As a multi-frequency identification method, the MUSIC method has received more and more attention in the field of blade tip-timing (BTT) signal reconstruction. So far, an improved MUSIC method and a subspace dimension-reduced MUSIC (SDR-MUSIC) method were proposed to analyze BTT signals. However, they must rely on the expanded snapshot matrix to overcome the spectrum aliasing. The computational complexity of these methods was analyzed. The computation time of BTT signal reconstruction increased cubically as the size of the expanded matrix increased. This is unfavorable for real-time processing. In this paper, reconstruction conditions based on the MUSIC algorithm were proposed. This makes the traditional MUSIC method overcome spectrum aliasing without expanding the snapshot matrix. The computational complexity is greatly reduced. The feasibility of the reconstruction conditions was verified through simulations and aero-engine experiments. Under the reconstruction conditions, the frequency identification accuracy of the traditional MUSIC can reach that of the improved MUSIC method. Besides, an amplitude identification method was proposed based on the discrete Fourier transformation (DFT) and remainder theorem. It provides a feasible solution for the spectrum methods that cannot directly extract amplitude from the pseudo spectrum, such as the improved MUSIC, SDR-MUSIC, etc. The error of the amplitude identification was analyzed by simulations. And its feasibility was further verified by identifying all blade vibration amplitudes in the aero-engine experiments.

MUSIC方法作为一种多频识别方法，在叶尖定时（BTT）信号重构领域越来越受到重视。到目前为止，提出了一种改进的MUSIC方法和一种子空间降维MUSIC（SDR-MUSIC）方法来分析BTT信号。然而，他们必须依靠扩展的快照矩阵来克服频谱混叠。分析了这些方法的计算复杂度。BTT 信号重建的计算时间随着扩展矩阵的大小增加而呈三次增加。这不利于实时处理。本文提出了基于MUSIC算法的重构条件。这使得传统的 MUSIC 方法在不扩展快照矩阵的情况下克服了频谱混叠。计算复杂度大大降低。通过仿真和航空发动机实验验证了重建条件的可行性。在重构条件下，传统MUSIC的频率识别精度可以达到改进MUSIC方法的频率识别精度。此外，提出了一种基于离散傅立叶变换(DFT)和余数定理的幅度识别方法。为不能直接从伪频谱中提取幅度的频谱方法，如改进的MUSIC、SDR-MUSIC等提供了一种可行的解决方案。通过仿真分析了幅度识别的误差。并通过在航空发动机实验中识别所有叶片振动幅度进一步验证了其可行性。在重构条件下，传统MUSIC的频率识别精度可以达到改进MUSIC方法的频率识别精度。此外，提出了一种基于离散傅立叶变换(DFT)和余数定理的幅度识别方法。为不能直接从伪频谱中提取幅度的频谱方法，如改进的MUSIC、SDR-MUSIC等提供了一种可行的解决方案。通过仿真分析了幅度识别的误差。并通过在航空发动机实验中识别所有叶片振动幅度进一步验证了其可行性。在重构条件下，传统MUSIC的频率识别精度可以达到改进MUSIC方法的频率识别精度。此外，提出了一种基于离散傅立叶变换(DFT)和余数定理的幅度识别方法。为不能直接从伪频谱中提取幅度的频谱方法，如改进的MUSIC、SDR-MUSIC等提供了一种可行的解决方案。通过仿真分析了幅度识别的误差。并通过在航空发动机实验中识别所有叶片振动幅度进一步验证了其可行性。提出了一种基于离散傅立叶变换(DFT)和余数定理的幅度识别方法。为不能直接从伪频谱中提取幅度的频谱方法，如改进的MUSIC、SDR-MUSIC等提供了一种可行的解决方案。通过仿真分析了幅度识别的误差。并通过在航空发动机实验中识别所有叶片振动幅度进一步验证了其可行性。提出了一种基于离散傅立叶变换(DFT)和余数定理的幅度识别方法。为不能直接从伪频谱中提取幅度的频谱方法，如改进的MUSIC、SDR-MUSIC等提供了一种可行的解决方案。通过仿真分析了幅度识别的误差。并通过在航空发动机实验中识别所有叶片振动幅度进一步验证了其可行性。