不完备测点结构损伤与荷载的同步识别算法研究
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摘要
输入信息未知、输出测试信息不完备条件下的结构损伤检测与荷载识别是土木工程结构识别领域中的一个重要问题。据此,本文以结构动态响应灵敏度为基础,提出一种仅利用结构少数测试自由度上的动态响应同步识别结构物理参数和输入时程的方法,并将识别的结构物理参数用于检测结构的局部损伤,同时,针对该方法的关键问题进行了一系列探讨,主要内容如下:
(1)提出了一种基于动态响应灵敏度同步识别结构物理参数和输入的方法。首先,通过将结构输入力进行正交多项式展开和对结构物理参数进行摄动,引入正交展开系数和单元刚度分数作为待识别的力参数和结构参数;然后,推导了结构动态响应对两类参数的灵敏度,构造了识别方程,并采用迭代形式进行求解。数值模拟表明,所提出的同步识别算法可实现仅利用结构少数测试自由度上的动态响应同步识别结构物理参数和输入时程。
(2)将同步识别算法推广用于未知基底激励作用下的结构损伤检测与荷载识别。首先,通过对未知基底激励进行正交展开,推导基于动态响应灵敏度、利用结构动态响应同步识别结构局部损伤和未知基底激励的识别方程;然后,采用正则化算法以迭代的形式求解识别方程。数值模拟和试验研究表明,测量噪声较小时,该方法的识别精度较高,正则化方法的引入可提高其抗噪能力;测量噪声较大时,该方法不能有效地识别出结构的损伤状况,但通过去除线性趋势项后处理的识别基底激励可以反映其真实值的变化趋势。
(3)提出了一种基于动态响应灵敏度概念、从待识别子结构上的动态响应同步识别其损伤及其与相邻子结构之间的界面力的方法。首先推导了子结构系统的动力方程;其次,将子结构之间的界面力进行正交展开,并推导待识别子结构上的动态响应对该子结构物理参数和界面力正交展开系数的灵敏度计算公式;再次,构造了识别方程并采用正则化方法对方程进行迭代求解。数值模拟表明,该方法仅利用待识别子结构内部几个自由度上的动态响应即可识别其上的局部损伤和界面力。
(4)提出了一种利用复杂结构系统中的某一子结构上的测量响应检测另外一个子结构上局部损伤的方法。首先,利用状态空间法表述两个子结构之间界面力的识别方程;然后,推导界面力对结构物理参数的灵敏度方程,同时构造利用界面力识别待识别子结构内局部损伤的识别方程,并采用正则化方法进行求解。数值模拟表明,所提出的基于界面力识别的子结构损伤检测方法可以精确地识别远离结构响应测点的子结构上的局部损伤。
(5)提出了一种基于概率可靠度理论、适用于未知输入下不确定性结构损伤与荷载的同步识别方法。首先,推导通过动态响应灵敏度方法同步反演结构损伤与荷载的不确定性公式;其次,利用数据摄动技术和蒙特卡罗法研究测量响应中的不确定性对识别结果的影响,并基于概率统计理论推导了损伤概率的计算公式。数值模拟和试验研究表明,该方法可在观测噪声水平较高的条件下实现多位置损伤的定位与定量,并可较准确地识别出结构的基底激励时程。
Damage detection and load identification of structures with unknown input and incomplete measured output information is an important problem in the area of identification of civil engineering structures. A method based on dynamic response sensitivity is therefore proposed to simultaneously identify structural physical parameters and input time-history from only several responses of structures. The identified structural physical parameters are used to detect structural local damages. Some key problems of the proposed method are studied in the dissertation. Main contents are as follows:
(1) A method based on dynamic response sensitivity is proposed to simultaneously identify structural physical parameters and input. The input force on structure is represented by using orthogonal polynomial approximation. By representing the input force on structure using orthogonal polynomial approximation and perturbing structural physical parameters, the orthogonal expansion coefficients and the fractional stiffness of structural elements are adopted as the force parameters and the structural physical parameters respectively, which are need to be identified. The sensitivity of structural dynamic response with respect to orthogonal coefficients and structural physical parameters is derived. The identification equation is set up and is solved with the damped least-squares method in an iterative process. Numerical simulation results show that the proposed simultaneous identification algorithm can simultaneously identify structural physical parameters and input from only several responses of structure.
