被动与智能隔震结构地震响应分析及控制算法
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摘要
结构减震控制能有效减小地震对结构物造成的损害，已经成为广泛的共识。在所有已经开发的结构减震控制技术中，基础隔震概念简单、性能稳定、造价相对低廉，目前在世界范围内应用最广。但是，在被动隔震结构中，隔震层的位移响应往往较大。当地震激励较强时，隔震层的位移响应在很大程度上制约着隔震体系总体的工作性能。为此，国内外学者尝试将主动或半主动控制元件与隔震系统结合起来，构成所谓的智能隔震体系。对被动隔震结构的动力分析，首先要处理非比例阻尼问题；而智能隔震结构的动力分析，则首先要解决控制算法。此外，地震激励具有很强的不确定性，采用随机响应分析的方法可以更全面地反映隔震体系减震效果的统计特性。本文围绕被动和智能隔震体系的几个热点问题展开研究，主要做了如下几个方面的工作：
1) 隔震结构是一种非比例阻尼体系。本文揭示了基础隔震系统对非比例阻尼的解耦效应，指出基础隔震结构是一种特殊的非比例阻尼体系，建立了一般多自由度隔震结构的实振型分解算法。通过将所获得的计算结果用MATLAB软件包下的通用动力模拟工具Simulink进行验证，并与复振型分解法闭合解、用FORTRAN语言编制的Wilson-θ法的计算结果进行对比，证实本文方法用于最常见的基础隔震实际工程时域动力分析具有很高的精度。另外，利用本文的实振型分解法一般表达式，导出了双自由度隔震体系最大响应的估算模型，改进了Kelly建议的同类估算方法精度。直接模拟的结果表明，本文方法的结果更为合理。
2) 对于装有理想控制器的线性系统，最优控制算法是非常有效的理论工具之一，在土木工程中也有很多应用。但经典的最优控制理论用于结构地震响应控制时，Riccati方程一般要出现一个非齐次项，无法直接求解。现有的两种结构最优控制算法，都是在对问题做了简化处理后导出的。本文采用脉冲响应构造控制目标函数，利用最优控制模型中的伴随方程与状态空间方程形式上的相似性，提出了对偶动力系统的概念，解决了结构地震响应最优控制力的求解问题，建立了序列最优控制算法。与现有同类算法相比，本文算法不但建立模型的概念更合理，求解方式上更加严密，而且数值模拟结果表明，本文算法的控制力能更好地跟踪外部激励和响应的特征。在同等控制能量下，本文算法比同类算法更能有效地削减结构响应峰值，具有更高的减震效率，并且稳定性良好。同时，本文导出的最优控制力系数，用代数公式取代传统的Riccati微分方程的求解，使本文算法的计算效率也有了明显优势。
3) 在强震作用下，结构一般都要发生弹塑性变形，成为滞变体系。建立滞变体系的控制算法要比线性系统困难得多。然而，正是在大震下，结构的抗震成为突出问题，最需要采取控制措施，保护结构安全。因此，针对滞变结构建立控制算法，具有更为显著的工程意义。本文采用等效线性化的Bouc-Wen模型建立控制力的反馈关系，将序列最优控制算法推广到滞变结构中。数值模拟结果表明，与同类算法相比，本文“大震”控制算法同样具有更高的减震效率，并且在常见的控制权重范围内有较好的稳定性。本文还利用Potriagin极值原理，建立了考虑控制器出力饱和的最优控制算法模型，并针对作者承担的实际隔震工程的参数，对本文算法用于智能隔震做了较系统的对比分析，给出了考虑和不考虑控制器出力饱和的最优控制力峰值范围。
4)对被动隔震及智能隔震结构的随机响应分析做了探讨。采用虚拟激励法分析了不
同功率谱模型、不同结构类型的随机响应，并结合Ly即unov迭代法及Monie carlo动力
模拟对响应特征进行对比。结果表明，用双过滤白噪声地震功率谱比Taj而i.Kanai谱更
适合于隔震结构和刚度退化型的非隔震结构随机响应分析，而本文算法比场apunov法更
能方便地处理这种功率谱。
5)在智能隔震结构中，半主动控制器在某个时刻的开启及关闭一般是以该时刻耗能
所需的力是否与控制器能提供的力性质相协调为判别依据的。本文建立了被动隔震和智
能隔震的瞬时能量平衡关系。从新的角度定性分析了被动隔震和智能隔震体系的能量耗
散与传输机理。借助于隔震体系的响应相位和耗能的关系提出了一个频域内定量的耗能
表征指标，作为评判阻尼对隔震结构减震效率影响的一个附加指标。还将该思想延伸到
智能隔震结构，用相位差定义了半主动控制器在频域中的开启及关闭的指示变量，满足
了智能隔震结构随机响应分析的需要。
6)本文还介绍了实振型分解法在实际隔震工程动力分析中的应用，利用实际工程的
参数对智能隔震系统的实现和在强震作用下的减震特性及参数范围进行了仿真分析:简
介了作者主持的对叠层橡胶隔震支座在一20℃一50℃低温环境中的力学性能试验和作者
参与过的一项智能隔震模型试验的概况，论述了与本文有关的一些主要结论。
Structural vibration control is widely recognized as an effective way of mitigating catastrophic damage of structures induced by earthquakes. Among various techniques for structural vibration control, base isolation is the most widely used method in the world because of its simplicity, stability, and cost effectiveness. However, in passive isolated structures, the base drift is always very large. When the earthquake excitation is strong, the overall performance of the structural system is largely suppressed by the response of base isolator. Therefore, a lot of research work has been carried out to improve the adaptiveness of base isolation by combining active or semi-active devices with the passive isolation system, resulting in so-called "smart" isolated system. To calculate the seismic response of passive isolated structures, non-proportional damping must be handled, and to analyze the response of smart isolated structures, control algorithms must be worked out. Besides, seismic excitation is of strong randomness, evaluating controlled response using random vibration analysis can provide better statistical information. This paper investigates several key issues concerning passive and smart isolated structures, and mainly focuses on the following things:
41) Base isolated building is usually a kind of non-proportionally damped system. But, this paper revealed that base isolated structure is a special type of non-proportionally damped system by showing the damping decoupling effect of base isolation. A real mode superposition method for analyzing time domain response of non-proportionally damped base isolated structures is derived for general MDOF system, and the results calculated by the proposed method are verified using the dynamic simulation tool of Simulink method in Matlab, and compared with those from the complex mode superposition, the Wilson- method coded in double precision Fortran. The result shows that under the design damping level defined in this paper, the proposed method in this study has good accuracy, which shows the applicability of the proposed method for the large class of isolated building in common use. Besides, the proposed general MDOF model of real mode superposition method can be used to derive a spectral estimation of maximum response for 2-DOF isolated structures which is similar to the method proposed by Kelly, but the method proposed in this study has a wider range of validity, and the result is more reasonable when examined by direct simulation.
