Multi‐objective optimal design of FLC driven hybrid mass damper for seismically excited structures

Structural vibration control using active or passive control strategy is a viable technology for enhancing structural functionality and safety against natural hazards such as strong earthquakes and high wind gusts. Both the active and passive control systems have their limitations. The passive control system has limited capability to control the structural response whereas the active control system depends on external power. The power requirement for active control of civil engineering structures is usually quite high. Thus, a hybrid control system is a viable solution to alleviate some of the limitations. In this paper a multi‐objective optimal design of a hybrid control system for seismically excited building structures has been proposed. A tuned mass damper (TMD) and an active mass driver (AMD) have been used as the passive and active control components of the hybrid control system, respectively. A fuzzy logic controller (FLC) has been used to drive the AMD as the FLC has inherent robustness and ability to handle the non‐linearities and uncertainties. The genetic algorithm has been used for the optimization of the control system. Peak acceleration and displacement responses non‐dimensionalized with respect to the uncontrolled peak acceleration and displacement responses, respectively, have been used as the two objectives of the multi‐objective optimization problem. The proposed design approach for an optimum hybrid mass damper (HMD) system, driven by FLC has been demonstrated with the help of a numerical example. It is shown that the optimum values of the design parameters of the hybrid control system can be determined without specifying the modes to be controlled. The proposed FLC driven HMD has been found to be very effective for vibration control of seismically excited buildings in comparison with the available results for the same example structure but with a different optimal absorber. Copyright © 2002 John Wiley & Sons, Ltd.     

Design of dampers for structures based on optimal control theory

The aim of this paper was to propose a design guideline for using visco‐elastic dampers for the control of building structures subjected to earthquake loading as well as suspension roof structures subjected to wind loading. The active control algorithm was used to calculate the control forces. Based on the single‐mode approach the control forces were transformed to the forces which visco‐elastic dampers can provide. Application of the method to the design of the building structure with passive damping devices in the bracing system and to the suspension roof with dampers was studied. Through the application of optimal control theory a systematic design procedure to implement dampers in structures is proposed. Copyright © 2000 John Wiley & Sons, Ltd.     

结构瞬时最优控制参数影响的数值分析

在瞬时最优控制算法理论分析的基础上，分别以单自由度和三自由度结构模型为例，研究了时间间隔和权矩阵对结构控制反应的影响。首先，进行了瞬时最优控制算法的理论分析，提出了控制算法的影响参数；其次，分别对单自由度和三自由度结构在无控、LQR和瞬时最优三种方法控制下，分析了时间间隔和权矩阵对结构反应的影响。结果表明：时间间隔和权矩阵对结构瞬时最优控制效果影响很大。     

Semi‐active multi‐step predictive control of structures using MR dampers

A semi‐active multi‐step predictive control (SAMPC) system with magnetorheological (MR) dampers is developed to reduce the seismic responses of structures. This system can predict the next multi‐step responses of structure according to the current state and has a function of self‐compensation for time delay that occurred in real application. To study the performance of the proposed control algorithm for addressing time delay and reducing the seismic responses, a numerical example of an 11‐story structure with MR dampers is presented. Comparison with the uncontrolled structure indicates that both the peak and the norm values of structural responses are all clearly reduced when the predictive length l?10 and the delayed time step d?20 are selected, and the SAMPC strategy can guarantee the stability of the controlled structure and reduce the effects of time delay on controlled responses to a certain extent. A performance comparison is also made between the SAMPC strategy and the passive‐off and passive‐on methods; results indicate that this SAMPC system is more effective than the two passive methods in reducing structural responses subjected to earthquakes. Copyright © 2008 John Wiley & Sons, Ltd.     

