基于卡尔曼滤波和递推最小二乘在部分观测信息下的参数识别法
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摘要
有限观测信息下的参数识别是结构健康监测领域内的一个热点问题,传统的卡尔曼滤波(Kalman Filter,KF)不能识别结构参数,递推最小二乘法(Recursive Least Square Estimation,RLSE)可用于参数识别,但需已知结构全部响应,为此提出一种基于KF和RLSE的参数联合识别法,该方法首先利用部分自由度上的加速度响应观测值,通过KF估计下一步的系统响应信息,包括速度和位移响应;然后,基于该响应估计信息和当前步的结构参数估计值,根据运动平衡方程,获得下一步的加速度响应估计值;最后,利用已观测的有限加速度响应,获得改进的加速度响应向量,进而基于RLSE获得下一步的结构参数识别值。简支梁数值算例结果表明,该方法能准确识别结构参数,同时能实现系统响应的有效估计。
System identification using limited outputs is of importance for structural health monitoring. The traditional Kalman filter( KF) cannot be used for parameters identification. The recursive least-squares estimation( RLSE) can be employed for system identification while the complete structural responses are available. Here,based on KF and RLSE,a structural parameter identification method is proposed. Firstly,the structural states including displacement and velocity responses at the next step are estimated by means of KF using limited acceleration measurements. Then,based on these estimated responses and the structural parameters identified at the current step,the acceleration responses at the next step are estimated by the differential equation of motion. Finally,the updated acceleration responses are obtained using the limited measurements,and the structural parameters at the next step can be identified by means of RLSE. The effectiveness and robustness of the proposed approach is verified via the numerical example of a simply supported beam model. Numerical results show that the proposed approach can accurately identify the structure parameters and structural states.
System identification using limited outputs is of importance for structural health monitoring. The traditional Kalman filter( KF) cannot be used for parameters identification. The recursive least-squares estimation( RLSE) can be employed for system identification while the complete structural responses are available. Here,based on KF and RLSE,a structural parameter identification method is proposed. Firstly,the structural states including displacement and velocity responses at the next step are estimated by means of KF using limited acceleration measurements. Then,based on these estimated responses and the structural parameters identified at the current step,the acceleration responses at the next step are estimated by the differential equation of motion. Finally,the updated acceleration responses are obtained using the limited measurements,and the structural parameters at the next step can be identified by means of RLSE. The effectiveness and robustness of the proposed approach is verified via the numerical example of a simply supported beam model. Numerical results show that the proposed approach can accurately identify the structure parameters and structural states.
引文
[1]闫桂荣,段忠东,欧进萍.基于结构振动信息的损伤识别研究综述[J].地震工程与工程振动,2007,27(3):95-103.YAN Guirong,DUAN Zhongdong,OU Jinping. Review on structural damage detection based on vibration data[J]. Earthquake Engineering and Engineering Dynamics,2007,27(3):95-103.(in Chinese)
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[15] Xiao M,Zhang Y,Wang Z. An adaptive three-stage extended Kalman filter for nonlinear discrete-time system in presence of unknown inputs[J]. ISA Transactions,2018,75:101-117.
[16]林淋,孙景江.地震动参数与地震烈度的多元回归研究[J].地震工程与工程振动,2011,34(3):33-38.LIN Lin,SUN Jingjiang. Study on model of multiple regression between strong ground motion parameters and seismic intensity[J]. Earthquake Engineering and Engineering Dynamics,2011,34(3):33-38.(in Chinese)
[17] Xu B,He J,Rovekamp R,et al. Structural parameters and dynamic loading identification from incomplete measurements:Approach and validation[J]. Mechanical Systems and Signal Processing,2012,28:244-257.
[18]李世龙,马立元,王天辉,等.一种改进的响应面方法及其在损伤识别中的应用[J].地震工程与工程振动,2014,34(6):145-152.LI Shilong,MA Liyuan,WANG Tianhui,et al. Improved response surface method and its application in damage identification[J]. Earthquake Engineering and Engineering Dynamics,2014,34(6):145-152.(in Chinese)
[19] Xu B,He,J. Data-based model-free hysteretic restoring force and mass identification for dynamic systems[J]. Computer-Aided Civil and Infrastructure Engineering,2015,30(1):2-18.
[20] Yang J N,Pan S,Lin S. Least square estimation with unknown excitations for damage identification of structures[J]. Journal of Engineering Mechanics,2007,133(1):12-21.
[21] Yang J N,Huang H. Sequential non-linear least-square estimation for damage identification of structures with unknown inputs and unknown outputs[J]. International Journal of Non-Linear Mechanics,2007,42(5):789-801.
[22] Huang Q,Xu Y L,Liu H J. An efficient algorithm for simultaneous identification of time-varying structural parameters and unknown excitations of a building structure[J]. Engineering Structures,2015,98:29-37.
[23] Pappalardo C M,Guida D. A time-domain system identification numerical procedure for obtaining linear dynamical models of multibody mechanical systems[J]. Archive of Applied Mechanics,2018,88(8):1325-1347.
