基于双树复小波降噪和Katz分形维迹线融合的板类结构损伤检测

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摘要目前基于振动响应的板类结构损伤检测技术存在着噪声免疫力弱、对轻微损伤难以识别等困难。对此，本文提出一种对板振型进行双树复小波变换（DT-CWT）降噪和仿射变换预处理的Katz分形维迹线扫描融合的板结构损伤检测方法。该方法首先利用DT-CWT对原始实测板结构的振型信号进行降噪；然后将降噪后的振型沿板纵、横向离散分解为振型曲线；将分解后的振型曲线进行仿射变换，得到拉伸后的线型面图；对变换后的线型面图分别进行Katz分形维迹线扫描，得到沿板纵向和横向的分形维迹线曲面图，将二者取均值得到融合后的分形维迹线曲面图；此融合后的曲面图中的凸起预示了损伤的发生，凸起的位置、形状和尺寸反应了损伤所在的位置、形状和尺寸。通过两个模型试验证明了本文方法对板结构损伤识别的有效性；对比分析说明了对振型进行DT-CWT降噪和仿射变换预处理的重要性。

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	白润波?1
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关键词 ：损伤检测, 板, 双树复小波, 分形维, 仿射变换, 振型

Abstract：

The existing vibration-based damage detection methods are commonly suffered from several limitations,such as,low immunity to noises and insensitivity to weak damages.To solve these problems,here a novel damage detection method was developed for plate-like structures using Katz’s fractal dimension sweep trace technique based on denoising with the dual-tree complex wavelet transformation (DT-CWT) and the affine transformation pretreatment. Firstly,the DT-CWT was used to denoise a original measured vibration signal,the denoised vibration signal was then decomposed into a set of modal shape curves in aplate’s vertical and horizontal directions.The decomposed modal shape corves were then transformed with affine transformation with affine transformation to make the lines no curvature turning point.Secondly,the fractal dimension scanning was applied to the transformed lines to form vertical and horizontal fractal dimension trace surfaces.Finally,the fused fractal dimension trace surface obtained by averaging vertical and horizontal ones was formed for the damage detection.The location and sizes of the damage were determined with the location and sizes of the sudden changes in the fused fractal dimension trace surface.The effectiveness of the proposed method and the importance of the DT-CWT denoising and the affine transformation pretreatment were demonstrated with two model tests.

Key words： damage detection plate DT-CWT fractal dimension affine transformation modal shape

收稿日期: 2015-10-08 出版日期: 2017-02-25

引用本文:

白润波?1,2，徐宗美1，张建刚1. 基于双树复小波降噪和Katz分形维迹线融合的板类结构损伤检测[J]. 振动与冲击, 2017, 36(5): 87-94.
BAI Runbo1,2,XU Zongmei1,ZHANG Jiangang1. Damage detection for plate-like structures based on DT-CWT denoising and fusion of Katz’s fractal dimension trajectories. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(5): 87-94.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2017/V36/I5/87

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