A risk‐based life cycle cost strategy for optimal design and evaluation of control methods for nonlinear structures

The lack of direct correspondence between control objectives and hazard risks over the lifetime of systems is a key shortcoming of current control techniques. This along with the inability to objectively analyze the benefits and costs of control solutions compared with conventional methods has hindered widespread application of control systems in seismic regions. To address these gaps, this paper offers 2 new contributions. First, it introduces risk‐based life cycle–cost (LCC) optimal control algorithms, where LCC is incorporated as the performance objective in the control design. Two strategies called risk‐based linear quadratic regulator and unconstrained risk‐based regulator are subsequently proposed. The considered costs include the initial cost of the structure and control system, LCC of maintenance, and probabilistically derived estimates of seismic‐induced repair costs and losses associated with downtime, injuries, and casualties throughout the life of the structure. This risk‐based framework accounts for uncertainties in both system properties and hazard excitations and uses outcrossing rate theory to estimate fragilities for various damage states. The second contribution of this work is a risk‐based probabilistic framework for LCC analysis of existing and proposed control strategies. The proposed control designs are applied to the nonlinear model of a 4‐story building subjected to seismic excitations. Results show that these control methods reduce the LCC of the structure significantly compared with the status quo option (benefits of up to $1 351 000). The advancements offered in this paper enhance the cost‐effectiveness of control systems and objectively showcase their benefits for risk‐informed decision making.     

Predictive control of seismic structures with semi‐active friction dampers

In this paper a predictive control method especially suitable for the control of semi‐active friction dampers is proposed. By keeping the adjustable slip force of a semi‐active friction damper slightly lower than the critical friction force, the method allows the damper to remain in its slip state throughout an earthquake of arbitrary intensity, so the energy dissipation capacity of the damper can be improved. The proposed method is formulated in a discrete‐time domain and cast in the form of direct output feedback for easy control implementation. The control algorithm is able to produce a continuous and smooth slip force for a friction damper and thus avoid exerting the high‐frequency structural response that usually exists in structures with conventional friction dampers. Using a numerical study, the control performance of a multiple degrees of freedom (DOF) structural system equipped with passive friction dampers and semi‐active dampers controlled by the proposed method are compared. The numerical case shows that by merely using a single semi‐active friction damper and a few sensors, the proposed method is able to achieve better acceleration reduction than the case using multiple passive dampers. Copyright © 2004 John Wiley & Sons, Ltd.     

Predictive optimal control for seismic analysis of non-linear and hysteretic structures

In this paper, an effective active predictive control algorithm is developed for the vibration control of non-linear hysteretic structural systems subjected to earthquake excitation. The non-linear characteristics of the structural behaviour and the effects of time delay in both the measurements and control action are included throughout the entire analysis (design and validation). This is very important since, in current design practice, structures are assumed to behave non-linearly, and time delays induced by sensors and actuator devices are not avoidable. The proposed algorithm focuses on the instantaneous optimal control approach for the development of a control methodology where the non-linearities are brought into the analysis through a non-linear state vector and a non-linear open-loop term. An autoregressive (AR) model is used to predict the earthquake excitation to be considered in the prediction of the structural response. A performance index that is quadratic in the control force and in the predicted non-linear states, with two additional energy related terms, and that is subjected to a non-linear constraint equation, is minimized at every time step. The effectiveness of the proposed closed-open loop non-linear instantaneous optimal prediction control (CONIOPC) strategy is presented by the results of numerical simulations. Since non-linearity and time-delay effects are incorporated in the mathematical model throughout the derivation of the control methodology, good performance and stability of the controlled structural system are guaranteed. Copyright © 1999 John Wiley & Sons, Ltd.     

Statistical performance analysis of seismic‐excited structures with active interaction control

This paper presents a statistical performance analysis of a semi‐active structural control system for suppressing the vibration response of building structures during strong seismic events. The proposed semi‐active mass damper device consists of a high‐frequency mass damper with large stiffness, and an actively controlled interaction element that connects the mass damper to the structure. Through actively modulating the operating states of the interaction elements according to pre‐specified control logic, vibrational energy in the structure is dissipated in the mass damper device and the vibration of the structure is thus suppressed. The control logic, categorized under active interaction control, is defined directly in physical space by minimizing the inter‐storey drift of the structure to the maximum extent. This semi‐active structural control approach has been shown to be effective in reducing the vibration response of building structures due to specific earthquake ground motions. To further evaluate the control performance, a Monte Carlo simulation of the seismic response of a three‐storey steel‐framed building model equipped with the proposed semi‐active mass damper device is performed based on a large ensemble of artificially generated earthquake ground motions. A procedure for generating code‐compatible artificial earthquake accelerograms is also briefly described. The results obtained clearly demonstrate the effectiveness of the proposed semi‐active mass damper device in controlling vibrations of building structures during large earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

