循环小波变换及其应用  

A CYCLIC WAVELET TRANSFORM AND ITS APPLICATION

作　　者：于开平[1] 邹经湘[1] 谢礼立[1] 

机构地区：[1]哈尔滨工业大学航天工程与力学系

出　　处：《工程力学》2002年第6期6-10,共5页Engineering Mechanics

基　　金：国家自然科学基金资助(19972017)

摘　　要：介绍了循环小波的概念及其循环小波变换的快速算法,详细描述了由原正交小波获得其相应的循环小波的过程,从其中的缠绕叠加过程中,给出了信号的循环小波分解的一般公式,对任意长度数据的信号使用任意偶数的Daubechies小波的变换矩阵的构成给出了统一的描述。接着对使用循环小波变换识别结构系统脉冲响应函数的思想进行了仿真研究。在仿真中以两自由度和悬臂梁结构系统为例考虑了不同的小波对识别精度的影响,还讨论了循环小波变换方法的总体平均性能。The concept of cyclic wavelet transform and its fast algorithm are introduced. A process oftransforming original wavelet into corresponding cyclic wavelet is discussed in detail. A general formula of cyclicwavelet decomposition of a signal is given by wrapping round and adding process. A uniform description of even Daubechies cyclic wavelet transform matrix for a signal with the arbitrary power of 2 lengths is presented. The extraction procedure of impulse response via cyclic wavelet transform for structural system identification isintroduced, then simulation of the presented procedure for two DOF and cantilever system is studied. In the simulation, ensemble-averaging performance and influence of using the Daubechies wavelet with variable length on the identification accuracy is discussed and compared with that of the extraction procedure based on the FFT.

关 键 词：循环小波 小波变换 结构系统 脉冲响应函数 

分 类 号：O241.82[理学—计算数学] O342[理学—数学]