2) For linear structure implemented with ideal controller, optimal control is a powerful tool for determining control force, and has found wide application in civil engineering. However, when classical optimal control is applied to seismic control, a non-homogeneous term will appear in the traditional Riccati equation, which causes the model not to be solved directly. Two current optimal control algorithms, i.e., the approximate classical optimal control algorithms (COC) and instantaneous optimal control algorithms (IOC), were derived based on a lot of simplification. In this paper, the control objective function is reconstructed using impulse response of both seismic excitation and the control force, which leads to a new style
optimal control model. By defining a dual system according to the resemblance between the companion equation and the state equation, the optimal control force is directly calculated by state transition algorithm. An improved optimal control algorithm is thus developed, and is named as Sequential Optimal Control (SOC). The proposed SOC not only improved the two current optimal control algorithms conceptually, but also numerically. Simulation result shows that the proposed method is advantageous over the two current optimal control algorithms in terms of the ability of reducing the peak response, the control efficiency, and has almost the same stability range with the classical optimal control algorithms.
3) Under strong earthquakes, a structure will always come to its elasto-plastic stage, and thus becomes a kind of
1) 隔震结构是一种非比例阻尼体系。本文揭示了基础隔震系统对非比例阻尼的解耦效应，指出基础隔震结构是一种特殊的非比例阻尼体系，建立了一般多自由度隔震结构的实振型分解算法。通过将所获得的计算结果用MATLAB软件包下的通用动力模拟工具Simulink进行验证，并与复振型分解法闭合解、用FORTRAN语言编制的Wilson-θ法的计算结果进行对比，证实本文方法用于最常见的基础隔震实际工程时域动力分析具有很高的精度。另外，利用本文的实振型分解法一般表达式，导出了双自由度隔震体系最大响应的估算模型，改进了Kelly建议的同类估算方法精度。直接模拟的结果表明，本文方法的结果更为合理。
2) 对于装有理想控制器的线性系统，最优控制算法是非常有效的理论工具之一，在土木工程中也有很多应用。但经典的最优控制理论用于结构地震响应控制时，Riccati方程一般要出现一个非齐次项，无法直接求解。现有的两种结构最优控制算法，都是在对问题做了简化处理后导出的。本文采用脉冲响应构造控制目标函数，利用最优控制模型中的伴随方程与状态空间方程形式上的相似性，提出了对偶动力系统的概念，解决了结构地震响应最优控制力的求解问题，建立了序列最优控制算法。与现有同类算法相比，本文算法不但建立模型的概念更合理，求解方式上更加严密，而且数值模拟结果表明，本文算法的控制力能更好地跟踪外部激励和响应的特征。在同等控制能量下，本文算法比同类算法更能有效地削减结构响应峰值，具有更高的减震效率，并且稳定性良好。同时，本文导出的最优控制力系数，用代数公式取代传统的Riccati微分方程的求解，使本文算法的计算效率也有了明显优势。
3) 在强震作用下，结构一般都要发生弹塑性变形，成为滞变体系。建立滞变体系的控制算法要比线性系统困难得多。然而，正是在大震下，结构的抗震成为突出问题，最需要采取控制措施，保护结构安全。因此，针对滞变结构建立控制算法，具有更为显著的工程意义。本文采用等效线性化的Bouc-Wen模型建立控制力的反馈关系，将序列最优控制算法推广到滞变结构中。数值模拟结果表明，与同类算法相比，本文“大震”控制算法同样具有更高的减震效率，并且在常见的控制权重范围内有较好的稳定性。本文还利用Potriagin极值原理，建立了考虑控制器出力饱和的最优控制算法模型，并针对作者承担的实际隔震工程的参数，对本文算法用于智能隔震做了较系统的对比分析，给出了考虑和不考虑控制器出力饱和的最优控制力峰值范围。
4)对被动隔震及智能隔震结构的随机响应分析做了探讨。采用虚拟激励法分析了不
同功率谱模型、不同结构类型的随机响应，并结合Ly即unov迭代法及Monie carlo动力
模拟对响应特征进行对比。结果表明，用双过滤白噪声地震功率谱比Taj而i.Kanai谱更
适合于隔震结构和刚度退化型的非隔震结构随机响应分析，而本文算法比场apunov法更
能方便地处理这种功率谱。
5)在智能隔震结构中，半主动控制器在某个时刻的开启及关闭一般是以该时刻耗能
所需的力是否与控制器能提供的力性质相协调为判别依据的。本文建立了被动隔震和智
能隔震的瞬时能量平衡关系。从新的角度定性分析了被动隔震和智能隔震体系的能量耗
散与传输机理。借助于隔震体系的响应相位和耗能的关系提出了一个频域内定量的耗能
表征指标，作为评判阻尼对隔震结构减震效率影响的一个附加指标。还将该思想延伸到
智能隔震结构，用相位差定义了半主动控制器在频域中的开启及关闭的指示变量，满足
了智能隔震结构随机响应分析的需要。
6)本文还介绍了实振型分解法在实际隔震工程动力分析中的应用，利用实际工程的
参数对智能隔震系统的实现和在强震作用下的减震特性及参数范围进行了仿真分析:简
介了作者主持的对叠层橡胶隔震支座在一20℃一50℃低温环境中的力学性能试验和作者
参与过的一项智能隔震模型试验的概况，论述了与本文有关的一些主要结论。
