BTT signals is derived in order domain. Two metrics of the support reconstruction ratio and the relative root mean square are defined to characterize the reconstruction performance in order and angular domains, respectively. In next simulations, the performances of four reconstruction algorithms are compared, i.e., Orthogonal Matching Pursuit, Multiple Signal Classification, Modified Focal Under-determined System Solver and Basis Pursuit Denoising algorithms. Influences of different algorithms and measurement noises on the reconstruction performance are simulated.