基于小波奇异性的梁结构损伤评估方法研究

Research on beam damage diagnosis based on wavelet singularity

通过一个简支梁的数值模拟,根据小波奇异性检测原理,利用两种方法对梁的损伤进行诊断,提出了利用Gaus1小波进行梁结构的损伤诊断方法.首先利用Gaus1小波对转角进行小波变换,对简支梁结构的振型求一阶导数,得到转角,再确定损伤位置、损伤程度与Lipschitz指数的关系,并与利用Gaus2小波对振型直接进行小波变换的方法进行比较研究,发现第一种方法在损伤定位、模极大值线的求取方面比后者优越.所提出的Gaus1小波方法可以对实际梁结构进行有效的损伤诊断,这将为小波理论的深入研究提供一种新的思考问题思路和方法.

According to the wavelet singularity theory and numerical simulation studies of beam structure, two methods of wavelet damage diagnosis are employed to analyze the damage diagnosis of beam structure based on Gausl wavelet. Firstly, the first derivative of the mode shape （rotation） is studied and gotten. Then, the continuous wavelet transform（CWT） by a Gausl wavelet is employed to deeply analyze the rotation of beam structure, the damage position and the relation between damage extent and Lipschitz exponent, and some significant results are gotten. Finally, by comparing the above-mentioned method and the methods through CWT by Gaus2 applied to the mode shape, it is found that the above-mentioned method is much better than Gaus2 method. So, the above-mentioned method can be employed to study practical beam structure damage diagnosis, which suggests the new ideas and methods for the advanced development of the wavelet theory.