结构地震反应性态的物理随机最优控制
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摘要
本研究发展了结构地震反应性态的随机最优控制理论和方法。这一研究建立在物理随机系统思想的新理论框架下,突破了以I^to随机微分方程描述动力系统的经典随机最优控制的藩篱。提出了基于系统二阶统计量评价、单目标超越概率和多目标能量均衡的控制器参数设计准则,以及基于概率可控指标的控制器位置设计准则,并将它们统一为物理随机最优控制的广义最优控制律。数值算例分析表明,本文发展的物理随机最优控制方法能够实现结构地震反应性态的精细化控制。
A family of optimal control schemes for enhancing seismic performance of randomly base-driven structures is developed in this paper.Its principles are derived from the novel theoretical framework of physical stochastic systems,towards breaking through the barriers inherent in the classical stochastic optimal controls described by Ito[DD(-*3/5]^ stochastic differential equations.Having this knowledge,we proposed three classes of probabilistic criteria associated with parameters of control devices,including the probabilistic criterion in conjunction with system statistics assessment,the probabilistic criterion in conjunction with the exceedance probability of single objective and the probabilistic criterion in conjunction with the energy trade-off of multiple objective.These criteria are logically integrated into the generalized optimal control policy with probabilistic criterion for optimal allocation of control devices based on probabilistic controllability index.Two cases of randomly base-driven structural systems,controlled by active tendons,are investigated for illustrative purposes.The numerical results reveal that the proposed methodology can implement the accurate control of seismic performance of base-driven structures.
A family of optimal control schemes for enhancing seismic performance of randomly base-driven structures is developed in this paper.Its principles are derived from the novel theoretical framework of physical stochastic systems,towards breaking through the barriers inherent in the classical stochastic optimal controls described by Ito[DD(-*3/5]^ stochastic differential equations.Having this knowledge,we proposed three classes of probabilistic criteria associated with parameters of control devices,including the probabilistic criterion in conjunction with system statistics assessment,the probabilistic criterion in conjunction with the exceedance probability of single objective and the probabilistic criterion in conjunction with the energy trade-off of multiple objective.These criteria are logically integrated into the generalized optimal control policy with probabilistic criterion for optimal allocation of control devices based on probabilistic controllability index.Two cases of randomly base-driven structural systems,controlled by active tendons,are investigated for illustrative purposes.The numerical results reveal that the proposed methodology can implement the accurate control of seismic performance of base-driven structures.
引文
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[4]Roussis P C,Constantinou M C,Erdik M,et al.Assessment of performance of seismic isolation systemof Bolu Viaduct[J].Journal of Bridge Engineering,2003,8(4):182-190.
[5]Yang J N.Application of optimal control theory tocivil engineering structures[J].ASCE Journal of theEngineering Mechanics Division,1975,101(EM6):819-838.
[6]Li J,Peng Y B,Chen J B.A physical approach tostructural stochastic optimal controls[J].Probabilistic Engineering Mechanics,2010,25(1):127-141.
[7]李杰,彭勇波.基于广义密度演化方程的结构随机最优控制[J].计算力学学报,2010,27(6):976-982.Li J,Peng Y B.Generalized density evolutionequation based structural stochastic optimal control[J].Chinese Journal of Computational Mechanics,2010,27(6):976-982.
[8]李杰,彭勇波,陈建兵.随机动力系统最优控制准则研究[J].地震工程与工程振动,2010,30(1):117-122.Li J,Peng Y B,Chen J B.Analysis of optimal controlcriteria for stochastic dynamic systems[J].Journal ofEarthquake Engineering and Engineering Vibration,2010,30(1):117-122.
[9]Li J,Peng Y B,Chen J B.Probabilistic criteria ofstructural stochastic optimal controls[J].Probabilistic Engineering Mechanics,2011,26(2):240-253.
