连续小波变换由于其在信号奇异性检测中的出色表现，而被广泛地应用到基于振动的无损检测方法中。本文以二维Morlet小波和Pethat小波为例，分别对各向同性和各向异性二维连续小波变换在空间信号的奇异性检测中的应用进行了研究。首先，我们分别对两种小波函数各自处理空间信号的特点进行了分析；其次，我们采用数值分析方法，应用这两种小波函数对二维空间信号进行二维连续小波变换，并提取其小波系数进行奇异性识别。最后，针对含损伤的复合材料层合板的奇异性检测结果，分析比较两种小波函数在模态振型奇异性检测中的适用性，并为基于振动的无损检测方法提供技术支持。
Continuous wavelet transform is widely applied in damage detection methods based on vibration because of its excellent ability of singularity detection. In this paper, two kinds of two-dimensional wavelet functions, Morlet and Pethat, as anisotropic and isotropic wavelets, were studied for their abilities in singularity detection. Firstly, characteristics of these two wavelet functions were figured out. Then, the singularity detection of two-dimensional signal was conducted numerically by these two wavelet functions. Finally, a comparative analysis of these two wavelet functions was carried out for damage detection of composite laminate by mode shapes. Results show that these two wavelet functions have different singularity sensitivities, which can be developed in application of non-destructive testing method based on vibration.
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