Discrete‐time variable structure control of seismically excited building structures

Generally, the active structural control system belongs to the discrete‐time control system, and the sampling period is one of the most important factors that would directly affect the performance of the control system. In this paper, active control approaches by using the discrete‐time variable structure control theory are studied for reducing the dynamic responses of seismically excited building structures. Based on the discrete reaching law method, a feedback controller which includes the sampling period is presented. The controller is extended by introducing the saturated control method to avoid the adverse effect when the actuators are saturated due to unexpected extreme earthquakes. The simulation results are obtained for a single‐degree‐of‐freedom (SDOF) system and a MDOF shear building equipped with active brace system (ABS) under seismic excitations. It is found that the discrete variable structure control approach and its saturated control method presented in this paper are quite effective. Copyright © 2001 John Wiley & Sons, Ltd.     

Discrete‐time variable structure control method for seismic‐excited building structures with time delay in control

The discrete‐time variable structure control method for seismically excited linear structures with time delay in control is investigated in this paper. The control system with time delay is first discretized and transformed into standard discrete form which contains no time delay in terms of the time delay being integer and non‐integer times of sampling period, respectively. Then the discrete switching surface is determined using ideal quasi‐sliding mode and discrete controller is designed using the discrete approach‐law reaching condition. The deduced controller and switching surface contain not only the current step of state feedback but also linear combination of some former steps of controls. Numerical simulations are illustrated to verify the feasibility and robustness of the proposed control method. Since time‐delay effect is incorporated in the mathematical model for the structural control system throughout the derivation of the proposed algorithm, system performance and dynamic stability are guaranteed. Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling mid‐channel bars in meandering channels

An analytical modelling framework is proposed to reproduce the frequently observed but poorly studied occurrence of mid‐channel bars in meandering channels. Mid‐channel bars occur in meanders and may characterize transitional morphologies between pure meandering and braided rivers. Based on existing field and experimental observations, we propose that two different mechanisms can generate central topographical patterns in meanders. A former mechanism (‘width‐forced’) is related to spatial width oscillations which determine a laterally symmetrical bed shear stress pattern that promotes mid‐channel bars. A second mechanism (‘curvature‐forced’) can take place also in curvilinear equiwidth streams since also longitudinal variations of channel curvature can produce laterally symmetrical alterations of the sediment transport capacity. A perturbation approach is employed to model both mechanisms within a common framework, allowing reproduction, at least qualitatively, of several observed features. While width‐forced mid‐channel bars are a symmetric linear altimetric response, to reproduce curvature‐forced mid‐channel bars requires modelling nonlinear flow‐bed topography interactions at the second order of the perturbation expansion. Hypotheses on how these mechanisms operate are further discussed through an application to field cases. The amplitude of the nonlinear response can be relevant compared to that of the point bar in equiwidth meanders and the location of mid‐channel bars seldom coincides with bend apexes, mainly depending upon the intrinsic meander wavelength. Central bars tend to symmetrically divert the flow against the two banks, a process which is proposed as a possible cause of cross‐sectional overwidening, along with the asymmetry between the rates of bank erosion and of the opposite bank accretion. The outcomes of this first modelling step on the subject allow discussion of the mutual feedback processes that characterize interactions between mid‐channel bars and width variations in river meanders. Copyright © 2010 John Wiley & Sons, Ltd.     

