Optimal design of hysteretic dampers connecting adjacent structures using multi-objective genetic algorithm and stochastic linearization method

An optimal design method is proposed for nonlinear hysteretic dampers that enhance the seismic performance of two adjacent structures. The proposed method employs nonlinear random vibration analyses by use of a stochastic linearization method in order to efficiently estimate the stochastic responses of coupled buildings without performing numerous nonlinear time-history analyses. The main objectives of the optimal design are not only to reduce the seismic responses but also to minimize the total cost of the damper system. To deal with such conflicting objectives, a multi-objective genetic algorithm is adopted. This approach systematically obtains a set of Pareto optimal solutions that are non-inferior or non-superior to each other. The process for choosing a reasonable design from the optimal surface of Pareto solutions is also discussed. As an example of a nonlinear hysteretic damping device, this study considers passive-type magneto-rheological dampers with fixed input voltages. The optimal voltages and numbers of installed dampers are simultaneously determined. The robustness of the optimal design against uncertain characteristics of ground motions is examined through extensive nonlinear random vibration analyses.     

Life-cycle cost optimal design of passive dissipative devices

The cost-effective performance of structures under natural hazards such as earthquakes and hurricanes has long been recognized to be an important topic in the design of civil engineering systems. A realistic comprehensive treatment of such a design requires proper integration of (i) methodologies for treating the uncertainties related to natural hazards and to the structural behavior over the entire life-cycle of the building, (ii) tools for evaluating the performance using socioeconomic criteria, as well as (iii) algorithms appropriate for stochastic analysis and optimization. A systematic probabilistic framework is presented here for detailed estimation and optimization of the life-cycle cost of engineering systems. This framework is a general one but the application of interest here is the design of passive dissipative devices for seismic risk mitigation. A comprehensive methodology is initially presented for earthquake loss estimation; this methodology uses the nonlinear time-history response of the structure under a given excitation to estimate the damage in a detailed, component level. A realistic probabilistic model is then presented for describing the ground motion time history for future earthquake excitations. In this setting, the life-cycle cost is uncertain and can be quantified by its expected value over the space of the uncertain parameters for the structural and excitation models. Because of the complexity of these models, calculation of this expected value is performed using stochastic simulation techniques. This approach, though, involves an unavoidable estimation error and significant computational cost, features which make efficient design optimization challenging. A highly efficient framework, consisting of two stages, is discussed for this stochastic optimization. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the seismic retrofitting of a four-story non-ductile reinforced-concrete building with viscous dampers.     

Structural dynamic optimal design based on dynamic reliability

In this work, dimension and shape optimization of structures under stochastic process excitation is addressed in the context of element or system dynamic reliability constraints, where the structural gross mass is taken to be the objective function. Firstly, based on the dynamic response analysis of truss structures under stochastic process loads, the dynamic reliability constraints are developed and simplified, and the normalization of design variables is discussed to avoid some variables being drowned by others during optimization due to their different dimensions and orders of magnitude. The optimal models of dimension and shape with element or system dynamic reliability constraints are then presented. Two numerical examples are finally used to illustrate the results of different optimal designs, which demonstrate that the efficiency to solve the structural optimization with dynamic reliability constraints can be significantly improved if the design variables and their initial values are selected properly.     

Optimal probabilistic design of seismic dampers for the protection of isolated bridges against near-fault seismic excitations

A probabilistic, simulation-based framework is presented in this paper for risk assessment and optimal design of supplemental dampers for multi-span bridge systems supported on abutments and intermediate piers through isolation bearings. The adopted bridge model explicitly addresses nonlinear characteristics of the isolators and the dampers, the dynamic behavior of the abutments, and the effect of pounding between the neighboring spans against each other as well as against the abutments. Nonlinear dynamic analysis is used to evaluate the bridge performance, and a realistic stochastic ground motion model is presented for describing the time history of future near-fault ground motions and relating their characteristics to the seismic hazard for the structural site. A probabilistic foundation is used to address the various sources of structural and excitation uncertainties and ultimately characterize the seismic risk for the bridge. This risk is given by the expected value of the system response over the adopted probability models. Stochastic simulation is used for evaluating the multi-dimensional integral representing this expected value and for performing the associated optimization when searching for the most favorable damper characteristics. An efficient probabilistic sensitivity analysis is also established for identifying the importance of each of the uncertain model parameters in affecting the overall risk. An illustrative example is presented that considers the design of nonlinear viscous dampers for the protection of a two-span bridge.     

