未知激励下的无迹卡尔曼滤波新方法
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摘要
无迹卡尔曼滤波(UKF)是一种识别非线性系统的有效方法,然而传统的UKF方法需要观测外部激励,这限制了UKF的应用范围。迄今为止,国内外对未知激励情况下的UKF方法的研究还非常少。该文在传统UKF的基础上,推导出在未知激励情况下的无迹卡尔曼滤波(UKF-UI)方法的递推公式,通过对观测误差的最小化,利用非线性方程求解,识别未知外部激励,进而识别非线性结构系统状态与结构未知参数。进一步采用融合部分观测的加速度响应及位移响应,消除识别结果的漂移问题。分别通过白噪声和未知地震作用下识别非线性迟滞模型的两个数值算例,考虑观测噪声对非线性系统进行识别,从而验证提出新方法的有效性。结果表明,该文所提出的UKF-UI方法,能够在部分观测结构系统响应的情况下,有效地识别非线性结构参数和未知激励。
The unscented Kalman filter(UKF) has been applied as an effective method for the identification of nonlinear systems. However, the conventional UKF method requires the information of external excitation(input), which causes a limitation to the applications of UKF. So far, there have been very few studies on UKF with unknown excitations. In this paper, a novel UKF with unknown input(UKF-UI) is proposed. The analytical recursive solutions are proposed based on the procedures of conventional UKF. The unknown input is identified by minimizing the error of predicted measurement errors with the solution of a nonlinear equation.Moreover, the data fusion of partially measured acceleration and displacement responses is applied to eliminate the drift problem in identification results. The numerical examples for the identification of nonlinear hysteric systems and excitation are used to verify the proposed UKF-UI approach. The computational results show that proposed UKF-UI method can effectively identify the nonlinear system and unknown input using partial measurements of system responses.
The unscented Kalman filter(UKF) has been applied as an effective method for the identification of nonlinear systems. However, the conventional UKF method requires the information of external excitation(input), which causes a limitation to the applications of UKF. So far, there have been very few studies on UKF with unknown excitations. In this paper, a novel UKF with unknown input(UKF-UI) is proposed. The analytical recursive solutions are proposed based on the procedures of conventional UKF. The unknown input is identified by minimizing the error of predicted measurement errors with the solution of a nonlinear equation.Moreover, the data fusion of partially measured acceleration and displacement responses is applied to eliminate the drift problem in identification results. The numerical examples for the identification of nonlinear hysteric systems and excitation are used to verify the proposed UKF-UI approach. The computational results show that proposed UKF-UI method can effectively identify the nonlinear system and unknown input using partial measurements of system responses.
引文
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[12]李炜明,朱宏平,吴贤国,等.未知激励下框架结构系统辨识的特征系统实现算法[J].振动与冲击,2010,29(8):228―231.Li Weiming,Zhu Hongping,Wu Xianguo,et al.System identification based on experimental responses of a frame structure with unknown inputs[J].Shock and Vibration,2010,29(8):228―231.(in Chinese)
[13]Astroza R,Ebrahimian H,Li Y,et al.Bayesian nonlinear structural FE model and seismic input identification for damage assessment of civil structures[J].Mechanical Systems&Signal Processing,2017,93:661―687.
[14]Yang J N,Lin S,Huang H W,et al.An adaptive extended Kalman filter for structural damage identification[J].Structural Control and Health Monitoring,2006,13(4):849―867.
[15]雷鹰,江永强.输入输出信息有限观测下的结构损伤诊断[J].振动、测试与诊断,2012,32(5):736―740.Lei Ying,Jiang Yongqiang.Structural damage detection with limited measurements of input and output[J].Journal of Vibration,Measurement and Diagnosis,2012,32(5):736―740.(in Chinese)
[16]Liu L J,Su Y,Zhu J J.Data fusion based EKF-UI for real-time simultaneous identification of structural systems and unknown external inputs[J].Measurement,2016,88:456―467.
[17]Al-Hussein A,Haldar A.Novel unscented Kalman filter for health assessment of structural systems with unknown input[J].Journal of Engineering Mechanics,2015,141(7):04015012.1―04015012.13.
[18]Al-Hussein A,Haldar A.Unscented Kalman filter with unknown input and weighted global iteration for health assessment of large structural systems[J].Structural Control and Health Monitoring,2015,23(1):156―175
[19]Alhussein A,Haldar A.Structural damage prognosis of three-dimensional large structural systems[J].Structure&Infrastructure Engineering,2017,13(1):1―13.
[20]Ding Y,Zhao B Y,Wu B,et al.Simultaneous identification of structure and external excitation with improved unscented Kalman filter[J].Advances in Structural Engineering,2015,18(11):1981―1998.
[21]R.Van der Merwe.Sigma-point Kalman filters for probability inference in dynamic state-space models[D].OR,USA:Oregon Health and Science University,2004.
[2]No?l J P,Kerschen G.Nonlinear system identification in structural dynamics:10 more years of progress[J].Mechanical Systems and Signal Processing,2017,83:2―35.
