结构地震反应随机最优控制的多目标概率准则研究
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摘要
建立了结构随机最优控制的一类多目标概率准则,包括以性态均衡的反应量等价极值过程的期望和超越概率为目标的准则,和以能量均衡的反应量等价极值过程的期望和超越概率为目标的准则。分析表明,各概率准则的控制效果依赖于其物理意义,能量均衡超越概率准则能够获得系统响应降低与控制力需求之间的合理均衡,是设计随机动力系统最优控制律的优选准则。算例分析表明,所提出的多目标概率准则可以实现地震动作用下结构反应性态的精细化控制。
A family of multi-objective probabilistic criteria for stochastic optimal control of base-excited structures was developed including the two criteria taking the ensemble-expectation and exceedance probability of equivalent extreme-value processes as objective functions in the sense of performance and energy trade-off respectively.Numerical investigations show that the effectiveness of response control hinges on the physical origin of the probabilistic criteria.The exceedance probability criterion in energy trade-off sense accommodates system performance to a better trade-off between response reductions and control requirements,compared with other control criteria currently used.A randomly base-excited eight-storey shear frame,controlled by active tendons was analysed as a numerical example.Numerical results reveal that using the advocated probabilistic criterion,the structural stochastic optimal control operates efficiently with a desirable objective performance achieved.
A family of multi-objective probabilistic criteria for stochastic optimal control of base-excited structures was developed including the two criteria taking the ensemble-expectation and exceedance probability of equivalent extreme-value processes as objective functions in the sense of performance and energy trade-off respectively.Numerical investigations show that the effectiveness of response control hinges on the physical origin of the probabilistic criteria.The exceedance probability criterion in energy trade-off sense accommodates system performance to a better trade-off between response reductions and control requirements,compared with other control criteria currently used.A randomly base-excited eight-storey shear frame,controlled by active tendons was analysed as a numerical example.Numerical results reveal that using the advocated probabilistic criterion,the structural stochastic optimal control operates efficiently with a desirable objective performance achieved.
引文
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[5]Zhang W S,Xu Y L.Closed form solution for along windresponse of actively controlled tall buildings with LQGcontrollers[J].Journal of Wind Engineering and IndustrialAerodynamics,2001,89:785-807.
[6]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.
[7]Mathews J H,Fink K D,Fink K.Numerical Methods UsingMatlab(4th Edition)[M].Boston:Prentice Hall,2003.
[8]Peng Y B,Ghanem R,Li J.Polynomial chaos expansions foroptimal control of nonlinear random oscillators[J].Journal ofSound and Vibration,2010,329(18):3660-3678.
[2]Li J,Peng Y B,Chen J B.A physical approach to structuralstochastic optimal controls[J].Probabilistic EngineeringMechanics,2010,25(1):127-141.
[3]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.
[4]Leondes C T,Salami M A.Algorithms for the weightingmatrices in sampled-data linear time-invariant optimal regulatorproblems[J].Computers&Electrical Engineering,1980,7:11-23.
[5]Zhang W S,Xu Y L.Closed form solution for along windresponse of actively controlled tall buildings with LQGcontrollers[J].Journal of Wind Engineering and IndustrialAerodynamics,2001,89:785-807.
[6]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.
[7]Mathews J H,Fink K D,Fink K.Numerical Methods UsingMatlab(4th Edition)[M].Boston:Prentice Hall,2003.
[8]Peng Y B,Ghanem R,Li J.Polynomial chaos expansions foroptimal control of nonlinear random oscillators[J].Journal ofSound and Vibration,2010,329(18):3660-3678.
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