基于模型更新的土木结构混合试验方法
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摘要
结构混合试验是将物理加载试验和数值模拟相结合来评估大型复杂土木结构地震反应和抗震性能的有效试验技术，目前正得到了研究者们的广泛关注。目前已在混合试验系统、数值积分算法、加载控制、时滞补偿、误差累计控制等关键技术方面取得了一定的研究成果。然而，对于高层建筑或者大跨度桥梁结构进行混合试验时，研究者们会遇到很大困难。当整体结构进入非线性，不可能将所有关键部分都进行物理试验，如何准确模拟数值子结构成为最大的挑战。为了能够提高混合试验中数值子结构模型的准确性，提出了基于约束隐性卡尔曼滤波器的模型更新混合方法。模型更新混合试验方法的研究对推动混合试验方法发展及客观揭示大型复杂土木结构的动力灾变过程具有重要的理论意义和实用价值。
本文针对基于模型更新的土木结构混合试验方法的一些关键科学问题进行了研究，主要研究内容如下：
(1)采用确定性最小二乘法在线识别双折线模型参数，通过数值模拟和试验验证了在相同加载路径下的在线模型更新效果。研究表明：该方法具有良好的参数识别精度和较高的计算效率。针对两层防屈曲支撑结构，首次进行了模型更新的混合试验验证。试验研究表明：与传统混合试验相比，在线模型更新可以有效地减小混合试验数值模型误差，提高混合试验精度。
(2)针对常量标量系统，推导了不考虑过程噪声和考虑过程噪声状态估计方差解析表达式，给出了卡尔曼滤波器影响参数对状态估计影响规律。采用状态估计方差作为状态估计评价标准，给出了使用卡尔曼滤波器进行状态估计时滤波器参数取值建议。验证了采用状态投影方法来解决界限约束状态估计的合理性。提出了考虑乘性噪声卡尔曼滤波器的最优估计递推算法，通过弹性结构刚度识别验证了算法的有效性。
(3)研究了基于隐性卡尔曼滤波器(UKF)的模型更新方法，搭建了基于dSPACE控制平台的FTS作动器试验系统，针对弹性试件首次进行了基于UKF的模型更新混合试验。试验表明：与传统混合试验相比，该试验方法大幅度地提高了混合试验精度。提出了基于修改Sigma点(Sigma Points)位置及权重的约束隐性卡尔曼滤波器算法(约束UKF)。与UKF相比，约束UKF算法主要有两个方面的改进：1)在预测步中，将违反界限约束的Sigma点移至边界上，同时将约束界限内的Sigma点做相应对称调整，并从理论上证明当κ=0.5时考虑约束的UT变换算法具有一阶精度；2)在校正步中，采用状态更新方程产生变换后的Sigma点，当更新的状态估计违反界限约束时，直接将超出约束边界的Sigma点投影到边界上，并给出了校正步状态估计均值和协方差计算公式的理论证明。所提出的算法可以同时考虑了界限约束对状态估计均值和协方差的影响，而且具有较高的计算效率，能够实现实时模型更新。给出了Bouc-Wen模型在线参数识别方法。研究表明：与UKF方法相比，约束UKF方法能够有效地减小参数识别值前期波动幅度，确保参数识别值的物理意义，提高参数识别收敛速度和模型更新精度。进行了滤波器初始参数影响分析，并给出参数选择建议。
(4)针对两个自由度非线性结构进行了基于约束UKF模型更新的混合试验数值模拟，验证了该试验方法的有效性和可行性。采用dSPACE-MTS实时混合试验系统，分别针对防屈曲支撑结构首次进行了慢速和实时的模型更新混合试验。试验表明：与传统混合试验和基于UKF模型更新的混合试验相比，基于约束UKF模型更新的混合试验方法可以更大程度地提高混合试验精度。
(5)提出基于OpenSees的模型更新混合试验方法，针对一榀六层框架-支撑结构，进行了多种情况下的模型更新混合试验数值仿真。数值子结构和试验子结构均采用OpenSees进行数值模拟，模型参数识别采用Matlab编程实现。通过修改原OpenSees程序源代码，建立可以模型更新的twoNodeLink单元。采用Socket通信技术实现OpenSees和Matlab程序的数据传输。分别讨论试验支撑采用Bouc-Wen模型和考虑强度、刚度退化的Bouc-Wen模型两种情况下模型误差对混合试验精度的影响。研究表明，模型误差将导致模型参数识别值很难收敛到一个稳态值，具有较强的时变性，这会降低模型更新混合试验精度。提出了将模型更新与多个试验子结构混合试验相结合来减小模型误差影响的方法，尝试选择多个关键部位的构件作为试验子结构，然后分别更新与其加载路径和非线性程度相近的数值子结构模型。研究表明，该方法能够有效地减小模型误差对模型更新的影响，提高了模型更新混合试验精度。
Hybrid testing is a combination of numerical simulation and physical testing, which is increasingly being recognized as a powerful emerging technique that offers the opportunity for evaluation of large scale civil structures subjected to dynamic loading. In recent decades, a great deal of progress has been made in hybrid testing such as numerical integration algorithms, loading control methods, actuator delay compensation and testing error analysis. However, researchers generally might still encounter a number of difficulties when conducting hybrid testing for complex structures like high-rise buildings or large-scale bridges. One of the challenging issues is how to model the numerical substructure, when the whole structure exhibit strong nonlinearity subjected to extreme loading like strong earthquake and it is not economically realistic to physically test all the critical parts of the structure. To improve accuracy of numerical model during the hybrid testing, the hybrid testing method based on model updating with constrainted unscented Kalman filter(CUKF) is presented, which is of great theory significance and practical value in improving the hybrid tesing method and revealing the dynamic behavior of large scale civil structures.
