基于TSVD和Hilbert变换的相位差测量方法及应用  

Method and Its Application of Phase Difference Measurement Based on TSVD and Hilbert Transformation

作　　者：王国富[1] 吕晓凡[1] 高平东[1] 张法全[1] 

机构地区：[1]桂林电子科技大学信息与通信学院,广西桂林541004

出　　处：《仪表技术与传感器》2014年第6期144-146,149,共4页Instrument Technique and Sensor

基　　金：国家自然科学基金(61102115);广西自然科学基金(2012GXNSFBA053177);广西研究生教育创新计划资助项目(YCSZ2013067)

摘　　要：针对工程应用中的信号缓变特性,提出截断奇异值分解(TSVD)和希尔伯特(Hilbert)变换联合使用的相位差计算方法。首先对离散的含噪一维信号分段并构成汉克尔(Hankel)矩阵,根据TSVD的奇异值依次降序排列的规律,用奇异熵变化量的拐点确定奇异谱阶次,使该阶次内的信号饱和度基本代替原信号。将降噪后的矩阵重构得到降噪后的信号,对降噪后的信号进行Hilbert变换计算两路信号的相位差。仿真分析及实测数据表明:该联合计算方法满足工程应用,且具有一定的通用性。A method of combining TSVD with Hilbert transformation was introduced,and was used for calculating phase difference of slowly changing signals in engineering application.Firstly,discrete one-dimensional signal was divided into several segments,which are composed into a Hankel matrix.Hankel matrix was decomposed by TSVD,by means of singular entropy variation tendency,finding the optimal inflexion in order to include main signal components.The noise-reduced matrix was then used to reconstruct the noise-reduced signal.According to Hilbert transformation of the noise-reduced signal,phase difference value could be calculated.Simulated analysis and practical data show that this jointed method would be suited for engineering application and also has a certain commonality.

关 键 词：截断奇异值分解 希尔伯特变换 奇异熵 相位差 汉克尔矩阵 

分 类 号：TP274[自动化与计算机技术—检测技术与自动化装置]