基于小波分析的梁裂缝识别研究

利用小波分析对筒支梁的裂缝进行识别。将带裂缝筒支梁的基本振型用Mexican Hat小波进行连续小波变换，从小波系数在裂缝处出现模极大值可以识别出裂缝位置，利用由小波系数计算得到的Lipschitz指数来识别裂缝深度，Lipschitz指数随着裂缝深度的增加而减小。通过分析和仿真计算获得满意结果，在仿真算例中分析了裂缝位置对Lipschitz指数的影响很小，可以忽略；振型的测点距离越大，Lipschitz指数越大。同时指出噪声对Lipschitz指数有影响但在噪声不很大时仍能较好地识别裂缝。该方法同样适用于多条裂缝的识别和其他构件的裂缝识别。

Cracks identification by means of the wavelet analysis

A wavelet-based approach is proposed for crack identification in beam structure. The fundamental vibration mode of a cracked simple-supported beam is analyzed using continuous wavelet transform and both the location and depth of the crack are estimated. The position of the crack is identified by the modulus maximun of the wavelet coefficients. The Lipschits exponent estimated by the wavelet coefficients is used as a useful indicator of the crack depth and it decays with the increase of crack depth. The influence of the crack location and the sampling distance of the vibration mode to Lipschits exponent is also disscussed. The validity of the proposed method is investigated both by analysis and simulations. The simulations show that the noisy data lowers Lipschits exponent but the Lipschits exponent is also in effect as an indicator of the depth of crack when noise is small. The method presented here may also be used to detect several cracks and cracks in other structures.