基于最大坡度法提取非平稳信号小波脊线和瞬时频率  

WAVELET RIDGE AND INSTANTANEOUS FREQUENCY EXTRACTION BASED ON MAXIMUM GRADIENT METHOD

作　　者：刘景良 任伟新[2] 王超[3] 黄文金 

机构地区：[1]福建农林大学交通与土木工程学院,福州350002 [2]合肥工业大学土木与水利工程学院,合肥230009 [3]华中科技大学土木工程与力学学院,武汉430074

出　　处：《工程力学》2018年第2期30-37,46,共9页Engineering Mechanics

基　　金：国家自然科学基金青年基金项目(51608122;51408250);福建省自然科学基金青年科技人才创新项目(2016J05111);福建农林大学校杰出青年基金项目(XJQ201728)

摘　　要：提出一种基于最大坡度法的非平稳信号小波脊线提取和瞬时频率识别新方法。该方法首先对非平稳响应信号进行连续复Morlet小波变换,其时间轴、小波尺度轴及小波系数模值构成一个三维坐标系(x,y,z);其次从预先设定的小波脊线初始点出发,在一定范围内进行搜索,并分别计算其在时间-尺度平面(x-y)的距离、z方向的距离及小波脊线的坡度值。最后,求解位于最大坡度方向上的各空间点并将其连接成线即为所求的小波脊线。采用三个非平稳信号数值算例和一个拉力时变的拉索试验验证了最大坡度法的有效性,并与基于小波系数模局部极大值的脊线提取方法、动态规划法及瞬时频率理论值进行比较。数值模拟和试验结果表明,该方法能够有效提取非平稳响应信号的瞬时频率,且识别精度优于基于小波系数模局部极大值和基于动态规划的小波脊线提取方法。Firstly, continuous wavelet transform is performed on non-stationary response signals, and as a result, the vectors time, scale and wavelet coefficients modulus constitute a three dimensional coordinate system （x, y, z）. Secondly, the searching step is conducted from the initial point of the wavelet ridge, and meanwhile the distance in the time-scale plane （x-y） and height direction （z） and the gradient of wavelet ridge are calculated. Finally, the wavelet ridge curves can be successfully extracted by connecting the points with the maximum gradient. The effectiveness and accuracy of the proposed method are validated via numerical examples and a time-varying cable test. The results demonstrate that the method can extract the instantaneous frequency effectively and that its identification accuracy is superior to the method based on the maximum of wavelet transform modulus and dynamic optimization.

关 键 词：最大坡度法 瞬时频率 非平稳信号 小波变换 小波脊线提取 

分 类 号：TN911.6[电子电信—通信与信息系统] TU311.3[电子电信—信息与通信工程]