地震下结构振动的最优控制算法模型比较与改进

模拟地震激励输入结构的过程,将控制目标函数化解到每个时间步长上。用激励所产生的脉冲响应重新构造控制目标函数,直接从泛函变分出发,推导出了一种改进的最优控制算法,并用状态转移的数值方法加以实现。从概念上讲,本算法是一种更为合理的结构最优控制算法。算例表明,在相同控制能量下,本算法能更有效地削减响应峰值,且稳定性良好。     

OPTIMAL POLYNOMIAL CONTROL FOR SEISMICALLY EXCITED NON-LINEAR AND HYSTERETIC STRUCTURES

In this paper, we present an optimal polynomial controller for reducing the peak response quantities of seismically excited non-linear or hysteretic building systems. A performance index, that is quadratic in control and polynomial of any order in non-linear states, is considered. The performance index is minimized based on the Hamilton–Jacobi–Bellman equation using a polynomial function of non-linear states, which satisfies all the properties of a Lyapunov function. The resulting optimal controller is a summation of polynomials in non-linear states, i.e. linear, cubic, quintic, etc. Gain matrices for different parts of the controller are determined from Riccati and Lyapunov matrix equations. Numerical simulation results indicate that the percentage of reduction for the selected peak response quantity increases with the increase of the earthquake intensity. Such load adaptive properties are very desirable, since the intensity of the earthquake ground acceleration is stochastic in nature. The proposed optimal polynomial controller is an effective and viable control method for non-linear or hysteretic civil engineering structures. It is an addition to available control methods in the literature.     

Performance‐based design using structural optimization

A new methodology for seismic design is proposed based on structural optimization with performance‐based constraints. Performance‐based criteria are introduced for the seismic design of new buildings. These criteria are derived from the National Guidelines for Seismic Rehabilitation of Buildings (Reference [19], Federal Emergency Management Agency (FEMA), ‘NHERP Guidelines for seismic rehabilitation of buildings’, Report Nos 273 and 274, Washington, DC, 1997) for retrofitting existing structures. The proposed design methodology takes into account the non‐linear behaviour of the structure. The goal is to incorporate in the design the actual performance levels of the structure, i.e. how much reserve capacity the structure has in an earthquake of a given magnitude. The optimal design of the structure minimizes the structural cost subjected to performance constraints on plastic rotations of beams and columns, as well as behavioural constraints for reinforced concrete frames. Uncertainties in the structural period and in the earthquake excitation are taken into account using convex models. The optimization routine incorporates a non‐linear analysis program and the procedure is automated. The proposed methodology leads to a structural design for which the levels of reliability (performance levels) are assumed to be quantifiable. Furthermore, the entire behaviour of the structure well into the non‐linear range is investigated in the design process. Copyright © 2000 John Wiley & Sons, Ltd.     

基于输出反馈的建筑结构闭开环次优控制

对传统的结构抗震闭开环控制算法进行改进。基于地面运动自回归模型,采用Kalman滤波利用可以量测到的地面加速度激励对未来时段即将发生的地面加速度激励进行预估,并在微分方程的求解中引入精确高效的精细积分算法。考虑到实际控制中量测全部状态变量的困难,改进算法仅需量测部分状态变量。数值仿真表明,基于输出反馈的闭开环次优控制策略能大大降低结构的地震响应。     

双向偏心结构扭转耦联地震反应的序列最优控制

本文分析了不对称建筑结构平移-扭转耦联振动的动力特性及地震作用下的响应;根据地震动输入结构的过程,推导出一种更为一般的最优控制算法,所获得的控制力表达式同时包括地震响应和地震激励。通过对一非规则四层框架结构的扭转耦联地震反应控制分析表明,该算法不仅能有效地控制结构的平移地震反应,而且更有效地抑制结构的扭转耦联地震反应。     

Optimal control of linear buildings under seismic excitations

Considerable effort has been devoted to develop optimal control methods for reducing structural response under seismic forces. In this study analytical solution of the linear regulator problem applied widely to the control of earthquake‐excited structures is obtained by using the sufficient conditions of optimality even though almost all of the optimal controls proposed previously for structural control are based on the necessary conditions of optimality. Since the resulting optimal closed–open‐loop control cannot be implemented for civil structures exposed to earthquake forces, the solution of the optimal closed–open‐loop control is carried out approximately based on the prediction of the seismic acceleration values in the near future. Upon obtaining the relation between the exact optimal solution and future values of seismic accelerations, it is shown numerically that the solution of the optimal closed–open‐loop control problem can be performed approximately by using only the first few predicted seismic acceleration values if a given norm criteria is satisfied. Calculated performance measures indicate that the suggested approximate solution is better than the closed‐loop control and as we predict the future values of the excitation more accurately, it will approach the optimal solution. Copyright © 2001 John Wiley & Sons, Ltd.     