Several key issues of hybrid testing method for civil engineering based on model updating are inestigated in this paper. The main research work and concludings are as follows:
(1) Online parameter identification method for the bilinear hysteretic model using the least square estimation is researched, which is verified by numerical simulation and experiment under the same loading paths. It is demonstrated that the on-line identification algorithm is in high precision and computational efficiency. Hybrid tesings with model updating for frame-brace structure of two degrees of freedom using MTS system are conducted firstly. The test results indicate that online model updating can decrease model errors and improve the precision of hybrid testing compared with conventional hybrid testing.
(2) For constant scalar systems, analytic expression of Kalman filter was deduced under the system process noise available and unavailable, and the effects of parameters of kalman filter on the state estimation convariance are researched. Using state estimation variance as an evaluation standard state estimation, suggests of parameter selection in application of the Kalman filter is given. The rationality of the projection method to solve constraints problem in the state estimation method is verified. An optimal recursion algorithm considering the multiplicative noise based the Kalman filter is derived, the effectiveness of the algorithm is verified by elastic stiffness identification.
(3) Hybrid testing method based on model updating with the unscented Kalman filter (UKF) is researched and its effectiveness is first confirmed by an actual test with a steel spring as the experimental substructure compared to conventional testing. A new constrained unscented Kalman filter (CUKF) algorithm is proposed based on the Unscented Kalman Filter (UKF) by adjusting the position of the sample points and weights. Compared to existing CUKF, the approach proposed in this paper features the following two aspects.(i) In prediction step, sigma points (i.e., sample point) violating bound constraints are moved onto the bounds, and the relevant sigma points within the boundary are moved correspondingly to retains the symmetry of the new set of sigma points. The proof is given to prove that the proposed replacement of sigma points results in a first-order accuracy for the unscented transformation of mean value if=0.5.(ii) In correction step, the state updating equation is used to generate transformed sigma points, and those transformed sigma points that violate bound constraints are projected to constraints boundary only when the updated state estimate exceeds the boundary. It can be proved that the reformulated equations give exactly the same result of updated mean and covariance with the standard UKF. The algorithm can consider the effect of the boundary constraints on the state estimation of mean as well as covariance, and has high computing efficiency and can realize real-time model updating. Research of Bouc-Wen model updating shows that: compared with UKF methods, CUKF method can effectively reduce volatility of the parameter identification at the early stage, ensure physical meaning of identification parameters, improve the convergence speed and precision of model updating. Filter Parameter Analysis is conducted and advice of initial parameter selection is given.
(4) The hybrid testing method based on model updating with CUKF is presented. The effectiveness and feasibility of hybrid testing method based on model updating with CUKF is verified by a hybrid testing numerical simulation for the two freedom nonlinear system. Using dSPACE-MTS test platform, both increased-time and real-time hybrid testing based on model updating for frame structure incorporating all-steel buckling-restrained braces (BRBs) are finished. The results show that the proposed hybrid testing method has better accuracy compared with conventional hybrid testing and hybrid testing based on model updating with UKF.
(5) The hybrid testing with model updating using OpenSees is proposed, and a series of numerical simulations of hybrid testing with model updating for a six story frame with BRBs are conducted. The numeirical and physical substructures are simulated by OpenSees, and online identification of the model parameters is realized by Matlab programming. A new twoNodeLink element is set up by modifying source codes of twoNodeLink element in the original OpenSees program to realized online model updating. The data transmission between OpenSees and Matlab is realized using Socket communication technology. The classical Bouc-Wen and Bouc-Wen considering the strength and stiffness degradation are respectively selected to analyze the influences of model error on accuracy of the hybrid testing with model updating. Simulation results show that parameter identification values are difficult to converge to a steady value due to the model error, which can reduce precision of hybrid test with model updating. Combining model updating with distributed hybrid test is put forward to reduce the negative influence of model error. Try to select more than one key component as testing substructure, then update respectively model of the numerical substructure which has the similar loading path and degree of the nonlinear to case of the corresponding testing substructure. Results show that when the model error is inevitable, the proposed method can effectively reduce the effect of model error on model updating, and the precision of hybrid testing with model updating is improved further.