[10]Peng Y B,Li J.Exceedance probability criterionbased stochastic optimal polynomial control of duffingoscillators[J].International Journal of Non-LinearMechanics,2011,46(2):457-469.
[11]Li J,Peng Y B,Chen J B.Nonlinear stochasticoptimal control strategy of hysteretic structures[J].Structural Engineering&Mechanics,2011,38(1):39-63.
[12]彭勇波,李杰.非线性随机动力系统的最优多项式控制[J].振动工程学报,2010,23(4):366-372.Peng Y B,Li J.Optimal polynomial control of nonli-near stochastic dynamical systems[J].Journal ofVibration Engineering,2011,23(4):366-372.
[13]彭勇波,李杰.随机动力系统磁流变阻尼最优控制策略[J].同济大学学报(自然科学版),2010,38(2):164-169.Peng Y B,Li J.Optimal control strategy of stochasticdynamical systems with MR damping[J].Journal ofTongji University(Natural Science),2010,38(2):164-169.
[14]彭勇波,陈建兵,李杰.随机激励滞回系统的非线性最优控制[J].武汉理工大学学报,2010,32(9):35-39.Peng Y B,Chen J B,Li J.Nonlinear optimal controlof random excited hysteretic systems[J].Journal ofWuhan University of Technology,2010,32(9):35-39.
[15]Peng Y B,Ghanem R,Li J.Generalized optimalcontrol policy for stochastic optimal control ofstructures[J].Structural Control and HealthMonitoring,2011(in press).
[16]Li J,Chen J B.Stochastic Dynamics of Structures[M].Singapore:John Wiley&Sons,2009.
[17]李杰.结构工程研究中的关键科学问题[R].上海:同济大学土木工程学院,2006.Li J.Critical scientific challenges in studies ofstructural engineering[R].Shanghai:School of CivilEngineering,Tongji University,2006.
[18]Zhang W S,Xu Y L.Closed form solution foralongwind response of actively controlled tallbuildings with LQG controllers[J].Journal of WindEngineering and Industrial Aerodynamics,2001,(89):785-807.
[19]Stengel R F,Ray L R,Marrison C I.Probabilisticevaluation of control system robustness[C]∥IMAWorkshop on Control Systems Design for AdvancedEngineering Systems:Complexity,Uncertainty,Information and Organization,Minneapolis:[s.n.],1992.12-16.
[20]Zhu W Q,Ying Z G,Soong T T.An optimal nonli-near feedback control strategy for randomly excitedstructural systems[J].Nonlinear Dynamics,2001,(24):31-51.
[21]Amini F,Tavassoli M R.Optimal structural activecontrol force,number and placement of controllers[J].Engineering Structures,2005,(27):1306-1316.
[22]李杰,艾晓秋.基于物理的随机地震动模型研究[J].地震工程与工程振动,2006,26(5):21-26.Li J,Ai X Q.Study on random model of earthquakeground motion based on physical process[J].Journalof Earthquake Engineering and EngineeringVibration,2006,26(5):21-26.
[2]Housner G W,Bergman L A,Caughey T K,et al.Structural control:past,present,and future[J].Journal of Engineering Mechanics,1997,123(9):897-971.
[3]欧进萍.结构振动控制——主动、半主动与智能控制[M].北京:科学出版社,2003.Ou J P.Structural Vibration Control:Active,Semi-Active and Intelligent Control[M].Beijing:SciencePress,2003.
[4]Roussis P C,Constantinou M C,Erdik M,et al.Assessment of performance of seismic isolation systemof Bolu Viaduct[J].Journal of Bridge Engineering,2003,8(4):182-190.
[5]Yang J N.Application of optimal control theory tocivil engineering structures[J].ASCE Journal of theEngineering Mechanics Division,1975,101(EM6):819-838.
[6]Li J,Peng Y B,Chen J B.A physical approach tostructural stochastic optimal controls[J].Probabilistic Engineering Mechanics,2010,25(1):127-141.
