基于随机动力响应互相关函数分析的结构损伤识别方法研究
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摘要
结构的突发性损毁事件造成了巨大的生命和财产损失,结构的安全性问题引起了人们广泛的关注,并促进了结构健康监测领域研究的发展。基于动力测试的结构损伤识别方法是目前结构健康监测系统研究的热点和难点课题。利用结构在环境激励作用下的动力响应进行结构损伤识别是实际工程应用的切实需求。
本文在结构随机振动动力响应互相关函数分析的基础上开展了结构损伤识别的方法研究,具体内容如下：
(1)推导了理想白噪声环境激励下,结构位移、加速度及速度响应之间互相关函数的表达式,针对有限带宽白噪声激励,对该系列表达式进行了修正。建立了相邻测点动力响应互相关函数幅值向量,证明了幅值向量的固形原理,为基于结构动力响应互相关函数的结构损伤识别方法奠定了理论基础。
(2)研究了基于结构动力响应互相关函数分析的损伤判定、定位及量化识别方法,讨论了该方法使用中的抗噪能力、采样时长及识别盲区等问题。通过数值模拟的连续梁损伤识别及八层钢框架模型损伤模拟试验分析,验证了环境激励下结构动力响应互相关函数用于结构损伤识别的可行性。
(3)利用小波包对结构的动力响应信号进行分解,以各分解频带的“振动能量”构造损伤特征向量作为支持向量机的输入信息,从模式分类的角度进行结构损伤识别。通过框架模型的损伤模拟试验数据,对比分析了利用单个测点加速度响应作为支持向量机损伤特征输入,以及多测点数据融合情况下的识别结果,指出了直接以动力响应的小波包分解频带能量作为损伤特征的不足。
(4)从解析表达式分析着手,指出了动力响应互相关函数比结构响应时程涵盖了更多的损伤信息,提出了将支持向量机与动力响应互相关函数结合的结构损伤识别方法,在ASCE-SHM benchmark模型Ⅱe阶段的算例分析中,分别从加速度响应、加速度响应间的互相关函数、互相关函数幅值向量提取结构的损伤特征建立支持向量机,对比了三者之间的识别效果,验证了从互相关函数提取的损伤特征具有优秀的损伤表征能力。
(5)探讨了如何解决支持向量机在样本训练中对损伤类别的先验条件局限性,提出了实际工程中如何将互相关函数与支持向量机结合进行结构损伤识别的两阶段方法。
Unexpected incidents always cause huge loss of life and property. The structural safety has aroused widespread concerns in recent years, which in turn promotes the development of the structural health monitoring system (SHMS). Dynamic based structural damage detection method is still a hot and difficult topic in the SHMS research. It is practically necessary to apply the dynamic responses induced by environment excitation in structural damage identification.
In this study the damage detection method is investigated based on the cross-correlation functions of structural random vibration. The following topics are included:
(1) The cross-correlation functions between the structural displacement, velocity and acceleration excited by the white noise are derived and then amended for the case of the bandlimited white noise. The amplitude vectors of the cross-correlation functions of adjacent measurement points are built and also proved satisfying the solid-shape principle. Theoretical foundations for damage detection method based on cross-correlation functions of dynamic responses are established.
(2) Cross-correlation functions of dynamic responses based method for damage determination, locating and quantification is proposed. Several key issues including noise immunity, sample length and identification "blind area" in the application of the method are discussed. By numerical simulation of a continuous beam and an eight-story steel frame, the dynamic responses cross-correlation functions are verified feasible for the structural damage detection under environmental excitation.
(3) By using wavelet package, dynamic responses are decomposed to several frequency bands and the "signal energy" of each band is used to build damage characteristic vector which is used as the input information of support vector machine. In this way, the damage is identified from the prospective of pattern classification. Based on the damage simulation of the frame structure where the acceleration responses are taken as input information of support vector machine, the comparative analysis between single-point and multi-point measurements indicates the deficiency of directly using the wavelet decomposed acceleration "band energy" as the damage characteristic quantity.
(4) The analytical expressions are also derived indicating that the dynamic responses cross-correlation functions contain more damage information than the time-history response. It is proposed to combine support vector machine and dynamic response cross-correlation as the new method for damage detection. Taking ASCE-SHM benchmark model of phase IIe as example, accelerations, acceleration cross-correlation functions and the amplitude vector of cross-correlation functions are respectively used to extract the damage feature and build the support vector machine. By comparing their damage identification results, it is shown that the damage feature extracted from the cross-correlation functions is an excellent characterization.
