Application of the recursive identification in linear regression model
Wang Jian-hong 1 Zhu Yong-hong1 Xiao Xuan1 Tang De-zhi 2
1 School of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen, 333403, China2 College of Automation Engineer, Nanjing university of Aeronautics and Astronautics, Nanjing Jiangsu, 210016, China.
Abstract：Abstract: Because the discrete difference equation can be adapted into a linear regression model about some structural modal parameters in vibration response of mechanical system. When identifying these structural modal parameters in this linear regression model, we can convey this problem to an identification estimation problem about some unknown parameter vector in system identification theory. When the system is excited by some white noise, the common least square identification method can give the unbiased values of the unknown parameters. But when the same system is excited by the other colored noise, we propose a new separable iterative least square identification method based on the common least square identification method. When considering the lack of any statistical information about the excited noise, based on the assumption of the unknown-but-bound noise we propose a least square method with dead zero. This new method not only give the consisted unbiased estimation values, but also guarantee that the iterative estimation values will approach the true values. The approximation degree of any two adjacent estimation is less than the upper bound of the noise. In the circumstance of the colored noise emerge, the new approach’s robustness can be strengthened by introducing some dead zeros in the parameter revised equations. Finally, the efficiency and possibility of the proposed strategy can be confirmed by a simulation example in theory and a vibration response in spring-mass-damp system.
2012, Vol. 31 
