基于数据驱动和物理模型的结构地震损伤识别方法研究
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摘要
近年来世界频繁发生大地震并造成了巨大的经济损失、人员伤亡及社会影响，这是因为一方面人们对地震地面运动的特征认识不足，另一方面是人们还无法准确把握工程结构在真实地震作用下的地震损伤机理和破坏机制。近30年发展起来的结构健康监测系统通过布设传感器获取原型结构在真实服役环境及荷载作用下的实际响应，实时地诊断结构的损伤并及时地发出预警警报，是当前研究和揭示工程结构在真实地震作用下结构地震响应、损伤机理和破坏机制的最直接、最有效的手段。传统的基于振动信号的结构损伤识别方法一般认为结构损伤前后都是线性的，由于强地震地面运动的非平稳性使得工程结构在强地震作用下表征明显的非线性行为，如混凝土裂缝的张开与闭合，钢筋或钢材的屈服或屈曲等，这使得传统的结构损伤识别方法并不直接适合识别结构的地震损伤。因此迫切需要重新审视地震地面运动的非平稳特性，发展利用结构地震作用下非线性特征和非线性系统识别方法的结构地震损伤识别方法和损伤评估方法。为此，本文研究地震地面运动时频能量分布、以及基于数据驱动提取非线性特征的结构地震损伤识别方法和基于物理模型识别非线性系统的结构地震损伤识别方法。主要研究内容如下：
研究基于匹配追踪分解算法和时频能量分布的地震地面运动生成方法。首先介绍匹配追踪分解算法的基本原理；然后构造具有相同峰值加速度和傅里叶幅度谱的简单人工地震地面运动，比较它们时频能量分布的差异以及时频能量分布对线性结构最大弹性位移的影响，进一步定义时频原子幅度、循环特征、滞后相位角和有效能量，分析地震地面运动有效能量与最大弹性位移的相关性；最后分析人工地震地面运动时频能量分布对弹塑性结构响应的影响规律，通过时频能量分布解释非线性结构地震响应的动态棘轮效应。
研究基于层间位移时频特征分形维数的剪切型结构地震损伤识别方法。首先定义时频特征并采用分形维数定量刻画；然后结合模态叠加原理推导线性结构各自由度处时频特征分形维数的性质，结合子结构方法得到非线性结构各子结构时频特征分形维数的性质；最后以10层剪切型结构为数值仿真对象，模拟结构在单层损伤和多层损伤，不同损伤程度，近场地震动和远场地震动、不同噪声水平下的识别效果，并讨论不同阻尼比和采用层间加速度对识别结果的影响。
研究基于位移信号时频特征分形维数的框架型结构地震损伤方法。首先结合静态缩聚法、模态叠加原理推导线性框架型结构各主自由度处时频特征分形维数的性质；然后对于梁、柱端产生塑性铰的非线性框架型结构，研究拟力法推导塑性铰到非弹性位移的转换矩阵并得到各主自由度的时频特征分形维数的性质，对于局部安装非线性构件如阻尼器的非线性框架型结构，研究逆反路径法分析局部非线性对结构相对位移的影响并得到各主自由度的时频特征分形维数的性质。其次通过16层框架型结构数值算例验证结构单层和多层梁、柱出现塑性铰时的时频特征分形维数的识别方法；最后通过安装了摩擦阻尼器（模拟结构体系的局部非线性）的16层钢框架型结构振动台试验验证所提方法。
研究基于扩展Kalman和无迹Kalman滤波相结合的结构地震损伤分散识别方法。首先介绍经典Kalman滤波，扩展Kalman滤波和无迹Kalman滤波的基本原理；然后研究分别用扩展Kalman滤波和无迹Kalman滤波识别线性和非线性子结构的扩展状态。其次以10自由度剪切型结构为数值仿真对象，模拟结构在单层损伤和多层损伤下的识别结果，并比较同基于扩展Kalman滤波和无迹Kalman滤波整体结构识别方法的识别结果。最后结合识别的力—位移曲线和修正的Park-Ang损伤指标对结构的地震损伤定量评估。
Great earthquakes in the world have caused huge economic damage, casualties andsocial implications in recent years. This is because that people on one hand, are lack ofknowledge of the characteristics of earthquake ground motion and on the other handpeople can not accurately understand the seismic damage mechanism of the realengineering structures under the strong ground motion. The structural health monitoring(SHM) systems, having been developed in recent30years, monitor the real responses ofthe prototype structures under the real environment and loads with placed sensors, andprovide real-time structural damage diagnosis and timely early warning alarm, thus theSHM is currently the most direct and effective measure to study and reveal the seismicresponses, damage mechanisms and failure mechanisms of engineering structures.Traditional structural damage detection methods based on vibration signals assume thestructure is linear before and after damage. Due to the non-stationarity of strong groundmotion, the engineering structures exhibit obvious nonlinear behavior, such as theopening and closing of cracks in concrete and the yielding and buckling of steels, etc.,which makes the traditional structural damage detection methods are not suitable fordetecting structural seismic damage directly. Therefore there is an urgent need to re-examine the non-stationary characteristics of the earthquake ground motion, and todevelopment structural seismic damage detection and assessment methods with the helpof nonlinear feature and nonlinear system identification approaches. To this end, thisthesis focuses on the time-frequency energy distribution of earthquake ground motion,data-driven based structural seismic damage detection method by extracting nonlinearfeature and model based structural seismic damage detection method by identifying thenonlinear system. The main contents are as follows:
