基于小波变换的时变结构参数识别研究
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摘要
近年来,越来越多大型土木工程结构安装了结构健康监测系统,结构参数识别是桥梁健康监测和损伤识别的关键核心技术,也是难点。对于时不变系统,目前已有许多模态参数识别方法。然而,许多实际的土木工程结构在其运营过程中表现出时变特性,识别这类结构的时变参数(模态参数和物理参数)对监测结构运营状况和诊断结构损伤情况十分重要。另外,实际土木工程结构在一定程度上表现出非线性行为,一方面由于材料本身的非线性及结构的几何非线性,另一方面由于结构发生损伤,也会表现出非线性行为,通常的线性理论不能很好反映非线性结构的本质特征。本文在总结前人工作的基础上,采用小波变换的方法识别时变结构的时变参数(模态参数和物理参数)和结构的非线性,从理论、数值模拟和试验三个方面做了比较深入的研究。主要研究工作如下:
(1)首先简要介绍了结构健康监测系统研究的发展现状,指出结构参数识别及非线性识别的重要性。其次对线性时不变结构、时变结构参数识别以及结构非线性识别研究进行了详细综述,明确了论文的研究背景、依据和意义,阐明了本文的主要研究内容。
(2)提出了两种提取小波脊线的方法:一种基于信号小波变换系数的相位信息,采用迭代法提取小波脊线,对于噪音影响对识别结果的干扰,提出了基于矩阵奇异值分解(SVD)的方法降低其影响。另一种方法基于小波变换系数的模信息,根据模的极大值,通过施加罚函数平滑噪音干扰引起的小波脊变化的不连续性,将小波脊的提取问题转变为最优化问题,采用动态规划方法计算得到小波脊,识别信号的瞬时频率。
(3)建立了基于连续复Morlet小波变换的小波脊线识别结构瞬时频率的方法,设计了一个时变拉索结构试验。分别对索施加线性和正弦变化的拉力,改变拉索结构的刚度从而实现结构瞬时频率的时变,同时测试结构的冲击响应,运用提出的方法成功地识别了索的瞬时频率,并将识别值与结构在固定拉力作用下的固有模态频率结果进行对比分析,提出的方法效果良好,具有一定的抗噪性。
(4)提出基于离散小波变换识别时变结构物理参数的方法。利用离散小波变换将时变结构的时变参数在多尺度上展开为概貌信号和细节信号,忽略高频细节信号,仅由低频概貌信号估计时变参数,将时变结构识别问题转化为时不变结构识别问题。然后采用最小二乘法识别出低频尺度展开系数,从而重构得到原始时变参数。对于噪音引起的方程不适定性问题,采用Tikhonov正则化法减小其影响,采用具有时变刚度和阻尼的两层框架结构的数值模拟验证进行了验证。
(5)提出了基于连续小波变换识别结构非线性特性的方法。采用非线性结构骨架曲线概念,将非线性结构系统近似等效为时变系统,根据小波系数模极大值提取小波变换的脊线和小波骨架曲线,识别出非线性结构的瞬时频率和瞬时振幅,得到非线性结构的骨架曲线,从而识别出结构的非线性特性。通过具有非线性刚度结构的数值模拟验证了该方法的有效性。
In recent years, more and more structural health monitoring (SHM) systems have been installed in large civil engineering structures. The parameter (modal and physical) identification is one of the key issues in SHM. For time invariant system, there are presently many identification methods available. However, many practical engineering structures are time-varying. It is very important to identify time-varying parameters, including modal parameters and physical parameters, for consistent structural health monitoring and damage detection. Another issue is the structural nonlinearity, which may aise from material, geometry and structural damage. The usual linear theory can't represent the behavior of nonlinear structures. This dissertation presents a wavelet-based parameter (modal and physical) and nonlinearity identification methodology of time-varying structures. The work is focused on theory, simulation and experiment verification. The main research work of the dissertation is as follows:
(1) The dissertation starts with the state-of-the-art research of SHM and damage detection and reviews of the recent development of parameter identification for time invariant and time-varying systems as well as nonlinear identification. The research background and importance values of the dissertation are clarified. The main contents and contribution of the dissertation are also summarized.