[2] Li Y Y,Chen Y. A review on recent development of vibration-based structural robust damage detection[J]. Structural Engineering and Mechanics,2013,45(2):159-168.
[3] Das S,Saha P,Patro S K. Vibration-based damage detection techniques used for health monitoring of structures:a review[J]. Journal of Civil Structural Health Monitoring,2016,6(3):477-507.
[4] Xu Y L,He J. Smart Civil Structures[M]. Boca Raton:CRC Press,2017:333-389.
[5]尚久栓.卡尔曼滤波法在结构动态参数估计中的应用[J].地震工程与工程振动,1991,11(2):62-72.SHANG Jiuquan. Application of Kalman filter method to dynamic parameter estimation of structure[J]. Earthquake Engineering and Engineering Dynamics,1991,11(2):62-72.(in Chinese)
[6] Yang J N,Lin S,Huang H,et al. An adaptive extended Kalman filter for structural damage identification[J]. Structural Control and Health Monitoring,2006,13(4):849-867.
[7]杜飞平,谭永华,陈建华.基于改进广义卡尔曼滤波的结构损伤识别方法[J].地震工程与工程振动,2010,30(4):109-114DU Feiping,TAN Yonghua,CHEN Jianhua. Structural damage identification methods based on improved generalized Kalman filter[J]. Earthquake Engineering and Engineering Dynamics,2010,30(4):109-114.(in Chinese)
[8] Lei Y,Jiang Y Q,Xu Z Q. Structural damage detection with limited input and output measurement signals[J]. Mechanical Systems and Signal Processing,2012,28:229-243.
[9] Liu L,Su Y,Zhu J,et al. Data fusion based EKF-UI for real-time simultaneous identification of structural systems and unknown external inputs[J]. Measurement,2016,88:456-467.
[10] Lai Z L,Lei Y,Zhu S Y,et al. Moving-window extended Kalman filter for structural damage detection with unknown process and measurement noises[J]. Measurement,2016,88:428-440.
[11] Zhang C,Huang J Z,Song G Q,et al. Structural damage identification by extended Kalman filter with l1–norm regularization scheme[J].Structural Control and Health Monitoring,2017,24(11):e1999.
[12] Ebrahimian H,Astroza R,Conte,J P. Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method[J]. Earthquake Engineering and Structural Dynamics,2015,44(10):1495-1522.
[13] Liu J,Lei Y,He M. A two-stage parametric identification of strong nonlinear structural systems with incomplete response measurements[J]. International Journal of Structural Stability and Dynamics,2016,16(4):1640022.
[14] Su H,Yang X,Liu L,et al. Identifying nonlinear characteristics of model-free MR dampers in structures with partial response data[J]. Measurement,2018,130:362-371.
[15] Xiao M,Zhang Y,Wang Z. An adaptive three-stage extended Kalman filter for nonlinear discrete-time system in presence of unknown inputs[J]. ISA Transactions,2018,75:101-117.
[16]林淋,孙景江.地震动参数与地震烈度的多元回归研究[J].地震工程与工程振动,2011,34(3):33-38.LIN Lin,SUN Jingjiang. Study on model of multiple regression between strong ground motion parameters and seismic intensity[J]. Earthquake Engineering and Engineering Dynamics,2011,34(3):33-38.(in Chinese)
[17] Xu B,He J,Rovekamp R,et al. Structural parameters and dynamic loading identification from incomplete measurements:Approach and validation[J]. Mechanical Systems and Signal Processing,2012,28:244-257.
[18]李世龙,马立元,王天辉,等.一种改进的响应面方法及其在损伤识别中的应用[J].地震工程与工程振动,2014,34(6):145-152.LI Shilong,MA Liyuan,WANG Tianhui,et al. Improved response surface method and its application in damage identification[J]. Earthquake Engineering and Engineering Dynamics,2014,34(6):145-152.(in Chinese)
[19] Xu B,He,J. Data-based model-free hysteretic restoring force and mass identification for dynamic systems[J]. Computer-Aided Civil and Infrastructure Engineering,2015,30(1):2-18.
[20] Yang J N,Pan S,Lin S. Least square estimation with unknown excitations for damage identification of structures[J]. Journal of Engineering Mechanics,2007,133(1):12-21.
[21] Yang J N,Huang H. Sequential non-linear least-square estimation for damage identification of structures with unknown inputs and unknown outputs[J]. International Journal of Non-Linear Mechanics,2007,42(5):789-801.
[22] Huang Q,Xu Y L,Liu H J. An efficient algorithm for simultaneous identification of time-varying structural parameters and unknown excitations of a building structure[J]. Engineering Structures,2015,98:29-37.
[23] Pappalardo C M,Guida D. A time-domain system identification numerical procedure for obtaining linear dynamical models of multibody mechanical systems[J]. Archive of Applied Mechanics,2018,88(8):1325-1347.