Composite robust active control of seismically excited structures with actuator dynamics

In this paper, composite robust active control schemes are proposed for a class of non-linear base isolated structures in the presence of unknown seismic excitation, parametrical uncertainties and actuator dynamics. Only the information on state variables of the structural base and the first floor of the main structure has been used in the control design. A numerical simulation example is given for a ten-storeyed base isolated structure under the El Centro earthquake to show the effectiveness of the proposed control scheme. © 1998 John Wiley & Sons, Ltd.     

Trust-region based instantaneous optimal semi-active control of long-span spatially extended structures with MRF-04K damper

In the field of civil engineering, magnetorheological fluid （MRF） damper-based semi-active control systems have received considerable attention for use in protecting structures from natural hazards such as strong earthquakes and high winds. In this paper, the MRF damper-based semi-active control system is applied to a long-span spatially extended structure and its feasibility is discussed. Meanwhile, a _trust-region method based instantaneous optimal semi-active control algorithm （TIOC） is proposed to improve the performance of the semi-active control system in a multiple damper situation. The proposed TIOC describes the control process as a bounded constraint optimization problem, in which an optimal semi- active control force vector is solved by the trust-region method in every control step to minimize the structural responses. A numerical example of a railway station roof structure installed with MRF-04K dampers is presented. First, a modified Bouc- Wen model is utilized to describe the behavior of the selected MRF-04K damper. Then, two semi-active control systems, including the well-known clipped-optimal controller and the proposed TIOC controller, are considered. Based on the characteristics of the long-span spatially extended structure, the performance of the control system is evaluated under uniform earthquake excitation and travelling-wave excitation with different apparent velocities. The simulation results indicate that the MR fluid damper-based semi-active control systems have the potential to mitigate the responses of full-scale long-span spatially extended structures under earthquake hazards. The superiority of the proposed TIOC controller is demonstrated by comparing its control effectiveness with the clipped-optimal controller for several different cases.     

近断层地震动作用下隔震结构的优化设计

首先讨论了近断层脉冲型地震动的特点,并以台湾集集地震实际脉冲型近震记录为地震动输入,应用含潜在约束策略的序列二次规划算法,对安装铅芯橡胶隔震支座的钢筋混凝土框架隔震结构的隔震器参数和上部结构构件截面几何尺寸进行一体化优化设计,然后输入E l Centro(1940)、Taft(1952)地震波对优化后的隔震结构进行地震反应分析。计算结果表明,对考虑脉冲型近断层地震动作用的隔震结构进行参数优化设计后,该隔震结构能同时满足脉冲型和普通非脉冲型近震作用的结构设计需求。     

磁流变阻尼器在相邻建筑结构体系弹塑性地震反应控制中的应用

研究应用磁流变阻尼器连接相邻建筑结构的弹塑性地震反应控制问题。首先介绍磁流变阻尼器的力学模型,并设计了磁流变阻尼器的结构参数;其次,介绍钢筋混凝土框架结构的退化三线型恢复力模型及相邻建筑结构体系的特点,建立体系的力学模型及运动方程;最后进行半主动控制研究,设计了半主动控制器,通过算例实现了结构的半主动控制。分析结果表明,采用磁流变阻尼器连接的相邻结构振动控制是十分有效的,可避免地震中相邻结构发生磁撞损坏。     

Optimal placement of sensors on buildings subjected to intermediate‐storey excitation according to QN control method

An algorithm to calculate direct velocity feedback gain with limited number of sensors is developed in a simple way such that a certain performance index is minimized according to QN control method. If a limited number of velocity outputs can be measured, full velocity responses of the whole structure can be interpolated based on the mode shapes. By defining the performance index function as a combination of the structure's velocity responses and control forces only, feedback gain can be determined according to QN control method with the external excitation being taken into account throughout the entire algorithm. Control forces are then regulated by the time‐invariant feedback gain matrix. The effective location of the active control devices for a building structure subjected to intermediate‐storey excitation has been determined to be in the three floors adjacent to the vibration source. Hence for the purpose of this paper, only the optimal placement of sensors is verified. It is shown in this paper that if the dynamic behaviour of the structure is well described by a mathematical model, sufficient response reduction effect can be achieved according to the new DVFC algorithm, and the degradation of control performance due to time delay can also be verified. Copyright © 2001 John Wiley & Sons, Ltd.     