Failure probability minimization of buildings through passive friction dampers

This paper proposes a methodology for robust optimization of the failure probability of buildings subjected to stochastic earthquakes, using a less common type of passive energy dissipation device: the friction dampers. There is a lack of studies on optimal positions and parameters of passive friction dampers, and additionally, the few studies found in the literature consider the problem in a deterministic way. The robust optimization proposed in this paper is carried out through the recently developed backtracking search optimization algorithm, which is able to deal with optimization problems involving mixed discrete (positions) and continuous (friction forces) design variables. In order to take into account uncertainties present in both the system and the dynamic excitation (earthquakes), some parameters are modeled as random variables, and consequently, the structural response becomes stochastic. For illustration purposes, a 10‐story building is analyzed. The results showed that the proposed method was able to reduce the failure probability in approximately 99% with only three friction dampers, installed in their best positions and with their optimized friction forces. The proposed methodology is quite general, and it is believed that it can be recommended as an effective tool for optimum design of friction dampers. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimum design of tuned mass dampers for different earthquake ground motion parameters and models

Tuned mass dampers are frequently used for passive control of vibrations in civil structures subject to seismic and wind actions. Their efficiency depends on selection of their mechanical properties in relation to main system and excitation characteristics. This paper proposes an optimum design strategy of single tuned mass dampers to control vibrations of principal mode of structures excited by earthquake ground motion. The main purpose of the paper is to investigate the influence of the time modulation of earthquake excitation upon the optimal tuned mass dampers design parameters: frequency and damping ratio. The study is based on numerical analyses carried out with different stochastic models for earthquakes: a simple filtered white noise model and two time modulated filtered white noise models. The numerical analyses are carried out to solve an optimization problem with a performance index defined by the reduction of the standard deviation of either the structure displacement or its inertial acceleration as objective function. To complete the work, the influence of the bandwidth excitation over the values of the optimal tuned mass damper parameters is investigated, as well the optimum mass ratio and the structure frequency. The results of the numeral analyses carried out infer that the earthquake excitation characteristics, including its modulation in time domain, highly affect the optimum tuned mass damper design parameters values.     

Investigations concerning seismic response control of self-anchored suspension bridge with MR dampers

To mitigate the seismic response of self-anchored suspension bridges, equations of motion governing the coupled system of bridge- magneto-rheological (MR) dampers subject to seismic excitation are formulated by employing the phenomenological model of MR dampers. A corresponding computer program is developed and employed for studying the seismic response control of a self-anchored suspension bridge with a main span of 350 m. The effect of variable current and number of dampers on seismic response control is investigated. The numerical results indicate the longitudinal displacement of the tower top and bridge girder decrease with the increase in input current and number of MR dampers attached longitudinally at the tower-girder connections, and the internal forces of the tower are effectively attenuated as well. It appears that small electronic current (0.5 A in this study) may sufficiently attenuate the seismic responses for practical engineering applications.     

Optimal design of passive viscous damping systems for buildings under seismic excitation

Nowadays, it is known that through the use of energy dissipation devices, the seismic performance of buildings can be improved. However, for efficiency and structural safety, the locations and sizes of these devices need to be properly defined. In this work, a procedure to optimally define the damping coefficients of added linear viscous dampers to meet an expected level of performance on buildings under seismic excitation is proposed. The performance criterion is expressed in terms of a maximum interstory drift, which is one of the most important limitations provided by the seismic design codes. For a given level of performance, the effectiveness of the damper distribution obtained by means of different objective functions is also assessed. Knowing that the main contribution to the total uncertainty is due to the excitation and with the aim of achieving robust results, the most appropriate approach to model the excitation is through a stationary stochastic process characterized by a power spectral density compatible with the response spectrum defined by the seismic design code. Accordingly, the structural response is obtained in the frequency domain. Through numerical examples, on planar and three-dimensional steel buildings with coupled lateral and torsional vibrations, the proposed procedure is verified.     

连接Kelvin阻尼器的对称双塔楼结构被动控制研究

将连接阻尼器的对称双塔楼结构耦合为单个连接着Kelvin型阻尼器的2-DOF（degree of freedom）体系,推导了耦合结构体系的运动微分方程并基于能量最小原理求出了连接阻尼器的优化参数解析解。参数化分析表明结构各层频率比、质量比和刚度比是影响阻尼器控制效果的重要参数。对于一个给定的对称双自由度体系,存在最优的Kelvin阻尼器阻尼参数解析解使得结构的位移峰值响应有最小值,同时从结构的自振特性也会影响结构最终的控制效果。最后,通过数值算例,分别讨论了塔楼多自由度体系在地震激励下的位移时程、结构振动能量和层间位移角,验证了该文所提Kelvin阻尼器优化参数解析表达式对控制带底盘对称双塔楼结构动力响应的有效性。     