Modified sliding‐mode bang–bang control for seismically excited linear structures

Recently, sliding‐mode control (SMC) methods have been investigated for application to seismically excited civil engineering structures and have proved to be effective control strategic methods. On the other hand, although another class of well‐known optimal control laws, the so‐called ‘bang–bang’ control, has been investigated for several decades, their potential in civil engineering structural control has not been fully exploited. The purpose of this paper is to present a new control law for civil engineering structures, which is the sliding‐mode bang–bang control (SMBBC). The SMBBC method is a combination of the SMC and the bang–bang control. In consideration of actuators not suitable for high‐speed switching of control forces in the SMBBC in practice, modified sliding‐mode bang–bang control (MSMBBC) law is proposed and demonstrated to be able to provide the same control effects as the SMBBC case. Condition modified sliding‐mode bang–bang control (CMSMBBC) law is also investigated in this paper. In the CMSMBBC case, actuators act only when response quantities exceed some designated threshold values. The determination method of maximum control‐forces for actuators is investigated through example computation. The performance and robustness of the proposed control methods are all demonstrated by numerical simulation. Simulation results demonstrate that the presented methods are viable and an attractive control strategy for application to seismically excited linear structures. Copyright © 2000 John Wiley & Sons, Ltd.     

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。     

Torsional response of nonductile structures with soft‐first‐storey

In this paper, torsional response of nonductile structures with soft‐first‐storey subjected to bidirectional ground motions is studied using a simplified two‐storey model with two‐way eccentricities. The stiffness ratio of second storey to first storey is varied to create different levels of soft‐first‐storey effect, while the stiffness eccentricity is varied to create torsional effects. Different overstrength ratios are used in the simplified models to study the response of structure with different structural capacity. Hysteretic model with strength deterioration and stiffness degradation properties is used to capture the deterioration of element stiffness and strength. Ductility capacity of 2.0 is used as the models are for nonductile structures. In general, displacement amplification of irregular model with respect to regular model increases as stiffness ratio increases, while no consistent trend of changes in displacement amplification is found with increase in stiffness eccentricity. It is found that the displacement amplification due to only soft‐first‐storey effect can be conservatively taken as 1.5. Coupling of torsional and soft‐first‐storey effects is more significant in affecting the displacement amplification of elements at flexible side. The trend of changes in displacement amplification of elastic system is similar to that of inelastic system. The displacement amplification of elements at the flexible side is larger than that at the stiff side. The elements at the flexible side in the direction of shorter uncoupled lateral period have larger displacement response than those in the orthogonal direction. Ductility demand–capacity curves subsequently constructed can be used to approximately assess the seismic performance of existing structures and as guidelines for designing structures in Singapore to withstand the maximum credible earthquake considering the coupling of torsional and soft‐first‐storey effects. Copyright © 2014 John Wiley & Sons, Ltd.     

Centralized semi‐active control of post‐tensioned steel frames

Centralized semi‐active control is a technique for controlling the whole structure using one main computer. Centralized control systems introduce better control for relatively short to medium high structures where the response of any story cannot be separated from the adjacent ones. In this paper, two centralized control approaches are proposed for controlling the seismic response of post‐tensioned (PT) steel frames. The first approach, the stiffness control approach, aims to alter the stiffness of the PT frame so that it avoids large dynamic amplifications due to earthquake excitations. The second approach, deformation regulation control approach, aims at redistributing the demand/strength ratio in order to provide a more uniform distribution of deformations over the height of the structure. The two control approaches were assessed through simulations of the earthquake response of semi‐actively and passively controlled six‐story post‐tensioned steel frames. The results showed that the stiffness control approach is efficient in reducing the frame deformations and internal forces. The deformation regulation control approach was found to be efficient in reducing the frame displacements and generating a more uniform distribution of the inter‐story drifts. These results indicate that centralized semi‐active control can be used to improve the seismic performance of post‐tensioned steel frames. Copyright © 2014 John Wiley & Sons, Ltd.     