(5) For the aim of practical application in structural damage detection, two steps of identification technique based on cross-correlation functions and support vector machine are provided.
本文在结构随机振动动力响应互相关函数分析的基础上开展了结构损伤识别的方法研究,具体内容如下：
(1)推导了理想白噪声环境激励下,结构位移、加速度及速度响应之间互相关函数的表达式,针对有限带宽白噪声激励,对该系列表达式进行了修正。建立了相邻测点动力响应互相关函数幅值向量,证明了幅值向量的固形原理,为基于结构动力响应互相关函数的结构损伤识别方法奠定了理论基础。
(2)研究了基于结构动力响应互相关函数分析的损伤判定、定位及量化识别方法,讨论了该方法使用中的抗噪能力、采样时长及识别盲区等问题。通过数值模拟的连续梁损伤识别及八层钢框架模型损伤模拟试验分析,验证了环境激励下结构动力响应互相关函数用于结构损伤识别的可行性。
(3)利用小波包对结构的动力响应信号进行分解,以各分解频带的“振动能量”构造损伤特征向量作为支持向量机的输入信息,从模式分类的角度进行结构损伤识别。通过框架模型的损伤模拟试验数据,对比分析了利用单个测点加速度响应作为支持向量机损伤特征输入,以及多测点数据融合情况下的识别结果,指出了直接以动力响应的小波包分解频带能量作为损伤特征的不足。
(4)从解析表达式分析着手,指出了动力响应互相关函数比结构响应时程涵盖了更多的损伤信息,提出了将支持向量机与动力响应互相关函数结合的结构损伤识别方法,在ASCE-SHM benchmark模型Ⅱe阶段的算例分析中,分别从加速度响应、加速度响应间的互相关函数、互相关函数幅值向量提取结构的损伤特征建立支持向量机,对比了三者之间的识别效果,验证了从互相关函数提取的损伤特征具有优秀的损伤表征能力。
(5)探讨了如何解决支持向量机在样本训练中对损伤类别的先验条件局限性,提出了实际工程中如何将互相关函数与支持向量机结合进行结构损伤识别的两阶段方法。
Unexpected incidents always cause huge loss of life and property. The structural safety has aroused widespread concerns in recent years, which in turn promotes the development of the structural health monitoring system (SHMS). Dynamic based structural damage detection method is still a hot and difficult topic in the SHMS research. It is practically necessary to apply the dynamic responses induced by environment excitation in structural damage identification.
In this study the damage detection method is investigated based on the cross-correlation functions of structural random vibration. The following topics are included:
(1) The cross-correlation functions between the structural displacement, velocity and acceleration excited by the white noise are derived and then amended for the case of the bandlimited white noise. The amplitude vectors of the cross-correlation functions of adjacent measurement points are built and also proved satisfying the solid-shape principle. Theoretical foundations for damage detection method based on cross-correlation functions of dynamic responses are established.
(2) Cross-correlation functions of dynamic responses based method for damage determination, locating and quantification is proposed. Several key issues including noise immunity, sample length and identification "blind area" in the application of the method are discussed. By numerical simulation of a continuous beam and an eight-story steel frame, the dynamic responses cross-correlation functions are verified feasible for the structural damage detection under environmental excitation.
(3) By using wavelet package, dynamic responses are decomposed to several frequency bands and the "signal energy" of each band is used to build damage characteristic vector which is used as the input information of support vector machine. In this way, the damage is identified from the prospective of pattern classification. Based on the damage simulation of the frame structure where the acceleration responses are taken as input information of support vector machine, the comparative analysis between single-point and multi-point measurements indicates the deficiency of directly using the wavelet decomposed acceleration "band energy" as the damage characteristic quantity.
(4) The analytical expressions are also derived indicating that the dynamic responses cross-correlation functions contain more damage information than the time-history response. It is proposed to combine support vector machine and dynamic response cross-correlation as the new method for damage detection. Taking ASCE-SHM benchmark model of phase IIe as example, accelerations, acceleration cross-correlation functions and the amplitude vector of cross-correlation functions are respectively used to extract the damage feature and build the support vector machine. By comparing their damage identification results, it is shown that the damage feature extracted from the cross-correlation functions is an excellent characterization.
(5) For the aim of practical application in structural damage detection, two steps of identification technique based on cross-correlation functions and support vector machine are provided.
引文
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