摘要
近20年来,基于振动的结构健康监测和损伤识别一直是国内外学者的研究热点。数字图像处理技术具有非接触、远距离和高精度3大特点,可以实现结构健康的实时在线监测。小波分析是一种信号的时间-尺度(时间-频率)分析方法,具有多分辨率分析的特点,在时域和频域都有表征信号局部特征的能力,在结构损伤识别领域得到越来越多的应用。结合数字图像处理和小波分析方法为结构振动信号的测量和损伤识别提供了新的思路。本论文在国家自然科学基金(50778077,50925828)的资助下,进行了基于数字图像处理和小波分析的损伤识别研究。
本文用理论分析、数值模拟和试验验证等方法从以下几个方面进行研究,取得了一些成果和结论：
1、分析了损伤识别中小波函数的选择方法。具有对称性的小波适合进行损伤识别。消失矩的阶数越高,其支撑长度会越长,对信号微小差异的刻画越明显,但是会增加计算时间。因此小波函数的选择应该在消失矩阶数和计算时间上找到一个平衡。消失矩的阶数至少应大于2,并且消失矩的阶数一般为4比较合适。
2、研究了一种基于结构振动响应能量密度函数统计矩的损伤识别方法。利用小波变换将振动响应分解为离散的能量分布,用小波系数构造相对零阶矩(RDI)、规格化零阶矩(NDI)损伤识别指标进行损伤识别。通过统计假设检验方法确定结构发生损伤的阈值。推导了单元模态应变能差的灵敏度矩阵,可以在较少实测模态的情况下识别板的损伤程度。板结构的数值算例表明这种方法在含有一定噪声干扰的情况下对单损伤和多损伤均能精确识别。
3、对结构自由振动的响应进行小波变换,建立基于残余小波力的损伤识别指标。将环境激励看成是平稳的随机过程,运用随机减量技术模拟自由振动的响应。结合矩阵分解在平面桁架的数值算例中进行了损伤识别,这种方法可以识别损伤的位置和程度,并且对噪声有很好的鲁棒性。
4、针对数字摄影测量进行多点动态位移的测量时面临数据量大、多路采集同步困难的问题,开发了多路位移监测系统。采用小波亚像素边缘检测方法使位移的精度达到0.01mm。磁盘阵列和同步信号发生器保证海量数据处理和多路相机之间的同步。在4层钢框架上实现了4路动态位移的同步采集,并与位移传感器进行对比。结果表明这套系统可以为结构健康监测和损伤识别提供比较准确的位移数据。
5、提出了一种结合数字图像测量系统和小波分析的方法进行结构的损伤识别方法。采用高速相机采集梁的位移时程曲线获取模态信息,再由模态位移计算曲率模态。在单损伤和多损伤的情况下,曲率模态和曲率模态小波变换都能准确识别损伤的位置。通过小波变换系数计算了Lipschitz指数指标识别损伤的程度。简支梁实验表明：这种方法对单损伤和多损伤的位置和程度有很好的识别。
In recent a few decades, the structural health monitoring (SHM) and damage detection based on vibration receive more attention among the scholars. The digital image processing technology has the features such as long distance, noncontact and high accuracy. It can achieve the real time and online monitoring in SHM. Wavelet analysis is a time-scale (time-frequency) analysis of signal. It is a multi-resolution method, and has the ability to detect the local features of the signal in time and frequency domain. There are more and more utilization in damage detection by using wavelet. Combination of digital image processing and wavelet analysis provides a new method for signal measurement of vibrational response and damage detection. With the fund of the national natural science foundation of China (50778077,50925828), the structural damage detection based on digital image processing and wavelet analysis is studied.
In this dissertation, following aspects have been studied theoretically, numerically and experimentally. Some important results and conclusions have been acquired:
(1) The selection of mother wavelet in damage detection is analyzed. The symmetrical wavelet is suitable for damage detection. When the order of vanishing moments is higher, the support length is longer and the damage detection result is more distinct, but more computational time is needed. Thus we should find the balance between the number of vanishing moments (NVM) and computational time. The NVM should be more than two at least, and the fourth vanishing moments should be very appropriate.
(2) The damage detection method is studied based on the statistical moments of the energy density function of the vibration responses in the time-scale domain. The continuous wavelet transform is conducted to decompose the vibrational responses into discrete energy distributions. The damage indices relative zeroth moments and normalized zeroth moments are established by the wavelet coefficients. The damage threshold is determined by the statistical hypothesis test. The sensitivity matrix of element modal strain energy change is derived to quantify the damage using a few numbers of lower modes. Simulation results of a plate show that the proposed approach is able to identify the single and multiple damage cases with artificial noises.
(3) The free vibration responses of structure are transformed by the wavelet, and the damage detection index is established based on the residual wavelet forces. The natural excitation is introduced to be a stationary random process, random decedent technique is used to simulate the free vibration responses. Combined with the matrix disassembly technique the damage is identified in the plane truss. The method is able to detect the location and extent of damage and is insensitive to the noises.
(4) The difficulties of traditional multi-dynamic displacement measurement are massive data and synchronization. In order to solve these problems, multi-point dynamic displacement-measurement system is developed based on digital image processing technology. The displacement accuracy can reach 0.01 mm by the wavelet subpixel edge detection method. The disk arrays and synchronization signal generator ensure massive data processing and multi-channel synchronization between cameras. The four-channel dynamic-displacement acquisition is carried out on a four-story steel frame structure. The results are compared with the displacement sensors. The system is able to provide the accuracy displacement data for structural health monitoring and damage detection.
(5) A method based on digital image processing and wavelet transform is presented for structural damage detection. The displacement time series of the beam at sub-pixel resolution are analyzed to obtain mode shape by high speed cameras. Then curvature mode shape is calculated by the mode shape. In single and multiple damage scenarios, curvature mode shapes and wavelet-transformed curvature mode shapes both can detect the damage location. The Lipschitz exponents are calculated by wavelet coefficients to identify the damage extents. Experimental results of a simple-supported beam show that the proposed approach is able to identify the locations and extents of the single and multiple damage scenarios.
引文
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