Non‐linear‐Maxwell‐element‐type hysteretic control force

A simple non‐linear control law is proposed for reducing structural responses against seismic excitations. This law defines control force dynamics by one differential equation involving a non‐linear term that restrains the control force amplitude. If non‐linearity is neglected, the control force becomes the force in a Maxwell element, so it is called the non‐linear‐Maxwell‐element‐type (NMW) control force. The NMW control force vs. deformation relation plots hysteretic curves. The basic performance of an SDOF model with the NMW control force is examined for various conditions by numerical analyses. Furthermore, the control law is extended to fit an MDOF structural model, and an application example is shown. The computational results show that the NMW control force efficiently reduces structural responses. Copyright © 2000 John Wiley & Sons, Ltd.     

随机动力系统最优控制准则研究

根据线性二次最优控制理论,给出了系统随机最优控制的控制律一般形式。从目标控制量的物理意义出发,提出了基于系统概率密度演化分析的最优控制准则,建立了递阶层次的演化过程控制准则类。以线性单自由度体系随机地震反应最优控制为例,分析了各控制准则类的权矩阵参数优化结果,并根据最优控制律进行了系统随机最优控制研究。结果表明,本文提出的系统随机最优控制的控制律确定方法可以对系统性态进行有效的控制。     

Comparative response and performance of base‐isolated and fixed‐base structures

A building with a seismic isolation system, in an earthquake, is recognized as producing substantially smaller accelerations and deformations compared with a building that use other systems. This type of system is therefore expected to better protect the building's nonstructural components, equipment, and other contents that are essential for the activities conducted in the building. Unlike many available studies on building responses, only a small number of studies on a buildings' nonstructural component responses are available, and no study has directly addressed building performance with regard to nonstructural component protection. This paper therefore measures the performance of various seismically isolated buildings. Specifically, the effects of important structural parameters, namely, isolation stiffness, isolation damping ratio, and number of stories on the response of base‐isolated structures are investigated parametrically. Ground motions with 2% exceedence in 50years Maximum Considered Earthquake (MCE) are used. Performance is compared with that of fixed‐base structures in order to present data that will be useful in justifying the more costly technology. The buildings are 3, 9, and 20 stories, represented by MDOF shear‐beam models. As examples of displacement‐sensitive and acceleration‐sensitive components, partition walls and ceilings are considered, respectively. The Pacific Earthquake Engineering Research Center performance‐based earthquake engineering methodology is adopted to evaluate the failure return periods of the examples based on their available fragility curves. In addition, the curves are varied hypothetically to understand the sensitivity of the return period to the curve features. Then, the median and dispersion of fragility curves required to satisfy the components' desired failure return period are obtained. Copyright © 2015 John Wiley & Sons, Ltd.     

A mathematical formulation for optimal control of air pollution

In recent years the urban air pollutions caused by emissions from industry, transportation and energy consuming for daily living are getting worse in many major cities of China. Peoples awareness on air quality is increasing. Routine monitoring and foreca…     

Evolution of scouring process downstream of grade‐control structures under steady and unsteady flows

For many incised channels, one of the most common strategies is to install some hard structures, such as grade‐control structures (GCSs), in the riverbed to resist further incision. In this study, a series of experiments, including both steady and unsteady flow conditions, were conducted to investigate the scouring process downstream of a GCS. Three distinct phases, including the initial, developing and equilibrium phases, during the evolution of scour holes were identified. In addition, a semi‐empirical method was proposed to predict the equilibrium scour‐hole profile for the scour countermeasure design. In general, the comparisons between the experimental and simulated results are reasonably consistent. As the studies on temporal variation of the scour depth at GCSs caused by floods are limited, the effect of flood hydrograph shapes on the scour downstream of GCSs without upstream sediment supply was also investigated experimentally in this study. Based on the dimensional analysis and the concept of superposition, a methodology is proposed to simulate the time evolution of the maximum scour depth downstream of a GCS for steady flows. Moreover, the proposed scheme predicts reasonably well the temporal variations of the maximum scour depth for unsteady flows with both single and multiple peak. Copyright © 2012 John Wiley & Sons, Ltd.