基于约束UKF模型更新的混合试验方法
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摘要
为了提高模型更新混合试验模型更新的准确性,在隐性卡尔曼滤波器(Unscented Kalman Filter,UKF)的基础上,提出约束UKF(Constrained UKF,CUKF)算法。算法采用样本点投影方法处理考虑界限约束的非线性模型参数在线识别问题。在预测步中同时修改违反约束条件的样本点位置和相应权重;在更新步中采用样本点更新方式,可同时实现约束对状态估计和协方差矩阵的影响。提出基于CUKF模型更新混合试验方法,在混合试验过程中,基于试验观测数据采用CUKF算法在线更新数值子结构模型。通过对两个自由度非线性结构混合试验数值模拟表明:与传统混合试验、基于UKF模型更新混合试验相比,基于CUKF模型更新混合试验结果具有更好的精度。
To improve accuracy of hybrid testing method based on model updating,a new Constrained Unscented Kalman Filter(CUKF) algorithm is proposed based on the Unscented Kalman Filter(UKF),which adopts the sample points projecting method to deal with nonlinear model parameter online estimation with bounds constraints.In prediction step,positions and weights of sample points violating constraints are modified at the same time.In updating step,state estimation and errors covariance matrix calculation are combined with state constraints by sample points updating method.The hybrid testing method based on model updating with CUKF is presented.During hybrid testing,the numerical substructure models are online updated with CUKF approach based on the measurement data from testing substructure.The effectiveness of the proposed test method is verified by a hybrid testing numerical simulation for a nonlinear system with two degrees of freedom.The results show the new hybrid testing method has better accuracy compared with conventional hybrid testing and hybrid testing based on model updating with UKF.
To improve accuracy of hybrid testing method based on model updating,a new Constrained Unscented Kalman Filter(CUKF) algorithm is proposed based on the Unscented Kalman Filter(UKF),which adopts the sample points projecting method to deal with nonlinear model parameter online estimation with bounds constraints.In prediction step,positions and weights of sample points violating constraints are modified at the same time.In updating step,state estimation and errors covariance matrix calculation are combined with state constraints by sample points updating method.The hybrid testing method based on model updating with CUKF is presented.During hybrid testing,the numerical substructure models are online updated with CUKF approach based on the measurement data from testing substructure.The effectiveness of the proposed test method is verified by a hybrid testing numerical simulation for a nonlinear system with two degrees of freedom.The results show the new hybrid testing method has better accuracy compared with conventional hybrid testing and hybrid testing based on model updating with UKF.
引文
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[2]王进廷,金峰,张楚汉.结构抗震试验方法的发展[J].地震工程与工程振动,2005,25(4):37-43.WANG Jinting,JIN Feng,ZHANG Chuhan.Advances in the dynamic testing method of structures[J].Journal of Earthquake Engineering and Engineering Vibration,2005,25(4):37-43.(in Chinese)
[3]许国山,吴斌.等效力控制方法在拟动力试验中的应用[J].地震工程与工程振动,2010,30(2):66-72.XU Guoshan,Wu Bin.Application of equivalent force control method to pseudo-dynamic testing[J].Journal of Earthquake Engineering and Engineering Vibration,2010,30(2):66-72.(in Chinese)
[4]冯帆,王强,王占飞.基于有限元软件ABAQUS的子结构拟动力试验技术[J].结构工程师,2011,27(增刊):82-87.FENG Fan,WANG Qiang,WANG Zhanfei.Research on hybrid simulation with finite element software ABAQUS[J].Structural Engineers,2011,27(Supple):82-87.(in Chinese)
[5]Yang W J,Nakano Y.Substructure online test by using real-time hysteresis modeling with a neural network[J].Advances in Experimental Structural Engineering,2004;267-274.
[6]Yang Y S,Tsai K C,Elnashai A S,et al.An online optimization method for bridge dynamic hybrid simulations[J].Simulation Modelling Practice and Theory,2012,28:42-54.
[7]王涛,吴斌,张健.基于最小二乘法的自适应拟动力子结构试验[J].结构工程师,2011,27(增刊):57-62.WANG Tao,WU Bin,ZHANG Jian.Adaptive pseudo-dynamic substructure testing based on least square method[J].Structural Engineers,2011,27(Supple):57-62.(in Chinese)
[8]Julier S,Uhmann J,Whyte H.A new method for the nonlinear transformation of means and covariances in filters and estimators[J].IEEE Trans.Automat.Control,2000,45:477-482.
[9]张健.自适应子结构拟动力试验方法[D].哈尔滨:哈尔滨工业大学,2010,70-83.ZHANG Jian.Adaptive substructure pseudo-dynamic testing method[D].Harbin:School of Civil Engineering,Harbin Institute of Technology,2010,1-83.(in Chinese)
[10]Wang T,Wu B.Model updating for hybrid testing with unscented Kalman filter[C].The 7th International Workshop on Advanced Smart Materials and Smart Structures Technology ANCRiSST2012,July 27-28,2012,Bangalore,India.
[11]Mandela R,Kuppuraj V,Rengaswmy R,et al.Constrained unscented recursive estimator for nonlinear dynamic systems[J].Journal of Process Control,2012,22:718-728.
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