消能摇摆钢框架结构抗震性能的影响因素与设计方法

消能摇摆钢框架结构包含主体钢框架结构、摇摆结构和耗能阻尼器三部分。刚度较大的摇摆结构可以使主体钢框架在地震作用下发生均匀的层间变形,抑制薄弱层产生。布设于摇摆结构底部的阻尼器,能够耗散地震动能量,减小整体结构的地震反应,提高结构的抗震性能。文中对消能摇摆钢框架结构抗震性能的影响因素进行参数分析,并基于我国建筑抗震设计规范的原则提出了抗震设计方法。根据消能摇摆钢框架结构的受力机理,提出简化分析模型,通过弹塑性地震反应分析,验证简化模型的有效性。基于简化分析模型对无量纲参数进行参数分析,根据各参数的影响规律得到无量纲参数的建议范围。结合我国“三阶段”抗震设防要求,提出消能摇摆钢框架结构的设计方法,并结合算例进行验证。研究表明,消能摇摆钢框架结构抗震性能良好,设计合理的摇摆结构与阻尼器能够抑制钢框架的薄弱层、减小结构的地震反应。     

Stochastic seismic response analysis of offshore wind turbine including fluid‐structure‐soil interaction

This paper presents the stochastic seismic response analysis of offshore wind turbines subjected to multi‐support seismic excitation by using a three‐dimensional numerical finite element model considering viscous boundaries. The seawater‐offshore wind turbine‐soil interaction system is modelled by the Lagrangian (displacement‐based) fluid and solid‐quadrilateral‐isoparametric finite elements. The random seismic excitation is described by the filtered white noise model and applied to each support point of the three‐dimensional finite element model of the coupled interaction system. The research conducts a parametric study to estimate the effects of variable seawater level, different foundation soil types and support site conditions on the stochastic behaviour of the offshore wind turbine coupled interaction system. The finite element model of coupled interaction system was also analyzed to examine the effect of the surrounding ice sheet on the stochastic response of the coupled system with and without ice sheet. The results obtained for different cases are compared with each other. Copyright © 2010 John Wiley & Sons, Ltd.     

消能摇摆高位隔震结构体系的地震反应特性

双段消能摇摆结构体系是通过两段串联的摇摆结构,控制主体结构各楼层在地震作用下均匀变形,抑制薄弱层的产生,也降低了主体结构对于摇摆结构的刚度需求。在变形集中的摇摆结构底部布设位移型阻尼器,可进一步提高结构的抗震性能。但是该体系存在承载力较低、上段结构地震反应相对较大的不足。基于此,提出了消能摇摆高位隔震结构体系,即在双段消能摇摆结构体系的分段楼层位置增设劲性支撑,以抑制上段结构的摇摆运动,提高结构的刚度与承载力;同时,下段结构允许发生摇摆,发挥高位隔震层的作用。以消能摇摆高位隔震结构体系为研究对象,分析对比了其他三种结构体系：传统支撑框架结构体系、双段消能摇摆结构体系、不含位移型阻尼器的摇摆高位隔震结构体系。采用OpenSees软件建立了弹塑性有限元分析模型,对四种结构体系进行弹塑性抗震分析和增量动力时程分析。研究表明,消能摇摆高位隔震结构体系的刚度与承载力较高,地震反应较小,抗震性能与抗倒塌性能良好。在摇摆结构分段位置加设劲性支撑层,可以抑制上段结构在地震作用下的变形,并发挥下段摇摆结构的隔震作用。布设于分段位置与摇摆结构底部的阻尼器,可以充分消耗地震能量,提高结构体系的抗震性能。     

Investigations concerning seismic response control of self-anchored suspension bridge with MR dampers

To mitigate the seismic response of self-anchored suspension bridges, equations of motion governing the coupled system of bridge-magneto-rheological (MR) dampers subject to seismic excitation are formulated by employing the phenomenological model of MR dampers. A corresponding computer program is developed and employed for studying the seismic response control of a self-anchored suspension bridge with a main span of 350 m. The effect of variable current and number of dampers on seismic response control is investigated. The numerical results indicate the longitudinal displacement of the tower top and bridge girder decrease with the increase in input current and number of MR dampers attached longitudinally at the tower-girder connections, and the internal forces of the tower are effectively attenuated as well. It appears that small electronic current (0.5 A in this study) may sufficiently attenuate the seismic responses for practical engineering applications. __________ Translated from China Civil Engineering Journal, 2006, 39(11): 84–89 [译自: 土木工程学报]     

大平台多塔楼新型隔震体系的智能磁流变控制

本文将隔震技术应用到大平台多塔楼结构中,研究了这种新型隔震体系的抗震性能,并将磁流变(MR)阻尼器设置于隔震层,探讨了这种新型隔震体系智能磁流变控制的减震效果.文中以北京通惠家园某典型小区为研究对象,建立了大平台多塔楼新型隔震减震体系的运动方程,考虑了隔震支座的非线性.本研究中MR阻尼器的半主动控制算法选用限幅最优控制算法,其主控制器采用H2/LQG方法来设计.仿真分析结果表明,这种新型隔震体系可以有效地减小上部住宅结构与下部平台的地震反应,为提高大平台多塔楼结构的抗震安全性提供了一条崭新的途径.采用MR阻尼器与这种新型隔震体系相结合可以进一步减小隔震结构下部平台的地震反应与隔震层的非线性反应,提高这种新型隔震体系的抗震安全性.     