The method of generating earthquake ground motion based on matching pursuitdecomposition (MPD) and time-frequency energy distribution (TFED) is researched.Firstly the theory of MPD is introduced. Secondly the artificial earthquake groundmotions with same peak ground acceleration and Fourier amplitude spectrum aregenerated and the difference between the two TFEDs and their effects on the maximalelastic displacements of linear structures are studied. The amplitude, cyclingcharacteristics, phase lag angle and effective energy of time-frequency atoms aredefined, and the correlation between maximal elastic displacement and effective energyare analyzed. Finally the regular pattern of TEFDs’s effects on the responses of elastic perfectly plastic model (EPP) for the artificial earthquake ground motions are studied,and explaination of the dynamic ratcheting effect of EPP model are given by using theTFED of the real earthquake ground motion.
The structural seismic damage detection method based on the fractal dimension(FD) of interstory displacement’s time-frequency feature (TFF) is proposed for shear-type structure. Firstly, the TFF is defined and the FD is used to quantify the TFF.Secondly, the FD of TFF at each degree of freedom (DOF) for linear system is derivedwith the help of modal superposition principle, and the FD of TFF for each substructurein nonlinear system is derived with the help of substructure method. Finally, thenumerical simulations of10-story shear-type structure with single or multiple damage,different damage extend, near field and far field ground motion and different noise levelare conducted, and the effects of damping ratios and using interstory acceleration on thedetection results are discussed.
The structural seismic damage detection method based on the FD ofdisplacements’ TFF is investigated for moment-resist frame (MRF) structure. Firstly, theFD of TFF at each main DOF of linear MRF is derived with the help of staticcondensation method and modal superposition principle. Secondly, for nonlinear MRFwith plastic hinges at the ends of beams and columns, the transformation matrix fromthe rotations of plastic hinges to the inelastic displacements are derived based on theforce analogy method and the characteristics of the FD of TFF are studied; for thenonlinear MRF with added local nonlinear component such as the damper, the effects oflocal nonlinearity on the relative displacements are discussed and the characteristics ofthe FD of TFF are also studied. Thirdly, the numerical simulation of16-story MRF withsingle and multiple plastic hinges at the ends of beams and columns is studied. Finally,the shaking table test of a16-story steel MRF with added frictional dampers, whichsimulate local nonlinearities in the whole structure, is conducted to verify the proposedmethod.
