三角样条小波的构造及其在故障检测中的应用

Application of Trigonometric Spine Wavelets to Fault Detection

本文首先给出了三角样条函数极其性质,然后在此基础上给出了一种构造三角样条小波的新方法。该方法简单易行,而且构造出的小波具有许多良好的性质,这些对信号处理是非常重要的。最后,将构造出的小波应用于故障信号的检测,与一些常用的小波相比,不但消除了边界效应,而且使故障信号在变换域内能量更集中,从而提高了故障检测的准确性。

This paper presents a new kind of trigonometric spine wavelet on the interval on the basis of trigonometric spine function. The method is very simple and easy, and these wavelets possess many good properties such as symmetry and anti-symmetry （linear phases or generalized linear phases）, good time-frequency locality, short support, semi-orthogonal. Finally, the trigonometric spine wavelets are applied to fault detection. Compared with some traditionally famous wavelets （Symmlets, Daubechies, Meyer, biorthogonal wavelets et al. ）, these wavelets show the advantages in eliminating the boundary effect and strong capability of getting more concentrated information in fault position.