结构半主动变阻尼控制的研究

作为经典范例之一,半主动变阻尼系统得到了广泛的应用,然而近来的研究显示仍需要对其控制性能重新认识。本文以谐波作用下支座激励的理论为出发点,讨论了粘性变阻尼控制系统可能成立的基本条件和适用范围。算例以一个设置在基础层的半主动变阻尼器控制系统为例,采用离复位控制策略进行了数值模拟,并得出了两个重要结论:(1)变阻尼控制系统只有在结构动力反应远离共振的情况下,才有可能同时取得位移峰值和加速度峰值的减小;(2)结构动力反应与控制效果的改善依赖地面运动特性,在一般情况下相比被动阻尼控制并不能明显提高控制效果,甚至有所不及。     

结构半主动控制研究中存在的若干问题

近年来,半主动控制系统在国内外受到了诸多关注,取得了很大的研究进展,但是仍然存在明显的不足之处。本文提出了半主动控制系统研究过程中有待解决的若干关键问题。首先综述了各种半主动控制装置和对应控制律设计的研究现状,然后分析了它们各自的优缺点。此外,也就足尺控制系统研发、控制律设计、控制装置优化和时滞补偿等半主动控制系统中的共性问题进行了分析,并给出了相应的建议。研究指出:常规变刚度控制系统抑制振动频带窄,并且不利于结构的加速度反应控制;粘性变阻尼控制与被动阻尼控制相比仅在结构远离共振时才有意义。     

风浪联合作用下的钢格构式基础海上浮式风机耦合动力响应分析

结合半潜式和单立柱式海上风机浮式基础的特点,提出了一种用于海上风机的新型钢格构式基础。首先,根据美国可再生能源实验室(National Renewable Energy Laboratory,NREL)提供的5 MW海上风机样机对提出的新型浮式基础进行了结构设计。然后,采用水动力-空气动力-控制系统-系泊系统耦合方法对风-浪联合作用下的新型海上浮式风机的动力响应进行了分析。结果表明:钢格构式浮式基础的纵荡运动主要受风速变化影响,纵摇运动受风速-波浪变化的显著影响,而垂荡运动主要受波浪变化控制。与单立柱式浮式风机相比,钢格构式基础海上浮式风机的纵摇、横摇及艏摇响应更小,具有更好的稳定性,对比结果表明提出的钢格构式浮式基础是一种适用于深海环境下海上风机的新型浮式基础。     

Application of endurance time method in seismic assessment of steel frames

In this paper, application of a new dynamic procedure called Endurance Time (ET) method in seismic analysis of steel frames is explained. In this method, structures are subjected to gradually intensifying ground shaking and their performance is assessed based on their response considering relevant design criteria at each intensity level. By considerably reducing the number of time history analyses for assessment of structural response at different intensities, this procedure tends to pave a way for practical performance based design of structures. The accuracy of ET method in predicting the response of structures in linear and nonlinear analysis is investigated by considering a set of steel frames. Different material models consisting of elastic-perfectly plastic, stiffness degrading and strength deteriorating models are considered. Application of ET method in assessment of frames that incorporate fluid viscous dampers as seismic mitigation devices is also demonstrated. It is shown that ET analysis can estimate the results of full response history analysis with reasonable accuracy at different excitation levels. ET analysis results are also shown to be reasonably consistent for different material models. Specific issues that should be considered for a successful ET analysis, including the potential loss of accuracy at highly nonlinear excitation levels are discussed. Capability of ET method in predicting collapse capacity of the studied frames is discussed.     

On the reliability-based design of structures including passive energy dissipation systems

This contribution presents a methodology for stochastic design of structures including vibration protection systems. The approach is then used to investigate the effect of uncertain model parameters on the reliability-based optimal design of structures with a class of passive energy dissipation systems. The uncertainty of structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. The optimal design problem is formulated as a non-linear constrained minimization problem involving multiple design requirements, including reliability constraints related to the structural performance. Failure events defined by a large number of random variables are used to characterize the reliability measures. A sequential optimization approach based on global conservative, convex and separable approximations is implemented for solving the optimization problem. The effects of uncertain model parameters on the performance, robustness and reliability of protected systems is illustrated by two example problems that consider multi-story buildings under stochastic ground excitation.