Application of compressed sensing in circumferential modal identification of axial compressor

Application of compressed sensing in the recognition of azimuthal modes in axial compressor ducts was studied. Compressed sensing of sparse mode signals with various sampling numbers and distributions was performed by means of numerical experiments. For determined signals with different sparsities, effects of the undersampling factor and the sensing constant on the probability of successful reconstruction were discussed. The probability of success was more than 90% when the sensing constant was larger than 3.5. For blind signals, no specific pattern of signal reconstruction was observed. On this basis, a dual-uniform distribution of sampling points was proposed, by combining the advantages of Nyquist-Shannon sampling theorem and compressed sensing. It indicates that the feasibility of sensing depends on the wave number differences and the number of measurement points. When appropriate number of sampling points was selected, the reconstruction of azimuthal modes was reliable. The robustness of this dual-uniform distribution was also investigated. It was verified that a signal composed of 5 modes can still be reconstructed with 3 of the sensors break down. Eventually, compressed sensing was successfully applied in the recognition of azimuthal modes arising from rotor-stator interference based on the Tyler-Sofrin theory. An innovative technique discussed gives a good option in measuring and analyzing azimuthal duct modes of axial compressors.