小波分析在悬臂梁裂纹识别中的应用

基于空间信号的小波分析理论,将含裂纹悬臂梁前四阶振型信息直接用于小波变换,小波系数在空间域上的突变反映了裂纹的存在并指出了裂纹的位置.本文分析了前四阶振型对小波识别结果的敏感性,利用小波系数模极大值在尺度上的表现与Lipschitz指数之闻的关系建立了集中因子和裂纹深度之间的关系,以此来估计裂纹深度.鉴于实测信号往往是含噪声信号,分析了噪声对识别结果的影响规律.数值算例表明利用sym4小波对含裂纹梁的四阶振型信息进行小波分析可以准确地识别出裂纹的位置和深度;高阶振型对结构损伤较为敏感,高阶振型更适合于微裂纹和含噪声信息的处理,但高阶振型的非线性也会给裂纹识别带来一定的困难.使用本文方法进行结构裂纹参数识别,噪声对裂纹位置的影响只是指示清晰度的影响,基本不会产生错误的识别,而对裂纹深度的影响远比对位置的影响复杂,由于小波系数混入了噪声成分,从而增加了集中因子的取值,致使识别结果总是比真实结果偏大.

Application of wavelet analysis to crack identification in a cantilever beam

The wavelet transform is applied to the spatial-frequency analysis of the first four modes of the cracked cantilever beam.The position of the crack is located by the sudden change in the spatial variation of the transformed response.The sensitivity of the first four mode shapes to crack location and depth are discussed.Furthermore,the defined intensity factor,which derives from a relation between behavior of the wavelet maxima for different scales and the Lipschitz exponent,can be used to estimate the size of the crack.To investigate the effect of noise or measurement error on the proposed detection process,the theoretical modes added some noise are also analyzed.The simulation results illustrate that both crack position and size can be detected exactly by sym4 wavelet transform of the first four mode shapes in spatial domain.And the second mode is considered as competitive candidate for crack parameter identification comparing the other mode for cantilever beam for excellent tolerance of the noise using the present method.It is also seen that the effect of the noise is negligible for identification of crack location,but the identified crack depth is always higher than the actual depth because of adding the components of noise.