电机故障信号小波变换边界问题及解决方法

Bound problem in fault signal processing of electric machine and its solution based on wavelet transform

小波变换比Fourier变换具有良好的时频局部化特性,是处理突变信号的有力工具。近年来,小波变换在电力系统故障信号的处理中得到广泛地应用。而故障信号的采样区间是有限的,小波变换在处理电力系统故障信号时存在两个边界问题:即靠近端点附近突变点很难识别出来;信号分解、压缩及重构时误差较大。因为传统处理方法将有限区间的信号通过补零、对称延拓和平滑扩充外来数据区间而造成人为误差,除Harr小波外任何正交的紧支撑小波不具有对称性或反对称性,因而不具有线性相位或广义线性相位,易出现信号恢复时失真现象。提出的区间双正交小波方法同时具有正交性、紧支撑性及对称性,实验结果表明这种小波误差小、精度高。

Wavelet transform has better local time-frequency charateristic than Fourier transform and is a powerful method of sudden-changeable signal processing,which is widely used in the fault signal processing of power system.As the sampling interval of fault signals is finite,two boundary problems in applying wavelet transform were ignored in many documents.It is not easy to recognize the sudden-changeable points near the boundary.The man-made errors induced by the data supplement through zero-adding,symmetrical expansion and smoothing in signal deconstruction,compression and re-construction are quite big.Furthermore,except Harr wavelet,the general orthogonal local-sup-ported wavelets are neither symmetric nor anti-symmetric,without linear phase or generalized linear phase,which causes distortion in signal reconstruction.The finite interval bi-orthogonal wavelet is or-thogonal,local-supported and symmetric,and is used to solve above two problems.Results demonstrate small errors and high precision.This project is supported by National Nature Science Foundation of China(50077008).