1.Aeronautics and Astronautics Engineering College, Air Force Engineering University, Xi’an 710038, China
2.Advanced Aero Engine Collaborative Innovation Center, Beijing 100191, China
3.The Chinese People’s Liberation Army 95606 Troops, Guiyang 550031, China
4.The Chinese People’s Liberation Army 93066 Troops, Shenyang 110015, China
摘要奇异值分解(Singular value decomposition, SVD)可以将信号线性分解成一系列分量。本文通过深入分析基于Hankel矩阵的奇异值分解的基本原理和存在问题，揭示了奇异值分解的线性分解、重构分量频域无序和带通滤波等三个基本特性，据此提出了共振加强奇异值分解方法。数值仿真结果表明：所提方法不但很好地解决了传统奇异值分解的频域无序性问题，而且可以在任意给定频率附近，实现给定带宽的线性带通滤波，完整提取原始信号的幅值、频率和相位特征。这是现有各信号处理方法都没有的优势。将所提方法成功应用于某型涡桨发动机振动监测中的特征频率提取，结果表明方法具有优异的特征提取效果。
Singular value decomposition (SVD) can linearly decompose a signal into a series of components.In this paper, the basic principles and problems of singular value decomposition (SVD) based on Hankel matrix were analyzed, and three basic properties of SVD were revealed, which are linear decomposition, frequency domain disorder of reconstructed components and band-pass filtering.Based on this, a resonance enhanced singular value decomposition (SVD) method was proposed.The numerical simulation results show that the proposed method not only solves the frequency-domain disorder problem of the traditional singular value decomposition (SVD) well, but also can realize the linear bandpass filtering with a given bandwidth near any given frequency.The amplitude, frequency and phase features of the original signal are extracted completely.This is the advantage the existing signal processing methods do not have.The proposed method was successfully applied to the characteristic frequency extraction of a turboprop engine vibration monitoring.The results show that the proposed method has excellent feature extraction effect.
程礼1,2，梁涛1，郭立3，程铭1,4，曾林1. 共振加强奇异值分解方法及其在涡桨发动机振动监测中的应用[J]. 振动与冲击, 2018, 37(22): 206-213.
CHENG Li1,2,LIANG Tao1,GUO Li3,CHENG Ming1,4,ZENG Lin1. Resonance enhanced singular value decomposition and its application to the vibration monitoring of turboprop engine. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(22): 206-213.
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