[3]李杰,陈隽.子结构物理参数识别与输入地震动的复合反演研究[J].振动与冲击,1998,17(1):58―62.X?o?ve?€?X?pyLàR?Li Jie,Chen Jun.Study on composite inversion of ground motion and sub-structural parameter identification[J].Shock and Vibration,1988,17(1):58―62.(in Chinese)
[4]陈隽,史凯.高层建筑损伤识别中的补偿算法[J].振动与冲击,2002,21(2):24―27.Chen Jun,Shi Kai.Compensation method for damage detection of tall buildings[J].Shock and Vibration,2002,21(2):24―27.(in Chinese)
[5]刘以龙,刘杰,刘江南.基于子结构分析的动态载荷和模型参数复合反演研究[J].机械强度,2013,35(5):553―558.Liu Yilong,Liu Jie,Liu Jiangnan.Research on composite inversion of dynamic loads and structural parameters based on sub-structure analysis[J].Journal of Mechanical Strength,2013,35(5):553―558.(in Chinese)
[6]Hoshiya M,Saito E.Structural identification by extended Kalman filter[J].Journal of Engineering MechanicsASCE,1984,110(12):1757―1771.
[7]Julier S J,Uhlmann J K,Durrant-Whyte H F.A new approach for filtering nonlinear systems[C]//Proceeds of American Control Conference,Seattle,WA,USA:IEEE,1995,3:1628―1632.
[8]Julier S J,Uhlmann J K.A new extension of the Kalman filter to nonlinear systems[C]//Proceeds of the 11th International Symposium on Aerospace/Defense Sensing,Simulation and Controls.Society of Photo-optical Instrumentation Engineers,Orlando,Florida,USA:1997:182―193
[9]梅竹,吴斌,杨格.钢筋混凝土结构材料本构模型参数的在线识别[J].工程力学,2016,33(7):108―115.Mei Zhu,Wu Bin,Yang Ge.Online parameter identification of concrete constitutive model[J].Engineering Mechanics,2016,33(7):108―115.(in Chinese)
[10]张纯,陈林,宋固全,等.基于l1正则化无迹卡尔曼滤波的结构损伤方法[J].工程力学,2017,34(8):76―84.Zhang Chun,Chen Lin,Song Guquan,et al.Structural damage identification by unscented Kalman filter with l1regularization[J].Engineering Mechanics,2017,34(8):76―84.(in Chinese)
[11]许斌,贺佳.部分输入未知条件下结构参数及激励识别[J].土木工程学报,2012,6(45):13―22.Xu Bin,He Jia.Structural parameters and dynamic loading identification with partially unknown[J].Journal of Civil Engineering,2012,6(45):13―22.(in Chinese)
[12]李炜明,朱宏平,吴贤国,等.未知激励下框架结构系统辨识的特征系统实现算法[J].振动与冲击,2010,29(8):228―231.Li Weiming,Zhu Hongping,Wu Xianguo,et al.System identification based on experimental responses of a frame structure with unknown inputs[J].Shock and Vibration,2010,29(8):228―231.(in Chinese)
[13]Astroza R,Ebrahimian H,Li Y,et al.Bayesian nonlinear structural FE model and seismic input identification for damage assessment of civil structures[J].Mechanical Systems&Signal Processing,2017,93:661―687.
[14]Yang J N,Lin S,Huang H W,et al.An adaptive extended Kalman filter for structural damage identification[J].Structural Control and Health Monitoring,2006,13(4):849―867.
[15]雷鹰,江永强.输入输出信息有限观测下的结构损伤诊断[J].振动、测试与诊断,2012,32(5):736―740.Lei Ying,Jiang Yongqiang.Structural damage detection with limited measurements of input and output[J].Journal of Vibration,Measurement and Diagnosis,2012,32(5):736―740.(in Chinese)
[16]Liu L J,Su Y,Zhu J J.Data fusion based EKF-UI for real-time simultaneous identification of structural systems and unknown external inputs[J].Measurement,2016,88:456―467.
[17]Al-Hussein A,Haldar A.Novel unscented Kalman filter for health assessment of structural systems with unknown input[J].Journal of Engineering Mechanics,2015,141(7):04015012.1―04015012.13.
[18]Al-Hussein A,Haldar A.Unscented Kalman filter with unknown input and weighted global iteration for health assessment of large structural systems[J].Structural Control and Health Monitoring,2015,23(1):156―175
[19]Alhussein A,Haldar A.Structural damage prognosis of three-dimensional large structural systems[J].Structure&Infrastructure Engineering,2017,13(1):1―13.
[20]Ding Y,Zhao B Y,Wu B,et al.Simultaneous identification of structure and external excitation with improved unscented Kalman filter[J].Advances in Structural Engineering,2015,18(11):1981―1998.
[21]R.Van der Merwe.Sigma-point Kalman filters for probability inference in dynamic state-space models[D].OR,USA:Oregon Health and Science University,2004.