用于线性时变系统辨识的固定长度平移窗投影估计递推子空间方法
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摘要
给出了一个新的用于线性时变参数结构系统模态参数识别的基于固定长度平移窗投影估计的递推子空间方法。首先推得基于平移窗投影估计的子空间跟踪算法,以代替奇异值分解,再推得系统数据矩阵的一阶修正形式,从而得到新的基于平移窗投影估计的递推子空间方法。该方法可有效地降低算法的计算量。最后通过刚度随时间变化的3自由度系统和一具有移动质量的机械臂系统的时变模态频率辨识仿真表明该方法可有效地辨识线性时变系统的伪模态参数。
A novel recursive subspace method is developed based on fixed length moving window (FLMW) projection approximation used for estimating the modal parameter of linear time-varying structural system. The projection approximation subspace tracking (PAST) method with FLMW is developed to replace a singular value decomposition in order to decrease the computational complexity. A 3 degree-of-freedom model with time-varying stiffness and a manipulator with moving mass are used to testify these two methods. The simulation results show that these two methods can avoid the influence of the old data efficiently, and the novel recursive method can estimate the parameter of linear time-varying system as efficiently as the recursive subspace method with FLMW, with the computational complexity decreasing at the same time.
A novel recursive subspace method is developed based on fixed length moving window (FLMW) projection approximation used for estimating the modal parameter of linear time-varying structural system. The projection approximation subspace tracking (PAST) method with FLMW is developed to replace a singular value decomposition in order to decrease the computational complexity. A 3 degree-of-freedom model with time-varying stiffness and a manipulator with moving mass are used to testify these two methods. The simulation results show that these two methods can avoid the influence of the old data efficiently, and the novel recursive method can estimate the parameter of linear time-varying system as efficiently as the recursive subspace method with FLMW, with the computational complexity decreasing at the same time.
引文
1 邹经湘,于开平,杨炳渊．时变结构的参数识别方法．力 学进展,2000,30(3):370-377
2 赵永辉,于开平,邹经湘．利用输出误差时间序列模 型识别结构时变模态参数．航空学报,2001,22(3): 277-280
3 续秀忠,张志谊,华宏星,等．应用时变参数建模方法 辨识时变模态参数．航空学报,2003,24(3):230-233
4 续秀忠,张志谊,华宏星,等．结构时变模态参数辨识 的时频分析方法．上海交通大学学报,2003,37(1): 122-126
5 吴日强,于开平,邹经湘．改进的子空间方法及其在 时变结构参数辨识中的应用．工程力学,2002,19(4): 67-70
6 于开平,谢礼立,樊久铭,等．移动质量-简支梁系统的 参数辨识．地震工程与工程振动,2002,22(5):14-17
7 全亚斌,张卫东,蔡云泽,等．基于双边迭代奇异值分 解的递推子空间辨识方法．上海交通大学学报,2002, 36(4):563-569
8 Tasker F, Bosse A, Fisher S. Real-time modal parameter estimation using subspace methods: theory. Mechanical Systems and Signal Processing, 1998, 12(6): 797-808
9 Lovera M, Gustafsson T, Verheagen M. Recursive subspace identification of linear and nonlinear wiener state-space models. Automatica, 2000,36(11): 1 639-1 650
10 Yang B.Projection approximation subspace tracking. IEEE Transactions on Signal Processing, 1995, 43( 1): 95-107
11 Liu K. Extension of modal analysis to linear time-varying systems. Journal of Sound and Vibration, 1999, 226(1): 149-167
2 赵永辉,于开平,邹经湘．利用输出误差时间序列模 型识别结构时变模态参数．航空学报,2001,22(3): 277-280
3 续秀忠,张志谊,华宏星,等．应用时变参数建模方法 辨识时变模态参数．航空学报,2003,24(3):230-233
4 续秀忠,张志谊,华宏星,等．结构时变模态参数辨识 的时频分析方法．上海交通大学学报,2003,37(1): 122-126
5 吴日强,于开平,邹经湘．改进的子空间方法及其在 时变结构参数辨识中的应用．工程力学,2002,19(4): 67-70
6 于开平,谢礼立,樊久铭,等．移动质量-简支梁系统的 参数辨识．地震工程与工程振动,2002,22(5):14-17
7 全亚斌,张卫东,蔡云泽,等．基于双边迭代奇异值分 解的递推子空间辨识方法．上海交通大学学报,2002, 36(4):563-569
8 Tasker F, Bosse A, Fisher S. Real-time modal parameter estimation using subspace methods: theory. Mechanical Systems and Signal Processing, 1998, 12(6): 797-808
9 Lovera M, Gustafsson T, Verheagen M. Recursive subspace identification of linear and nonlinear wiener state-space models. Automatica, 2000,36(11): 1 639-1 650
10 Yang B.Projection approximation subspace tracking. IEEE Transactions on Signal Processing, 1995, 43( 1): 95-107
11 Liu K. Extension of modal analysis to linear time-varying systems. Journal of Sound and Vibration, 1999, 226(1): 149-167
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