土木工程中结构识别方法的研究
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摘要
本文在深入分析现有结构识别方法的基础上，针对观测不完整及数据误差造成的识别困难，基于三种类型观测数据——静力位移观测数据、模态观测数据、时域动力响应数据，开展了结构识别方法的研究。本文的主要研究工作如下：
首先通过对土木工程结构识别方法的发展现状进行研究与总结，认识到观测自由度不完整及观测数据误差是制约结构识别发展与应用的主要因素，指出在观测不完整及不精确基础上进行结构识别方法的研究是土木工程结构识别的发展方向，阐述了本文研究的背景及意义，确定了本文研究的总体思路。
针对广泛存在于结构参数估计、结构损伤识别、大坝参数反演、岩土力学反演中的一类结构识别问题——基于静力位移观测的结构识别，建立了结构参数识别的部分特征结构分配法。对基于静力位移结构识别问题的参数分组及可辨识性标准进行了讨论，建立了基于模拟退火-单纯形的完全非线性识别算法。使用部分特征结构分配法对结构参数估计、结构损伤识别、大坝分区弹模反演问题进行数值模拟，结果表明本文方法在观测不完整及数据误差条件下具有较好的数值稳定性和鲁棒性。
为了克服柔度阵比较法可能出现错误损伤定位，提出了结构损伤定位的柔度投影法。首先，通过理论分析证明了柔度投影法对低阶模态参数敏感的特性及其损伤定位原理；其次，根据模型缩聚和振型扩展对柔度投影法定位能力影响的对比研究，将柔度投影法与多目标优化振型扩展算法结合使用，实现了观测自由度不完整条件下的结构损伤定位；最后，在统计意义的框架下定义了加权柔度投影误差，解决了数据误差条件下的损伤定位问题。通过对典型结构的数值模拟研究表明，本文建立的柔度投影法能够在观测不完整、不精确条件下有效地解决结构损伤定位问题。
在柔度投影法的基础上，建立了基于观测柔度阵的结构损伤识别方法。从观测柔度阵出发，提出了结构识别的部分特征结构分配识别模型，建立了识别问题的线性化、拟线性化和完全非线性算法，并通过对三种算法的对比研究，确定了用于结构损伤识别的完全非线性识别算法。将结构损伤识别的完全非线性算法与柔度投影法结合，利用频率观测数据较为精确的特点，使用混合法研究了数据误差条件下的损伤识别问题。
地震动作用下的时域识别技术是结构识别领域的一个重要研究方向。针对观测自由度不完整的剪切型结构，建立了地震动输入和未知结构参数的复合反演方法。本文所建立的方法分为两个阶段：地震动子结构反演和单元结构参数识别。首先，使用子结构识别技术，研究了未知参数、观测不完整条件下的地震动输入反演问题，建立了未知输入的最小二乘估计算法；其次，在估计地震动输入的基础上，使用广义Kalman滤波器方法，识别全部单元结构参数。研究结果显示，复合反演的两阶段方法能够为结构无损检测和状态评估提供理论依据。
In order to overcome the identification difficulties caused by measurement incompleteness and data error, this dissertation is devoted to study the methods and application of structural identification in civil engineering using the static displacement, the modal data and the response in the time domain.
Based on the extensive investigation of the literature, research situation of structural identification in civil engineering was summarized. The incomplete and noisy measurement was realized the main adverse factor to hamper the development of structural identification. Study on the identification method with the incomplete and noisy measurement was the research direction in the future. The significance of this dissertation was expounded and the research scheme was determined.
Aiming at the structural identification problem based on the static displacement extensively existing in civil engineering, the partial eigenstructure assigned method was presented to identify the structural parameters. Then the parameter group and identifmbility criterions were discussed. The identification algorithm based on the Simulated Annealing-Simplex Shape algorithm was proposed. Several numerical examples of structural parameter estimation, structural damage identification, dam parameter inversion and geotechnical engineering were demonstrated that the proposed method had the good numerical steadiness and robustness to resist the data error with the condition of the incomplete and noisy measurement.
In order to avoid the possible error of damage location by the flexibility comparison method, the flexibility projection method to locate the damage was proposed. Firstly, the sensitive property to the low modes and the location principle of the flexibility projection method was theoretical proved. Secondly, based on the comparative study on the model reduction and the mode shape expansion, the flexibility projection method was combined with the multi-objective optimum mode shape expansion algorithm to achieve the damage location with the limited measurement. Finally, the weighed flexibility error was defined on the frame of the statistical meaning to solve the damage location problem with the condition of data error. The numerical simulations were carried on the typical structures, and the results show that the flexibility projection method can effectively locate the damage with the incomplete and noisy measurement.
On the basis of the flexibility projection method, the method of damage identification using the measured flexibility was proposed. Based the measured flexibility, the identification model of the partial eigenstructure assignment was presented. The linear algorithm, the pseudolinear algorithm and the fully nonlinear algorithm were established, and the comparative studies were carried on the above algorithms. The fully nonlinear algorithm was determined to solve the identification problem based on the measured flexibility. By using of the frequency, which is more accurate than the mode shape, the fully nonlinear identification algorithm using the frequency data was coupled with the flexibility projection method to estimate the magnitude of damage in a structure.