The decentralized identification method of structural seismic damage based on theextended Kalman filter (EKF) and unscented Kalman filter (UKF) is proposed. Firstly,the principles of classical KF, EKF and UKF are introduced. Secondly, the method thatidentifies the extended state spaces of the linear and nonlinear substructures using EKFand UKF respectively is investigated. Thirdly, a10-story shear-type structure withsingle or multiple damages is used for numerical simulation, and the identified resultsare compared with those using EKF or UKF for the complete structure identification.Finally, the quantitative evaluation of the structural seismic damage is obtained bycombining the estimated force-displacement curve and the modified Park-Ang damage index.
研究基于匹配追踪分解算法和时频能量分布的地震地面运动生成方法。首先介绍匹配追踪分解算法的基本原理；然后构造具有相同峰值加速度和傅里叶幅度谱的简单人工地震地面运动，比较它们时频能量分布的差异以及时频能量分布对线性结构最大弹性位移的影响，进一步定义时频原子幅度、循环特征、滞后相位角和有效能量，分析地震地面运动有效能量与最大弹性位移的相关性；最后分析人工地震地面运动时频能量分布对弹塑性结构响应的影响规律，通过时频能量分布解释非线性结构地震响应的动态棘轮效应。
研究基于层间位移时频特征分形维数的剪切型结构地震损伤识别方法。首先定义时频特征并采用分形维数定量刻画；然后结合模态叠加原理推导线性结构各自由度处时频特征分形维数的性质，结合子结构方法得到非线性结构各子结构时频特征分形维数的性质；最后以10层剪切型结构为数值仿真对象，模拟结构在单层损伤和多层损伤，不同损伤程度，近场地震动和远场地震动、不同噪声水平下的识别效果，并讨论不同阻尼比和采用层间加速度对识别结果的影响。
研究基于位移信号时频特征分形维数的框架型结构地震损伤方法。首先结合静态缩聚法、模态叠加原理推导线性框架型结构各主自由度处时频特征分形维数的性质；然后对于梁、柱端产生塑性铰的非线性框架型结构，研究拟力法推导塑性铰到非弹性位移的转换矩阵并得到各主自由度的时频特征分形维数的性质，对于局部安装非线性构件如阻尼器的非线性框架型结构，研究逆反路径法分析局部非线性对结构相对位移的影响并得到各主自由度的时频特征分形维数的性质。其次通过16层框架型结构数值算例验证结构单层和多层梁、柱出现塑性铰时的时频特征分形维数的识别方法；最后通过安装了摩擦阻尼器（模拟结构体系的局部非线性）的16层钢框架型结构振动台试验验证所提方法。
研究基于扩展Kalman和无迹Kalman滤波相结合的结构地震损伤分散识别方法。首先介绍经典Kalman滤波，扩展Kalman滤波和无迹Kalman滤波的基本原理；然后研究分别用扩展Kalman滤波和无迹Kalman滤波识别线性和非线性子结构的扩展状态。其次以10自由度剪切型结构为数值仿真对象，模拟结构在单层损伤和多层损伤下的识别结果，并比较同基于扩展Kalman滤波和无迹Kalman滤波整体结构识别方法的识别结果。最后结合识别的力—位移曲线和修正的Park-Ang损伤指标对结构的地震损伤定量评估。
Great earthquakes in the world have caused huge economic damage, casualties andsocial implications in recent years. This is because that people on one hand, are lack ofknowledge of the characteristics of earthquake ground motion and on the other handpeople can not accurately understand the seismic damage mechanism of the realengineering structures under the strong ground motion. The structural health monitoring(SHM) systems, having been developed in recent30years, monitor the real responses ofthe prototype structures under the real environment and loads with placed sensors, andprovide real-time structural damage diagnosis and timely early warning alarm, thus theSHM is currently the most direct and effective measure to study and reveal the seismicresponses, damage mechanisms and failure mechanisms of engineering structures.Traditional structural damage detection methods based on vibration signals assume thestructure is linear before and after damage. Due to the non-stationarity of strong groundmotion, the engineering structures exhibit obvious nonlinear behavior, such as theopening and closing of cracks in concrete and the yielding and buckling of steels, etc.,which makes the traditional structural damage detection methods are not suitable fordetecting structural seismic damage directly. Therefore there is an urgent need to re-examine the non-stationary characteristics of the earthquake ground motion, and todevelopment structural seismic damage detection and assessment methods with the helpof nonlinear feature and nonlinear system identification approaches. To this end, thisthesis focuses on the time-frequency energy distribution of earthquake ground motion,data-driven based structural seismic damage detection method by extracting nonlinearfeature and model based structural seismic damage detection method by identifying thenonlinear system. The main contents are as follows:
