基于Hankel矩阵与奇异值分解（SVD）的滤波方法以及在飞机颤振试验数据预处理中的应用

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振动与冲击 ›› 2009, Vol. 28 ›› Issue (2) : 162-166.

论文

基于Hankel矩阵与奇异值分解（SVD）的滤波方法以及在飞机颤振试验数据预处理中的应用

张波李健君

作者信息 +

A DENOISING METHOD BASED ON HANKEL MATRIX AND SVD

IN APPLICATION FOR FLIGHT FLUTTER TESTING DATA

ZHANG Bo LI Jianjun

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文章历史 +

摘要

将Hankle矩阵与SVD分解相结合对受噪声污染的飞机颤振试验数据进行滤波，以提高颤振模态参数识别的精度，首先对由测量数据构造的Hankle矩阵进行SVD分解，再根据对噪声统计特性的掌握程度，采用两种不同的方法，即基于噪声统计特性的方法和基于奇异值变化曲线突变点的方法，将由含噪的测量数据所构成的Hankel矩阵分成两个互不相关的空间——真实信号空间和噪声空间，最后在真实信号空间中，利用平均的方法重构经过滤波的数据。通过数值仿真和应用于实际的飞机颤振试验数据，对Hankel矩阵取不同维数时对空间划分和滤波效果的影响进行了分析和研究，并验证了该方法是有效和可行的。

Abstract

Hankel matrix is combined with SVD for denoising fight flutter testing data corrupted by noise, in order to improve the precision of identifying flutter modal parameters. Firstly Hankel matrix made of measured data is used in SVD; then on the basis of the extent of mastering the statistic property of noise, two different methods respectively based on the statistic property of noise and a sudden change of singular value varying curve are used, the Hankel matrix is divided into two uncorrelated spaces, real signal space and noise space; finally the denoising singal is constructed with a average algorithm in real signal space. According to the results of numerical simulation and application in fight flutter testing data, the influence of different dimensions of Hankel matrix on division of spaces and denoising effect is analyzed and studied , feasibility and effectiveness of the denoising methed are showed.