压缩感知在轴流压气机周向模态识别中的应用

研究了将压缩感知应用于轴流压气机管道周向模态识别的方法。采用数值实验的方法对稀疏模态信号进行压缩感知分析。对确定性信号，讨论了信号欠采样因子和感知常数对不同稀疏比信号重构成功率的影响，当感知常数大于3.5时，感知成功率超过90%；对未知信号，随机选取测量矩阵在感知失败时信号的模态分布没有规律。在此基础上，将Nyquist-Shannon采样定理和压缩感知方法结合，提出了轴流压气机管道周向模态传感器双均布测点布置方式，发现了其感知的成功与否与信号模态数的差值和测点数相关，选择合适的测点数，可用于基于动静干涉的压气机周向模态的可靠重构。讨论了双均布测点分布的鲁棒性，发现任意减少3个测点时仍可保证研究对象中至少5个叠加模态的成功感知。最后，将压缩感知方法应用于轴流压气机管道周向模态识别，成功感知到了基于Tyler-Sofrin的轴流压气机高阶动静干涉模态。该研究为轴流压气机管道模态分析和测量提供了新的实验数据处理方法。 

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.