Spectrum recovery of the blade tip timing signal via the block sparsity-induced Bayesian learning

Compressive sensing (CS) emerges as a potent strategy for the recovery of blade tip timing (BTT) signal spectrum under conditions of severe undersampling. Yet, the efficacy of prevailing CS methods is contingent upon meticulous parameter tuning, limiting their flexibility across varying operational scenarios. This paper presents a novel block sparse Bayesian learning (BSBL) methodology designed to precisely reconstruct the spectra of undersampled BTT signals. By embedding block sparsity constraints within the sparse Bayesian learning (SBL) prior, the BSBL approach notably refines the feature representation of BTT signals, surpassing the capabilities of traditional techniques. The BSBL algorithm's parameters are adaptively refined under diverse working conditions through an expectation–maximization algorithm-based iterative updating mechanism. Numerical simulations and rotating leaf disk experiments, spanning a spectrum of rotational velocities and signal-to-noise ratios (SNRs), substantiate the BSBL algorithm's exceptional accuracy in BTT signal spectrum recovery and target frequency identification, even under heterogeneous operating conditions. Experimental results illustrate that the BSBL algorithm achieves mode frequency errors of the first two orders below 0.3 Hz and energy error rates below 10 % for rotating blades across different settings.