Sampled-data H2 optimal output feedback control for civil structures

An optimal control method involving sampled data is considered for use in earthquake and wind engineering applications. The structure is modelled as a continuous system attached to a discrete-time controller using zero-order sample-and-hold devices. Examples of two buildings with active base isolators and a 163 m tall planar frame with an active mass damper are considered. The buildings with the base isolators are subjected to excitation input using the 1940 El Centro earthquake (NS component) as an example, while the planar frame is subjected to assumed sinusoidal gusts with a period close to that of the frame. The controlled responses (with and without time delays) are studied. To further analyze the features of the control designs, the building examples with base isolators are subjected to five other different earthquake excitation records. Trends in control performance and effectiveness are presented and discussed. The results suggest that such systems are potentially suited for implementation in the vibration control of civil infrastructures; such potentiality becomes more realistic with the current trends in software development and the increased use of digital computers. Copyright © 1999 John Wiley & Sons, Ltd.     

Design of passive systems for control of inelastic structures

A design strategy for control of buildings experiencing inelastic deformations during seismic response is formulated. The strategy is using weakened, and/or softened, elements in a structural system while adding passive energy dissipation devices (e.g. viscous fluid devices, etc.) in order to control simultaneously accelerations and deformations response during seismic events. A design methodology is developed to determine the locations and the magnitude of weakening and/or softening of structural elements and the added damping while insuring structural stability. A two‐stage design procedure is suggested: (i) first using a nonlinear active control algorithm, to determine the new structural parameters while insuring stability, then (ii) determine the properties of equivalent structural parameters of passive system, which can be implemented by removing or weakening some structural elements, or connections, and by addition of energy dissipation systems. Passive dampers and weakened elements are designed using an optimization algorithm to obtain a response as close as possible to an actively controlled system. A case study of a five‐story building subjected to El Centro ground motion, as well as to an ensemble of simulated ground motions, is presented to illustrate the procedure. The results show that following the design strategy, a control of both peak inter‐story drifts and total accelerations can be obtained. Copyright © 2008 John Wiley & Sons, Ltd.     

Continuous pulse control of structures with material non-linearity

A control method is presented for reducing the dynamic response of structures in the inelastic material range using a control force from an active bracing system. Recent full-scale experiments have verified the feasibility of implementing active control systems for control of seismic structures with existing technology. The proposed method of continuous pulse control uses closed-loop feedback control as a combination of two algorithms. The first is the instantaneous optimal algorithm which was derived assuming linear material behaviour, and the second is pulse control which applies a corrective pulse when a prespecified structural displacement, velocity, or acceleration threshold is exceeded. The three criteria of displacement, velocity, and acceleration lead to three pulse control schemes. Each of the three schemes is used in conjunction with the instantaneous optimal control to yield three continuous pulse algorithms, the displacement continuous pulse, velocity continuous pulse and acceleration continuous pulse. Comparisons between the three continuous pulse algorithms and the pulse control for seismic structures in the inelastic range show that the continuous pulse algorithms use less control energy and reduce the response better than pulse control. A comparison between the velocity continuous pulse and the non-linear optimal algorithm shows that the velocity continuous pulse uses a larger control force but is more adaptable than the non-linear optimal algorithm, in the sense that it can reduce the response of a given structure to various probable earthquakes. The non-linear optimal algorithm is more effective than the velocity continuous pulse for a single specific earthquake but is not as effective for other earthquakes which may occur in the life of the structure.     

Seismic structural control using semi-active tuned mass dampers

This paper focuses on how to determine the instantaneous damping of the semi-active tuned mass damper (SATMD) with continuously variable damping. An off-and-towards-equilibrium (OTE) algorithm is employed to examine the control performance of the structure/SATMD system by considering the damping as an assumptive control action. The damping modification of the SATMD is carried out according to the proposed OTE algorithm, which is formulated based on analysis of the structural movement under external excitations, and the measured responses of the structure at every time instant. As examples two numerical simulations of a five-storey and a ten-storey shear structures with a SATMD on the roof are conducted. The effectiveness on vibration reduction of MDOF systems subjected to seismic excitations is discussed. Analysis results show that the behavior of the structure with a SATMD is significantly improved and the feasibility of applying the OTE algorithm to the structural control design of SATMD is also verified.     

