基于压缩感知的整体叶盘多模态振动叶尖定时信号重构方法

叶尖定时测量技术是近年来发展的一种非接触式旋转叶片振动监测方法，具有非入侵性的优点，但是该系统测得的振动信号通常是欠采样的。为了能够重构叶尖定时欠采样信号，本文根据压缩感知理论以及叶尖定时采样原理引入了叶尖同步振动信号稀疏模型以及叶尖振动信号重构方法。对整体叶盘有限元模型进行瞬态分析得到叶尖振动信号，使用优化的正交匹配追踪算法以及基追踪对欠采样信号进行重构并和传统方法进行对比。计算结果表明：在信噪比为30dB的噪声环境下，限制频域的正交匹配追踪算法(OMP-RFD)可以准确地识别出叶尖振动信号的主要频率成分。最后使用试验所获得的叶尖振动信号进行重构，验证了OMP-RFD算法有效性。综上可知：压缩感知方法可以很好地应用于叶尖定时测量装置中，能够使用较少传感器识别叶尖同步振动欠采样信号参数,有效提高噪声环境下识别高阶频率的成功率以及准确度。

Multi-Modal Vibration Tip Timing Signal Reconstruction Method for Blisk Based on Compressed Sensing

Blade tip timing measurement is a non-contact rotating blade vibration monitoring method developed in recent years. It has the advantage of non-invasiveness. However, the vibration signal measured by this system is usually under-sampled. In order to reconstruct the blade tip timing under-sampled signal, a sparse model of blade tip synchronous vibration signals and a method of reconstruction of the blade tip vibration signal is introduced based on the compressed sensing theory and the principle of blade tip timing measurement. The blade tip vibration signal obtained by transient analysis of the finite element model of the blisks. The under-sampled signal is reconstructed by the optimized orthogonal matching pursuit algorithm and basis pursuit, and compared with traditional methods. The results show that in a noisy environment with SNR=30dB, the orthogonal matching pursuit restricted frequency domain algorithm (OMP-RFD) can accurately identify the main frequency components of the blade tip vibration signal. Finally, the blade tip vibration signals obtained from the experiment are used for reconstruction, and the effectiveness of OMP-RFD is verified. In conclusion, the compressive sensing method can be well applied to blade tip timing measurement. This method can identify the under-sampling signal parameters of the blade tip synchronous vibration with fewer sensors. Effectively improve the success rate and accuracy of identifying higher-order frequencies in a noisy environment.