(2) The proposed simultaneous identification algorithm is extended to identifying damage and load of structure under unknown support excitation. The support excitation on structure is represented by using orthogonal polynomial approximation. The simultaneous identification equation of structural local damages and unknown support excitation is derived based on dynamic response sensitivity. The regularization method is used to solve the identification equation in an iterative process. Numerical simulation and experimental results show that the proposed algorithm has higher identification accuracy when the level of measurement noise is lower. The regularization is helpful for improving the anti-noise ability of the algorithm. When the level of measurement noise is higher, the algorithm can not accurately identify structural damages, but the identified support excitation after removing the linear trend can reflect the true support excitation.
(3) A method based on dynamic response sensitivity is proposed to simultaneously identify local damages in a selected substructure and the interface forces between substructures from the dynamic responses on the selected substructure. The motion equation of substructural system is deduced. These interfacing forces between substructures are represented by orthogonal functions, and the sensitivity of the dynamic responses on the selected substructure to the substructural physical parameters and the orthogonal expansion coefficients of the interface forces is derived. An identification equation is set up and is solved by using regularization method in an iterative process. Numerical simulation results show that the proposed method can identify local damages and interface forces of the selected substructure from only several responses of the substructure.
(4) A method, which uses the measured responses of one substructure in a complex structural system to detect local damges in another substructure in the same structural system, is proposed. The identification equation of the coupling forces is formulated in state space. The sensitivity of interface forces to substructural physical parameters is derived. The equation of local damage identification in the selected substructure from the interface forces is set up and is solved with regularization method. Numerical simulation results show that the proposed damage detection method for substructure based on interface forces can accurately identify local damages of the substructure far from response measurements.
(5) A probabilistic method is proposed to identify damages of structures with uncertainties under unknown input. The uncertain equation for simultaneously identifying structural damage and load is derived based dynamic response sensitivity. The effect of uncertainties caused by measurement noise on the identified parameters is investigated with data perturbation technique and Monte Carlo method. The formula of probability of identified damages is further derived using the probabilistic method. Numerical simulation and experimental results show that the simultaneous identification method based on probability can locate and quantify multi-damages on structure, and accurately identify structural support excitation.
(1)提出了一种基于动态响应灵敏度同步识别结构物理参数和输入的方法。首先,通过将结构输入力进行正交多项式展开和对结构物理参数进行摄动,引入正交展开系数和单元刚度分数作为待识别的力参数和结构参数;然后,推导了结构动态响应对两类参数的灵敏度,构造了识别方程,并采用迭代形式进行求解。数值模拟表明,所提出的同步识别算法可实现仅利用结构少数测试自由度上的动态响应同步识别结构物理参数和输入时程。
(2)将同步识别算法推广用于未知基底激励作用下的结构损伤检测与荷载识别。首先,通过对未知基底激励进行正交展开,推导基于动态响应灵敏度、利用结构动态响应同步识别结构局部损伤和未知基底激励的识别方程;然后,采用正则化算法以迭代的形式求解识别方程。数值模拟和试验研究表明,测量噪声较小时,该方法的识别精度较高,正则化方法的引入可提高其抗噪能力;测量噪声较大时,该方法不能有效地识别出结构的损伤状况,但通过去除线性趋势项后处理的识别基底激励可以反映其真实值的变化趋势。
(3)提出了一种基于动态响应灵敏度概念、从待识别子结构上的动态响应同步识别其损伤及其与相邻子结构之间的界面力的方法。首先推导了子结构系统的动力方程;其次,将子结构之间的界面力进行正交展开,并推导待识别子结构上的动态响应对该子结构物理参数和界面力正交展开系数的灵敏度计算公式;再次,构造了识别方程并采用正则化方法对方程进行迭代求解。数值模拟表明,该方法仅利用待识别子结构内部几个自由度上的动态响应即可识别其上的局部损伤和界面力。
(4)提出了一种利用复杂结构系统中的某一子结构上的测量响应检测另外一个子结构上局部损伤的方法。首先,利用状态空间法表述两个子结构之间界面力的识别方程;然后,推导界面力对结构物理参数的灵敏度方程,同时构造利用界面力识别待识别子结构内局部损伤的识别方程,并采用正则化方法进行求解。数值模拟表明,所提出的基于界面力识别的子结构损伤检测方法可以精确地识别远离结构响应测点的子结构上的局部损伤。
(5)提出了一种基于概率可靠度理论、适用于未知输入下不确定性结构损伤与荷载的同步识别方法。首先,推导通过动态响应灵敏度方法同步反演结构损伤与荷载的不确定性公式;其次,利用数据摄动技术和蒙特卡罗法研究测量响应中的不确定性对识别结果的影响,并基于概率统计理论推导了损伤概率的计算公式。数值模拟和试验研究表明,该方法可在观测噪声水平较高的条件下实现多位置损伤的定位与定量,并可较准确地识别出结构的基底激励时程。
Damage detection and load identification of structures with unknown input and incomplete measured output information is an important problem in the area of identification of civil engineering structures. A method based on dynamic response sensitivity is therefore proposed to simultaneously identify structural physical parameters and input time-history from only several responses of structures. The identified structural physical parameters are used to detect structural local damages. Some key problems of the proposed method are studied in the dissertation. Main contents are as follows:
(1) A method based on dynamic response sensitivity is proposed to simultaneously identify structural physical parameters and input. The input force on structure is represented by using orthogonal polynomial approximation. By representing the input force on structure using orthogonal polynomial approximation and perturbing structural physical parameters, the orthogonal expansion coefficients and the fractional stiffness of structural elements are adopted as the force parameters and the structural physical parameters respectively, which are need to be identified. The sensitivity of structural dynamic response with respect to orthogonal coefficients and structural physical parameters is derived. The identification equation is set up and is solved with the damped least-squares method in an iterative process. Numerical simulation results show that the proposed simultaneous identification algorithm can simultaneously identify structural physical parameters and input from only several responses of structure.
(2) The proposed simultaneous identification algorithm is extended to identifying damage and load of structure under unknown support excitation. The support excitation on structure is represented by using orthogonal polynomial approximation. The simultaneous identification equation of structural local damages and unknown support excitation is derived based on dynamic response sensitivity. The regularization method is used to solve the identification equation in an iterative process. Numerical simulation and experimental results show that the proposed algorithm has higher identification accuracy when the level of measurement noise is lower. The regularization is helpful for improving the anti-noise ability of the algorithm. When the level of measurement noise is higher, the algorithm can not accurately identify structural damages, but the identified support excitation after removing the linear trend can reflect the true support excitation.
(3) A method based on dynamic response sensitivity is proposed to simultaneously identify local damages in a selected substructure and the interface forces between substructures from the dynamic responses on the selected substructure. The motion equation of substructural system is deduced. These interfacing forces between substructures are represented by orthogonal functions, and the sensitivity of the dynamic responses on the selected substructure to the substructural physical parameters and the orthogonal expansion coefficients of the interface forces is derived. An identification equation is set up and is solved by using regularization method in an iterative process. Numerical simulation results show that the proposed method can identify local damages and interface forces of the selected substructure from only several responses of the substructure.
(4) A method, which uses the measured responses of one substructure in a complex structural system to detect local damges in another substructure in the same structural system, is proposed. The identification equation of the coupling forces is formulated in state space. The sensitivity of interface forces to substructural physical parameters is derived. The equation of local damage identification in the selected substructure from the interface forces is set up and is solved with regularization method. Numerical simulation results show that the proposed damage detection method for substructure based on interface forces can accurately identify local damages of the substructure far from response measurements.
(5) A probabilistic method is proposed to identify damages of structures with uncertainties under unknown input. The uncertain equation for simultaneously identifying structural damage and load is derived based dynamic response sensitivity. The effect of uncertainties caused by measurement noise on the identified parameters is investigated with data perturbation technique and Monte Carlo method. The formula of probability of identified damages is further derived using the probabilistic method. Numerical simulation and experimental results show that the simultaneous identification method based on probability can locate and quantify multi-damages on structure, and accurately identify structural support excitation.
引文
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