[7]李杰,彭勇波.基于广义密度演化方程的结构随机最优控制[J].计算力学学报,2010,27(6):976-982.Li J,Peng Y B.Generalized density evolutionequation based structural stochastic optimal control[J].Chinese Journal of Computational Mechanics,2010,27(6):976-982.
[8]李杰,彭勇波,陈建兵.随机动力系统最优控制准则研究[J].地震工程与工程振动,2010,30(1):117-122.Li J,Peng Y B,Chen J B.Analysis of optimal controlcriteria for stochastic dynamic systems[J].Journal ofEarthquake Engineering and Engineering Vibration,2010,30(1):117-122.
[9]Li J,Peng Y B,Chen J B.Probabilistic criteria ofstructural stochastic optimal controls[J].Probabilistic Engineering Mechanics,2011,26(2):240-253.
[10]Peng Y B,Li J.Exceedance probability criterionbased stochastic optimal polynomial control of duffingoscillators[J].International Journal of Non-LinearMechanics,2011,46(2):457-469.
[11]Li J,Peng Y B,Chen J B.Nonlinear stochasticoptimal control strategy of hysteretic structures[J].Structural Engineering&Mechanics,2011,38(1):39-63.
[12]彭勇波,李杰.非线性随机动力系统的最优多项式控制[J].振动工程学报,2010,23(4):366-372.Peng Y B,Li J.Optimal polynomial control of nonli-near stochastic dynamical systems[J].Journal ofVibration Engineering,2011,23(4):366-372.
[13]彭勇波,李杰.随机动力系统磁流变阻尼最优控制策略[J].同济大学学报(自然科学版),2010,38(2):164-169.Peng Y B,Li J.Optimal control strategy of stochasticdynamical systems with MR damping[J].Journal ofTongji University(Natural Science),2010,38(2):164-169.
[14]彭勇波,陈建兵,李杰.随机激励滞回系统的非线性最优控制[J].武汉理工大学学报,2010,32(9):35-39.Peng Y B,Chen J B,Li J.Nonlinear optimal controlof random excited hysteretic systems[J].Journal ofWuhan University of Technology,2010,32(9):35-39.
[15]Peng Y B,Ghanem R,Li J.Generalized optimalcontrol policy for stochastic optimal control ofstructures[J].Structural Control and HealthMonitoring,2011(in press).
[16]Li J,Chen J B.Stochastic Dynamics of Structures[M].Singapore:John Wiley&Sons,2009.
[17]李杰.结构工程研究中的关键科学问题[R].上海:同济大学土木工程学院,2006.Li J.Critical scientific challenges in studies ofstructural engineering[R].Shanghai:School of CivilEngineering,Tongji University,2006.
[18]Zhang W S,Xu Y L.Closed form solution foralongwind response of actively controlled tallbuildings with LQG controllers[J].Journal of WindEngineering and Industrial Aerodynamics,2001,(89):785-807.
[19]Stengel R F,Ray L R,Marrison C I.Probabilisticevaluation of control system robustness[C]∥IMAWorkshop on Control Systems Design for AdvancedEngineering Systems:Complexity,Uncertainty,Information and Organization,Minneapolis:[s.n.],1992.12-16.
[20]Zhu W Q,Ying Z G,Soong T T.An optimal nonli-near feedback control strategy for randomly excitedstructural systems[J].Nonlinear Dynamics,2001,(24):31-51.
[21]Amini F,Tavassoli M R.Optimal structural activecontrol force,number and placement of controllers[J].Engineering Structures,2005,(27):1306-1316.
[22]李杰,艾晓秋.基于物理的随机地震动模型研究[J].地震工程与工程振动,2006,26(5):21-26.Li J,Ai X Q.Study on random model of earthquakeground motion based on physical process[J].Journalof Earthquake Engineering and EngineeringVibration,2006,26(5):21-26.
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