Structural vibration control is widely recognized as an effective way of mitigating catastrophic damage of structures induced by earthquakes. Among various techniques for structural vibration control, base isolation is the most widely used method in the world because of its simplicity, stability, and cost effectiveness. However, in passive isolated structures, the base drift is always very large. When the earthquake excitation is strong, the overall performance of the structural system is largely suppressed by the response of base isolator. Therefore, a lot of research work has been carried out to improve the adaptiveness of base isolation by combining active or semi-active devices with the passive isolation system, resulting in so-called "smart" isolated system. To calculate the seismic response of passive isolated structures, non-proportional damping must be handled, and to analyze the response of smart isolated structures, control algorithms must be worked out. Besides, seismic excitation is of strong randomness, evaluating controlled response using random vibration analysis can provide better statistical information. This paper investigates several key issues concerning passive and smart isolated structures, and mainly focuses on the following things:
41) Base isolated building is usually a kind of non-proportionally damped system. But, this paper revealed that base isolated structure is a special type of non-proportionally damped system by showing the damping decoupling effect of base isolation. A real mode superposition method for analyzing time domain response of non-proportionally damped base isolated structures is derived for general MDOF system, and the results calculated by the proposed method are verified using the dynamic simulation tool of Simulink method in Matlab, and compared with those from the complex mode superposition, the Wilson- method coded in double precision Fortran. The result shows that under the design damping level defined in this paper, the proposed method in this study has good accuracy, which shows the applicability of the proposed method for the large class of isolated building in common use. Besides, the proposed general MDOF model of real mode superposition method can be used to derive a spectral estimation of maximum response for 2-DOF isolated structures which is similar to the method proposed by Kelly, but the method proposed in this study has a wider range of validity, and the result is more reasonable when examined by direct simulation.
2) For linear structure implemented with ideal controller, optimal control is a powerful tool for determining control force, and has found wide application in civil engineering. However, when classical optimal control is applied to seismic control, a non-homogeneous term will appear in the traditional Riccati equation, which causes the model not to be solved directly. Two current optimal control algorithms, i.e., the approximate classical optimal control algorithms (COC) and instantaneous optimal control algorithms (IOC), were derived based on a lot of simplification. In this paper, the control objective function is reconstructed using impulse response of both seismic excitation and the control force, which leads to a new style
optimal control model. By defining a dual system according to the resemblance between the companion equation and the state equation, the optimal control force is directly calculated by state transition algorithm. An improved optimal control algorithm is thus developed, and is named as Sequential Optimal Control (SOC). The proposed SOC not only improved the two current optimal control algorithms conceptually, but also numerically. Simulation result shows that the proposed method is advantageous over the two current optimal control algorithms in terms of the ability of reducing the peak response, the control efficiency, and has almost the same stability range with the classical optimal control algorithms.
3) Under strong earthquakes, a structure will always come to its elasto-plastic stage, and thus becomes a kind of
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