Application of Compressed Sensing Method With ℓ1/2-Norm in Fan/Compressor Mode Detection

Abstract

Abstract In this paper, ℓ1/2-norm method is used to replace the traditional ℓ1-norm to improve the compressed sensing technique. Numerical experiments and fan/compressor tests were performed to validate the applicability and robustness of the CS method based on ℓ1/2-norm. Numerical experiments show that ℓ1/2-norm method can effectually eliminate the spurious mode peaks generated by failed recovery of ℓ1-norm method. Further study with random sensor failure shows the stronger robustness and applicability of ℓ1/2-norm method. In the low-order acoustic mode detection experiment on cooling fan, 24 sensors were used to conduct mode decomposition at blade passing frequency (BPF). The recovered signal using ℓ1/2-norm method was sparser than that using ℓ1-norm method. In the case two sensors were randomly removed as failed sensors, the deviation between results of ℓ1/2-norm method and original signal was also found smaller. In the condition that more sensors failed and ℓ1-norm method did not work properly, ℓ1/2-norm method could still detect the main mode. For further validation, the data from a high-order aerodynamic pressure mode detection experiment on axial compressor with two sensors damaged was processed through ℓ1/2-norm method. The mode decomposition results at both BPF and the rotating instability frequency (RIF) agreed with the conclusion of the first experiment. Numerical experiments and fan/compressor tests show that using ℓ1/2-norm can significantly improve the application and robustness of compressed sensing in mode detection.