(2) Two methods of extracting wavelet ridges are proposed. The one adopts the iterative algorithm based on phase information of wavelet coefficients. The singular value decomposition (SVD) technique is implemented to decrease the influence of noise. Another method extracts wavelet ridge based on the maximum modulus of wavelet coefficients. It uses a penalty function to smooth the discontinuous of wavelet ridges, so that the problem is transformed to an optimization problem. The wavelet ridges are finally extracted by using dynamic optimization method. Once the wavelet ridges are obatned, the instantaneous frequencies are identified from these wavelet ridges.
(3) A method of identifying instantaneous frequencies of time-varying structures is presented based on the continuous wavelet transform. A new time-varying cable experiment is designed and relized. The linear and sinusoidal varying tensions are respectively applied to the cable, which results in the time-varying cable stiffness. The instantaneous frequencies are identified using the presented method and the identified results are compared to the natural frequencies of the same cable bearing different fixed tensions. It is demonstrated that the method is effectively and anti-noise to some extent.
(4) A method of identifying physical parameters of time-varying structure based on discrete wavelet transform is presented. The time-varying parameters are expanded into approximate signal and detailed signal at multi-scale by discrete wavelet transformation. The time-varying physical parameters are eatracted only from the approximate signal with detailed signal being ignored. In such a way, the time-varying problem is transformed to the time invariant problem. The scale expand coefficients of low frequencies are identified using a least square method, and then the original time-varying parameters are reconstructed. The Tikhonov regularization is used to regularize the ill-posed problem of identification equation caused by noise. The effectiveness and accuracy of the proposed method are validated via a numerical simulation of a two-story frame structure with time-varying stiffness and damping. The results show that the presented algorithm can be used to identify effectively time-varying stiffness, and the identified damping is very sensitive to noise.
(5) A procedure to identify the nonlinear structure system is presented based on wavelet transform. By using a concept of the skeleton curve of nonlinear structure, a nonlinear system is approximately equivalent to a time-varying system. According to the maximum value of modulus of wavelet coefficient, the wavelet ridges and wavelet skeleton are extracted, which is used to identify the instantaneous frequencies and amplitudes. Then the skeleton curve of a nonlinear structure can be obtained. In such a way, the structural nonlinearity can be identified accordingly. The effectiveness and accuracy of the presented method are addressed via a numerical simulation of a structure with a cube-varying nonlinear stiffness.
(1)首先简要介绍了结构健康监测系统研究的发展现状,指出结构参数识别及非线性识别的重要性。其次对线性时不变结构、时变结构参数识别以及结构非线性识别研究进行了详细综述,明确了论文的研究背景、依据和意义,阐明了本文的主要研究内容。
(2)提出了两种提取小波脊线的方法:一种基于信号小波变换系数的相位信息,采用迭代法提取小波脊线,对于噪音影响对识别结果的干扰,提出了基于矩阵奇异值分解(SVD)的方法降低其影响。另一种方法基于小波变换系数的模信息,根据模的极大值,通过施加罚函数平滑噪音干扰引起的小波脊变化的不连续性,将小波脊的提取问题转变为最优化问题,采用动态规划方法计算得到小波脊,识别信号的瞬时频率。
(3)建立了基于连续复Morlet小波变换的小波脊线识别结构瞬时频率的方法,设计了一个时变拉索结构试验。分别对索施加线性和正弦变化的拉力,改变拉索结构的刚度从而实现结构瞬时频率的时变,同时测试结构的冲击响应,运用提出的方法成功地识别了索的瞬时频率,并将识别值与结构在固定拉力作用下的固有模态频率结果进行对比分析,提出的方法效果良好,具有一定的抗噪性。
(4)提出基于离散小波变换识别时变结构物理参数的方法。利用离散小波变换将时变结构的时变参数在多尺度上展开为概貌信号和细节信号,忽略高频细节信号,仅由低频概貌信号估计时变参数,将时变结构识别问题转化为时不变结构识别问题。然后采用最小二乘法识别出低频尺度展开系数,从而重构得到原始时变参数。对于噪音引起的方程不适定性问题,采用Tikhonov正则化法减小其影响,采用具有时变刚度和阻尼的两层框架结构的数值模拟验证进行了验证。
(5)提出了基于连续小波变换识别结构非线性特性的方法。采用非线性结构骨架曲线概念,将非线性结构系统近似等效为时变系统,根据小波系数模极大值提取小波变换的脊线和小波骨架曲线,识别出非线性结构的瞬时频率和瞬时振幅,得到非线性结构的骨架曲线,从而识别出结构的非线性特性。通过具有非线性刚度结构的数值模拟验证了该方法的有效性。
