基于扩展卡尔曼滤波的结构参数和荷载识别研究
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摘要
经典的扩展卡尔曼滤波(Extend Kalman Filter,EKF)方法可有效识别结构参数,但却需要已知外部激励,然而,在工程实际中,有些外激励往往难以实时获取。为此,该文提出了一种基于EKF的未知激励下的结构参数和荷载识别方法。通过在观测方程中引入投影矩阵,实现了结构参数的识别,同时,利用最小二乘估计实时识别了未知的外激励。为了验证该方法的有效性和鲁棒性,文中采用了三个数值算例:四层的Benchmark模型、分段线性系统和非线性Duffing系统。数值分析的结果表明,该方法不仅能够准确识别线性和非线性结构的参数,还能有效识别作用于这些结构的外激励。
The classical extended Kalman filter(EKF) method is capable of accurately identifying structural parameters with known external excitations. However, in some practical situations, the excitations are difficult or impossible to measure. A time-domain approach based on EKF is proposed in this paper for the simultaneous identification of structural parameters and unknown inputs. A projection matrix is introduced in the observation equation, based on which the structural parameters are identified. The unknown inputs are determined by means of least squares estimation using the estimated parameters. The effectiveness and robustness of the proposed approach is verified through three numerical examples including a four-story benchmark model, a piecewise linear structure and a Duffing hysteretic structure. The numerical results show that the proposed approach can not only accurately identify the parameters of linear and nonlinear structures, but also satisfactorily estimate the unknown external excitations.
The classical extended Kalman filter(EKF) method is capable of accurately identifying structural parameters with known external excitations. However, in some practical situations, the excitations are difficult or impossible to measure. A time-domain approach based on EKF is proposed in this paper for the simultaneous identification of structural parameters and unknown inputs. A projection matrix is introduced in the observation equation, based on which the structural parameters are identified. The unknown inputs are determined by means of least squares estimation using the estimated parameters. The effectiveness and robustness of the proposed approach is verified through three numerical examples including a four-story benchmark model, a piecewise linear structure and a Duffing hysteretic structure. The numerical results show that the proposed approach can not only accurately identify the parameters of linear and nonlinear structures, but also satisfactorily estimate the unknown external excitations.
引文
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[2]李惠,鲍跃全,李顺龙,等.结构健康监测数据科学与工程[J].工程力学,2015,32(8):1―7.Li Hui,Bao Yuequan,Li Shunlong,et al.Data science and engineering for structural health monitoring[J].Engineering Mechanics,2015,32(8):1―7.(in Chinese)
[3]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.
[4]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)
[5]Yang J N,Huang H,Lin S.Sequential nonlinear least square estimation for damage identification of structures[J].International Journal of Non-Linear Mechanics,2006,41(1):124―140.
[6]Wu M,Smyth A W.Application of the unscented Kalman filter for real-time nonlinear structural system identification[J].Structural Control and Health Monitoring,2007,14(7):971―990.
[7]Lei Y,Chen F,Zhou H.An algorithm based on two-step Kalman filter for intelligent structural damage detection[J].Structural Control and Health Monitoring,2015,22(4):694―706.
[8]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,2017,38(8):76―84.(in Chinese)
[9]Jin C,Jang S,Sun X.An integrated real-time structural damage detection method based on extended Kalman filter and dynamic statistical process control[J].Advances in Structural Engineering,2017,20(4):549―563.
[10]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):1―17.
[11]Lei Y,Xia D D,Chen F,et al.Synthesis of cross-correlation functions of partial responses and the extended Kalman filter approach for structural damage detection under ambient excitations[J].International Journal of Structural Stability and Dynamics,2018,18(8):1―20.
[12]Lei Y,Jiang Y,Xu Z.Structural damage detection with limited input and output measurement signals[J].Mechanical Systems and Signal Processing,2012,28:229―243.
[13]Yang J N,Pan S W,Huang H W.An adaptive extended kalman filter for structural damage identification II:Unknown inputs[J].Structural Control and Health Monitoring,2007,14(3):497―521.
[14]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].Measurement2016,88:456―467.
[15]雷鹰,毛亦可.部分观测下基于子结构的大型结构损伤诊断法[J].工程力学,2012,29(7):180―185.Lei Ying,Mao Yike.A damage detection algorithm based on substructures for large size structures under limited measurements[J].Engineering Mechanics,2012,29(7):180―185.(in Chinese)
[16]任鹏,周智,白石,等.桁架结构疲劳监测的应变响应估计方法研究[J].工程力学,2018,35(9):114―125.Ren Peng,Zhou Zhi,Bai Shi,et al.Research on a strain response estimation method for truss structure fatigue monitoring[J].Engineering Mechanics,2018,35(9):114―125.(in Chinese)
[17]Ni P,Xia Y,Li J,et al.Improved decentralized structural identification with output-only measurements[J].Measurement,2018,122:597―610.
[18]Johnson E A,Lam H F,Katafygiotis L S,et al.The phase I IASC-ASCE structural health monitoring benchmark problem using simulated data[J].Journal of Engineering Mechanics(ASCE),2004,130(1):3―15.