本文针对基于模型更新的土木结构混合试验方法的一些关键科学问题进行了研究，主要研究内容如下：
(1)采用确定性最小二乘法在线识别双折线模型参数，通过数值模拟和试验验证了在相同加载路径下的在线模型更新效果。研究表明：该方法具有良好的参数识别精度和较高的计算效率。针对两层防屈曲支撑结构，首次进行了模型更新的混合试验验证。试验研究表明：与传统混合试验相比，在线模型更新可以有效地减小混合试验数值模型误差，提高混合试验精度。
(2)针对常量标量系统，推导了不考虑过程噪声和考虑过程噪声状态估计方差解析表达式，给出了卡尔曼滤波器影响参数对状态估计影响规律。采用状态估计方差作为状态估计评价标准，给出了使用卡尔曼滤波器进行状态估计时滤波器参数取值建议。验证了采用状态投影方法来解决界限约束状态估计的合理性。提出了考虑乘性噪声卡尔曼滤波器的最优估计递推算法，通过弹性结构刚度识别验证了算法的有效性。
(3)研究了基于隐性卡尔曼滤波器(UKF)的模型更新方法，搭建了基于dSPACE控制平台的FTS作动器试验系统，针对弹性试件首次进行了基于UKF的模型更新混合试验。试验表明：与传统混合试验相比，该试验方法大幅度地提高了混合试验精度。提出了基于修改Sigma点(Sigma Points)位置及权重的约束隐性卡尔曼滤波器算法(约束UKF)。与UKF相比，约束UKF算法主要有两个方面的改进：1)在预测步中，将违反界限约束的Sigma点移至边界上，同时将约束界限内的Sigma点做相应对称调整，并从理论上证明当κ=0.5时考虑约束的UT变换算法具有一阶精度；2)在校正步中，采用状态更新方程产生变换后的Sigma点，当更新的状态估计违反界限约束时，直接将超出约束边界的Sigma点投影到边界上，并给出了校正步状态估计均值和协方差计算公式的理论证明。所提出的算法可以同时考虑了界限约束对状态估计均值和协方差的影响，而且具有较高的计算效率，能够实现实时模型更新。给出了Bouc-Wen模型在线参数识别方法。研究表明：与UKF方法相比，约束UKF方法能够有效地减小参数识别值前期波动幅度，确保参数识别值的物理意义，提高参数识别收敛速度和模型更新精度。进行了滤波器初始参数影响分析，并给出参数选择建议。
(4)针对两个自由度非线性结构进行了基于约束UKF模型更新的混合试验数值模拟，验证了该试验方法的有效性和可行性。采用dSPACE-MTS实时混合试验系统，分别针对防屈曲支撑结构首次进行了慢速和实时的模型更新混合试验。试验表明：与传统混合试验和基于UKF模型更新的混合试验相比，基于约束UKF模型更新的混合试验方法可以更大程度地提高混合试验精度。
(5)提出基于OpenSees的模型更新混合试验方法，针对一榀六层框架-支撑结构，进行了多种情况下的模型更新混合试验数值仿真。数值子结构和试验子结构均采用OpenSees进行数值模拟，模型参数识别采用Matlab编程实现。通过修改原OpenSees程序源代码，建立可以模型更新的twoNodeLink单元。采用Socket通信技术实现OpenSees和Matlab程序的数据传输。分别讨论试验支撑采用Bouc-Wen模型和考虑强度、刚度退化的Bouc-Wen模型两种情况下模型误差对混合试验精度的影响。研究表明，模型误差将导致模型参数识别值很难收敛到一个稳态值，具有较强的时变性，这会降低模型更新混合试验精度。提出了将模型更新与多个试验子结构混合试验相结合来减小模型误差影响的方法，尝试选择多个关键部位的构件作为试验子结构，然后分别更新与其加载路径和非线性程度相近的数值子结构模型。研究表明，该方法能够有效地减小模型误差对模型更新的影响，提高了模型更新混合试验精度。
Hybrid testing is a combination of numerical simulation and physical testing, which is increasingly being recognized as a powerful emerging technique that offers the opportunity for evaluation of large scale civil structures subjected to dynamic loading. In recent decades, a great deal of progress has been made in hybrid testing such as numerical integration algorithms, loading control methods, actuator delay compensation and testing error analysis. However, researchers generally might still encounter a number of difficulties when conducting hybrid testing for complex structures like high-rise buildings or large-scale bridges. One of the challenging issues is how to model the numerical substructure, when the whole structure exhibit strong nonlinearity subjected to extreme loading like strong earthquake and it is not economically realistic to physically test all the critical parts of the structure. To improve accuracy of numerical model during the hybrid testing, the hybrid testing method based on model updating with constrainted unscented Kalman filter(CUKF) is presented, which is of great theory significance and practical value in improving the hybrid tesing method and revealing the dynamic behavior of large scale civil structures.