At present, structural identification in time domain excited by ground motion is an important
research topic in civil engineering. A two-stage method, which can estimate structural parameters down to the element level based on incomplete response data alone without measuring the input excitations, was proposed. The method consists of two stages: sub-structural inversion of ground motion using least-square estimation, and parameter identification using extended Kalman Filter. Firstly, the inversion of the ground motion with the unknown parameters and limited measurements was studied by the sub-structural identification, and the least-square algorithm of unknown input was built. Secondly, based on the estimated input, structural parameter down to the element level was identified in time domain by extended Kalman filter algorithm. Several cases of a 6-sto
首先通过对土木工程结构识别方法的发展现状进行研究与总结，认识到观测自由度不完整及观测数据误差是制约结构识别发展与应用的主要因素，指出在观测不完整及不精确基础上进行结构识别方法的研究是土木工程结构识别的发展方向，阐述了本文研究的背景及意义，确定了本文研究的总体思路。
针对广泛存在于结构参数估计、结构损伤识别、大坝参数反演、岩土力学反演中的一类结构识别问题——基于静力位移观测的结构识别，建立了结构参数识别的部分特征结构分配法。对基于静力位移结构识别问题的参数分组及可辨识性标准进行了讨论，建立了基于模拟退火-单纯形的完全非线性识别算法。使用部分特征结构分配法对结构参数估计、结构损伤识别、大坝分区弹模反演问题进行数值模拟，结果表明本文方法在观测不完整及数据误差条件下具有较好的数值稳定性和鲁棒性。
为了克服柔度阵比较法可能出现错误损伤定位，提出了结构损伤定位的柔度投影法。首先，通过理论分析证明了柔度投影法对低阶模态参数敏感的特性及其损伤定位原理；其次，根据模型缩聚和振型扩展对柔度投影法定位能力影响的对比研究，将柔度投影法与多目标优化振型扩展算法结合使用，实现了观测自由度不完整条件下的结构损伤定位；最后，在统计意义的框架下定义了加权柔度投影误差，解决了数据误差条件下的损伤定位问题。通过对典型结构的数值模拟研究表明，本文建立的柔度投影法能够在观测不完整、不精确条件下有效地解决结构损伤定位问题。
在柔度投影法的基础上，建立了基于观测柔度阵的结构损伤识别方法。从观测柔度阵出发，提出了结构识别的部分特征结构分配识别模型，建立了识别问题的线性化、拟线性化和完全非线性算法，并通过对三种算法的对比研究，确定了用于结构损伤识别的完全非线性识别算法。将结构损伤识别的完全非线性算法与柔度投影法结合，利用频率观测数据较为精确的特点，使用混合法研究了数据误差条件下的损伤识别问题。
地震动作用下的时域识别技术是结构识别领域的一个重要研究方向。针对观测自由度不完整的剪切型结构，建立了地震动输入和未知结构参数的复合反演方法。本文所建立的方法分为两个阶段：地震动子结构反演和单元结构参数识别。首先，使用子结构识别技术，研究了未知参数、观测不完整条件下的地震动输入反演问题，建立了未知输入的最小二乘估计算法；其次，在估计地震动输入的基础上，使用广义Kalman滤波器方法，识别全部单元结构参数。研究结果显示，复合反演的两阶段方法能够为结构无损检测和状态评估提供理论依据。
In order to overcome the identification difficulties caused by measurement incompleteness and data error, this dissertation is devoted to study the methods and application of structural identification in civil engineering using the static displacement, the modal data and the response in the time domain.
Based on the extensive investigation of the literature, research situation of structural identification in civil engineering was summarized. The incomplete and noisy measurement was realized the main adverse factor to hamper the development of structural identification. Study on the identification method with the incomplete and noisy measurement was the research direction in the future. The significance of this dissertation was expounded and the research scheme was determined.
Aiming at the structural identification problem based on the static displacement extensively existing in civil engineering, the partial eigenstructure assigned method was presented to identify the structural parameters. Then the parameter group and identifmbility criterions were discussed. The identification algorithm based on the Simulated Annealing-Simplex Shape algorithm was proposed. Several numerical examples of structural parameter estimation, structural damage identification, dam parameter inversion and geotechnical engineering were demonstrated that the proposed method had the good numerical steadiness and robustness to resist the data error with the condition of the incomplete and noisy measurement.
In order to avoid the possible error of damage location by the flexibility comparison method, the flexibility projection method to locate the damage was proposed. Firstly, the sensitive property to the low modes and the location principle of the flexibility projection method was theoretical proved. Secondly, based on the comparative study on the model reduction and the mode shape expansion, the flexibility projection method was combined with the multi-objective optimum mode shape expansion algorithm to achieve the damage location with the limited measurement. Finally, the weighed flexibility error was defined on the frame of the statistical meaning to solve the damage location problem with the condition of data error. The numerical simulations were carried on the typical structures, and the results show that the flexibility projection method can effectively locate the damage with the incomplete and noisy measurement.
On the basis of the flexibility projection method, the method of damage identification using the measured flexibility was proposed. Based the measured flexibility, the identification model of the partial eigenstructure assignment was presented. The linear algorithm, the pseudolinear algorithm and the fully nonlinear algorithm were established, and the comparative studies were carried on the above algorithms. The fully nonlinear algorithm was determined to solve the identification problem based on the measured flexibility. By using of the frequency, which is more accurate than the mode shape, the fully nonlinear identification algorithm using the frequency data was coupled with the flexibility projection method to estimate the magnitude of damage in a structure.
At present, structural identification in time domain excited by ground motion is an important
research topic in civil engineering. A two-stage method, which can estimate structural parameters down to the element level based on incomplete response data alone without measuring the input excitations, was proposed. The method consists of two stages: sub-structural inversion of ground motion using least-square estimation, and parameter identification using extended Kalman Filter. Firstly, the inversion of the ground motion with the unknown parameters and limited measurements was studied by the sub-structural identification, and the least-square algorithm of unknown input was built. Secondly, based on the estimated input, structural parameter down to the element level was identified in time domain by extended Kalman filter algorithm. Several cases of a 6-sto
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