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1、第六届全国土木工程研究生学术论坛 清华大学 2008第六届全国土木工程研究生学术论坛 清华大学 2008 本文为国家杰出青年基金和国家科技支撑计划等项目资助。作者简介：黄永（1984-），男，湖南衡阳人，博士研究生，从事结构健康监测研究（Email： huangyong）；李惠（1966-），女，山东济南人，教授，从事防灾工程研究；欧进萍（1959-），男，湖南永州人，教授，从事防灾工程研究。 基于分形理论和小波包变换的损伤识别方法 黄永1，李 惠1，欧进萍1,2 (1.哈尔滨工业大学土木工程学院，哈尔滨 150090；2.大连理工大学土木水利学院，大连116024) 摘 要：大多数的结构损伤
2、识别方法都具有对噪声比较敏感的缺点，限制了方法的实际应用。在本文中，提出了一 种基于分形理论和小波包的新的损伤识别方法。在这个方法中，结构上每一个采样点的自由振动反应首先由NeXT 方法分析结构的随机振动信号获得，然后用DB5小波函数将其小波包分解到第j层，每一个小波包分量的时间序列 都需要计算结构几何分布的分形维数的平均值。梁的损伤位置可以由各小波包分量的分形维数曲线上的剧烈波动来 确定，损伤程度可以由基于分形维数的指标确定。为了验证方法的识别效果，将其应用于一个简支梁进行损伤 识别的数值试验，结果表明此方法不仅能成功地定位损伤，还能定量损伤程度。抗噪试验表明综合考虑各小波包分 量的信息此方
3、法既有很强的抗噪性能。 关键词：分形理论；小波包变换；基于分形损伤指标 Fractal theory and wavelet packet transform based damage identification method Huang Yong 1, LI Hui 1, OU Jinping 1,2 (1. School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China； 2. School of Civil and Hydraulic Engineering, Dalian Univer
4、sity of Technology, Dalian 116024, China) Abstract: Most of structural damage identification methods have the drawback of being sensitive to noise which restricts their practical application. In this study, a new damage identification method based on Fractal theory and wavelet packet transform is pr
5、esented. The free vibration of every sampling point were first obtained by NeXT method analysing signals of random vibration measured from structures and then decomposed into the j level wavelet packet components by adopting DB5 mother wavelet functions, for every time array of wavelet packet compon
6、ent then need to calculate the mean FD value along the structure. The location of damage in the beam can be determined by the dramatic fluctuation appearing on contour of estimated FD and the extent of the damage can be estimated by FD-based damage index of of all the wavelet packet component. As a
7、validation, the proposed method is applied to detect damage in a simply supported beam by numerical study. The successful detection of the damage in the beam demonstrates that the method is capable of assessing both the location and size of the damage. Noise stress tests are also carried out to demo
8、nstrate the strong robustness of the method under the influence of noise by considering all the information of every wavelet packet component synthetically. Key words: Fractal theory; wavelet packet transform; FD-based damage index 1. Introduction Damage present a serious threat to the performance o
9、f structures and for this reason damage identification have received growing attention over the last two decades and will be one of the important directions for future research. Damage identification has the advantage of identifying damage as soon as it is initiated, and it can maintain the safety a
10、nd integrity of the structures so as to avoid loss of human life and money. Vibration-based techniques for damage identification provide powerful methods allowing one to locate and size the damage.The mathematical tools to extract useful features from the vibration signals for damage identification
11、are significant. Among many signal analysis methods, the wavelet transform based method for vibration signal analysis is used more and more widely in damage identification due to its good time-frequency localization1-3.A possible drawback of the wavelet transform is that it have difficulties to disc
12、riminate signals containing high frequency components as the frequency resolution centralize in the low frequency region. The wavelet packet transform (WPT) is a mathematical tool, which provides a complete level-by-level decomposition of signal 4. It enables the extraction of features from the sign
13、als that combine the stationary and non-stationary characteristics with an arbitrary time- frequency resolution. Sun and Chang 5 proposed a wavelet packet component energy index which was combined with neural network models for damage assessment. S.S. Law et. al 6 have brought forward the sensitivit
14、y of wavelet packet transform component energy with respect to local change in the system parameters to 2 2 / 6 6 identify damage. The wavelet energy rate index computed by decomposeing Dynamic signals measured from structures into the wavelet packet components was proposed by Jiangang Han et.al7 wh
15、ich is used to locate damage. In the last several years, damage identification methods based on nonlinear theory such as attractor and fractal theory have received growing attentions. Hadjileontiadis L J et al.8 also brought forward a new technique for crack identification in beam structures based o
16、n fractal dimension analysis. The proposed approach adopts Katzs estimation of the fractal dimension employing the sliding window. The location and the size of the cracks are related to the fractal dimension measure which represent the local irregularity or nonlinear of mode shape. In the paper, a new arithmetic based on fractal theory and wavelet packet transf