In recent years, more and more structural health monitoring (SHM) systems have been installed in large civil engineering structures. The parameter (modal and physical) identification is one of the key issues in SHM. For time invariant system, there are presently many identification methods available. However, many practical engineering structures are time-varying. It is very important to identify time-varying parameters, including modal parameters and physical parameters, for consistent structural health monitoring and damage detection. Another issue is the structural nonlinearity, which may aise from material, geometry and structural damage. The usual linear theory can't represent the behavior of nonlinear structures. This dissertation presents a wavelet-based parameter (modal and physical) and nonlinearity identification methodology of time-varying structures. The work is focused on theory, simulation and experiment verification. The main research work of the dissertation is as follows:
(1) The dissertation starts with the state-of-the-art research of SHM and damage detection and reviews of the recent development of parameter identification for time invariant and time-varying systems as well as nonlinear identification. The research background and importance values of the dissertation are clarified. The main contents and contribution of the dissertation are also summarized.
(2) Two methods of extracting wavelet ridges are proposed. The one adopts the iterative algorithm based on phase information of wavelet coefficients. The singular value decomposition (SVD) technique is implemented to decrease the influence of noise. Another method extracts wavelet ridge based on the maximum modulus of wavelet coefficients. It uses a penalty function to smooth the discontinuous of wavelet ridges, so that the problem is transformed to an optimization problem. The wavelet ridges are finally extracted by using dynamic optimization method. Once the wavelet ridges are obatned, the instantaneous frequencies are identified from these wavelet ridges.
(3) A method of identifying instantaneous frequencies of time-varying structures is presented based on the continuous wavelet transform. A new time-varying cable experiment is designed and relized. The linear and sinusoidal varying tensions are respectively applied to the cable, which results in the time-varying cable stiffness. The instantaneous frequencies are identified using the presented method and the identified results are compared to the natural frequencies of the same cable bearing different fixed tensions. It is demonstrated that the method is effectively and anti-noise to some extent.
(4) A method of identifying physical parameters of time-varying structure based on discrete wavelet transform is presented. The time-varying parameters are expanded into approximate signal and detailed signal at multi-scale by discrete wavelet transformation. The time-varying physical parameters are eatracted only from the approximate signal with detailed signal being ignored. In such a way, the time-varying problem is transformed to the time invariant problem. The scale expand coefficients of low frequencies are identified using a least square method, and then the original time-varying parameters are reconstructed. The Tikhonov regularization is used to regularize the ill-posed problem of identification equation caused by noise. The effectiveness and accuracy of the proposed method are validated via a numerical simulation of a two-story frame structure with time-varying stiffness and damping. The results show that the presented algorithm can be used to identify effectively time-varying stiffness, and the identified damping is very sensitive to noise.
(5) A procedure to identify the nonlinear structure system is presented based on wavelet transform. By using a concept of the skeleton curve of nonlinear structure, a nonlinear system is approximately equivalent to a time-varying system. According to the maximum value of modulus of wavelet coefficient, the wavelet ridges and wavelet skeleton are extracted, which is used to identify the instantaneous frequencies and amplitudes. Then the skeleton curve of a nonlinear structure can be obtained. In such a way, the structural nonlinearity can be identified accordingly. The effectiveness and accuracy of the presented method are addressed via a numerical simulation of a structure with a cube-varying nonlinear stiffness.
引文
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