Seismic structural control using a novel high‐performance active mass driver system

To resolve difficulties encountered by current technology in structural control against earthquakes, this study proposes a novel high‐performance active mass driver (HP‐AMD) system. Based on an active mass driver system, the device is integrated with a mechanical pulley system for stroke amplification to enhance simultaneously efficiency and save power. Meanwhile, an instantaneous optimal direct output feedback control algorithm is derived alongside the hardware development. Numerical simulation is performed using a five‐storey steel frame as the object structure under the 1940 El Centro earthquake. To gain further insight into the HP‐AMD system, the effects of stroke amplification as well as damper weight on system performance are explored. Analysis results demonstrate that the proposed HP‐AMD system is a promising means to improving current active structural control techniques. Copyright © 2000 John Wiley & Sons, Ltd.     

Earthquake performance assessment and retrofit investigations of two suspension bridges in Istanbul

This paper presents the results from earthquake performance assessment and retrofit investigations for Fatih Sultan Mehmet and Bosporus suspension bridges, with main span lengths of 1090 and 1074 m in Istanbul. In the first part of the study, sophisticated three-dimensional finite element model of two suspension bridges were developed and the results of the free vibration analysis were presented. The models contain detailed structural components of the bridges and geometric non-linearity with cable sagging and stress stiffening, cumber of the deck and set-back of the towers. These components affect the natural frequencies and the corresponding mode shapes of the bridges. In the second part of the study, the seismic performance evaluation of two suspension bridges was undertaken. For performance assessments, non-linear 3-D finite-element time history analysis of with multi-support scenario earthquake excitation was used. Displacements and stresses at critical points of the bridges were investigated. Their earthquake performance under the action of scenario earthquake (site-specific ground motion that would result from the Mw=7.5 scenario earthquake on the Main Marmara Fault) were estimated and comparison with actual design data were also presented. Although both suspension bridges were originally designed for much lower earthquake loads they exhibited satisfactory performance. Finally, suggestions for retrofit need were made and retrofit design with hysteretic dampers for the Bosporus suspension bridge was calculated.     

非平稳地震激励下隔震曲线梁桥振动控制研究

曲线梁桥由于其平面不规则性导致结构在地震激励下产生弯扭耦合效应,使得隔震曲线梁桥的地震响应更加复杂。目前常用的控制方法是将隔震技术与附加减震装置相结合对曲线梁桥进行控制。本文将地震动考虑为一均匀调制非平稳随机过程,针对隔震曲线梁桥长周期、低频率的特点,选取Clough-Pension平稳地震动功率谱模型作为随机地震动输入模型,对无控(NON-C)、经典线性最优控制(COC)以及序列最优控制算法(SOC)三种状态下的曲线桥梁进行随机响应分析。通过建立曲线梁桥在随机地震动作用下的运动方程,求出减震控制结构的位移谱密度、加速度谱密度响应及时变方差。分析结果表明:序列最优控制算法(SOC)在使隔震层位移得到减小的同时,可以更有效地控制上部结构的地震响应,具有更好的控制效果。     

Predictive active control of MDOF structures

This paper presents a theoretical study of a predictive active control system used to improve the response of multi‐degree‐of‐freedom (MDOF) structures to earthquakes. As an example a building frame equipped with electrorheological (ER) dampers is considered. The aim of the design is to find a combination of forces that are produced by the ER dampers in order to obtain an optimal structural response. The mechanical response of ER fluid dampers is regulated by an electric field. Linear auto‐regressive model with exogenous input (ARX) is used to predict the displacements and the velocities of the frame in order to overcome the time‐delay problem in the control system. The control forces in the ER devices are calculated at every time step by the optimal control theory (OCT) according to the values of the displacements and of the velocities that are predicted at the next time step at each storey of the structure. A numerical analysis of a seven‐storey ER damped structure is presented as an example. It shows a significant improvement of the structural response when the predictive active control system is applied compared to that of an uncontrolled structure or that of a structure with controlled damping forces with time delay. The structure's displacements and velocities that were used to obtain the optimal control forces were predicted according to an ‘occurring’ earthquake by the ARX model (predictive control). The response was similar to that of the structure with control forces that were calculated from a ‘known’ complete history of the earthquake's displacement and velocity values, and were applied without delay (instantaneous control). Copyright © 2000 John Wiley & Sons, Ltd.