The method of generating earthquake ground motion based on matching pursuitdecomposition (MPD) and time-frequency energy distribution (TFED) is researched.Firstly the theory of MPD is introduced. Secondly the artificial earthquake groundmotions with same peak ground acceleration and Fourier amplitude spectrum aregenerated and the difference between the two TFEDs and their effects on the maximalelastic displacements of linear structures are studied. The amplitude, cyclingcharacteristics, phase lag angle and effective energy of time-frequency atoms aredefined, and the correlation between maximal elastic displacement and effective energyare analyzed. Finally the regular pattern of TEFDs’s effects on the responses of elastic perfectly plastic model (EPP) for the artificial earthquake ground motions are studied,and explaination of the dynamic ratcheting effect of EPP model are given by using theTFED of the real earthquake ground motion.
The structural seismic damage detection method based on the fractal dimension(FD) of interstory displacement’s time-frequency feature (TFF) is proposed for shear-type structure. Firstly, the TFF is defined and the FD is used to quantify the TFF.Secondly, the FD of TFF at each degree of freedom (DOF) for linear system is derivedwith the help of modal superposition principle, and the FD of TFF for each substructurein nonlinear system is derived with the help of substructure method. Finally, thenumerical simulations of10-story shear-type structure with single or multiple damage,different damage extend, near field and far field ground motion and different noise levelare conducted, and the effects of damping ratios and using interstory acceleration on thedetection results are discussed.
The structural seismic damage detection method based on the FD ofdisplacements’ TFF is investigated for moment-resist frame (MRF) structure. Firstly, theFD of TFF at each main DOF of linear MRF is derived with the help of staticcondensation method and modal superposition principle. Secondly, for nonlinear MRFwith plastic hinges at the ends of beams and columns, the transformation matrix fromthe rotations of plastic hinges to the inelastic displacements are derived based on theforce analogy method and the characteristics of the FD of TFF are studied; for thenonlinear MRF with added local nonlinear component such as the damper, the effects oflocal nonlinearity on the relative displacements are discussed and the characteristics ofthe FD of TFF are also studied. Thirdly, the numerical simulation of16-story MRF withsingle and multiple plastic hinges at the ends of beams and columns is studied. Finally,the shaking table test of a16-story steel MRF with added frictional dampers, whichsimulate local nonlinearities in the whole structure, is conducted to verify the proposedmethod.
The decentralized identification method of structural seismic damage based on theextended Kalman filter (EKF) and unscented Kalman filter (UKF) is proposed. Firstly,the principles of classical KF, EKF and UKF are introduced. Secondly, the method thatidentifies the extended state spaces of the linear and nonlinear substructures using EKFand UKF respectively is investigated. Thirdly, a10-story shear-type structure withsingle or multiple damages is used for numerical simulation, and the identified resultsare compared with those using EKF or UKF for the complete structure identification.Finally, the quantitative evaluation of the structural seismic damage is obtained bycombining the estimated force-displacement curve and the modified Park-Ang damage index.
引文
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