Several key issues of hybrid testing method for civil engineering based on model updating are inestigated in this paper. The main research work and concludings are as follows:
(1) Online parameter identification method for the bilinear hysteretic model using the least square estimation is researched, which is verified by numerical simulation and experiment under the same loading paths. It is demonstrated that the on-line identification algorithm is in high precision and computational efficiency. Hybrid tesings with model updating for frame-brace structure of two degrees of freedom using MTS system are conducted firstly. The test results indicate that online model updating can decrease model errors and improve the precision of hybrid testing compared with conventional hybrid testing.
(2) For constant scalar systems, analytic expression of Kalman filter was deduced under the system process noise available and unavailable, and the effects of parameters of kalman filter on the state estimation convariance are researched. Using state estimation variance as an evaluation standard state estimation, suggests of parameter selection in application of the Kalman filter is given. The rationality of the projection method to solve constraints problem in the state estimation method is verified. An optimal recursion algorithm considering the multiplicative noise based the Kalman filter is derived, the effectiveness of the algorithm is verified by elastic stiffness identification.
(3) Hybrid testing method based on model updating with the unscented Kalman filter (UKF) is researched and its effectiveness is first confirmed by an actual test with a steel spring as the experimental substructure compared to conventional testing. A new constrained unscented Kalman filter (CUKF) algorithm is proposed based on the Unscented Kalman Filter (UKF) by adjusting the position of the sample points and weights. Compared to existing CUKF, the approach proposed in this paper features the following two aspects.(i) In prediction step, sigma points (i.e., sample point) violating bound constraints are moved onto the bounds, and the relevant sigma points within the boundary are moved correspondingly to retains the symmetry of the new set of sigma points. The proof is given to prove that the proposed replacement of sigma points results in a first-order accuracy for the unscented transformation of mean value if=0.5.(ii) In correction step, the state updating equation is used to generate transformed sigma points, and those transformed sigma points that violate bound constraints are projected to constraints boundary only when the updated state estimate exceeds the boundary. It can be proved that the reformulated equations give exactly the same result of updated mean and covariance with the standard UKF. The algorithm can consider the effect of the boundary constraints on the state estimation of mean as well as covariance, and has high computing efficiency and can realize real-time model updating. Research of Bouc-Wen model updating shows that: compared with UKF methods, CUKF method can effectively reduce volatility of the parameter identification at the early stage, ensure physical meaning of identification parameters, improve the convergence speed and precision of model updating. Filter Parameter Analysis is conducted and advice of initial parameter selection is given.
(4) The hybrid testing method based on model updating with CUKF is presented. The effectiveness and feasibility of hybrid testing method based on model updating with CUKF is verified by a hybrid testing numerical simulation for the two freedom nonlinear system. Using dSPACE-MTS test platform, both increased-time and real-time hybrid testing based on model updating for frame structure incorporating all-steel buckling-restrained braces (BRBs) are finished. The results show that the proposed hybrid testing method has better accuracy compared with conventional hybrid testing and hybrid testing based on model updating with UKF.
(5) The hybrid testing with model updating using OpenSees is proposed, and a series of numerical simulations of hybrid testing with model updating for a six story frame with BRBs are conducted. The numeirical and physical substructures are simulated by OpenSees, and online identification of the model parameters is realized by Matlab programming. A new twoNodeLink element is set up by modifying source codes of twoNodeLink element in the original OpenSees program to realized online model updating. The data transmission between OpenSees and Matlab is realized using Socket communication technology. The classical Bouc-Wen and Bouc-Wen considering the strength and stiffness degradation are respectively selected to analyze the influences of model error on accuracy of the hybrid testing with model updating. Simulation results show that parameter identification values are difficult to converge to a steady value due to the model error, which can reduce precision of hybrid test with model updating. Combining model updating with distributed hybrid test is put forward to reduce the negative influence of model error. Try to select more than one key component as testing substructure, then update respectively model of the numerical substructure which has the similar loading path and degree of the nonlinear to case of the corresponding testing substructure. Results show that when the model error is inevitable, the proposed method can effectively reduce the effect of model error on model updating, and the precision of hybrid testing with model updating is improved further.
引文
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