线性回归模型中的递推辨识及其应用

摘要：因机械系统振动响应离散差分方程可以改写为关于结构模态参数的线性回归形式，对于此线性回归形式中的结构模态参数的辨识问题可转化为系统辨识理论中线性回归模型的未知参数矢量的辨识估计问题。当系统对象在白噪声激励下，常规的最小二乘辨识法可以给出参数估计的无偏估计。当系统对象在有色噪声作用下，在常规最小二乘辨识法的基础上提出一种新的可分离迭代最小二乘辨识法。在缺乏关于噪声的统计先验信息，仅有噪声为未知但有界的情况下，提出一种带死区的最小二乘辨识法，该辨识法不仅能给出未知参数矢量的一致性无偏估计，而且还能保证参数估计值逐渐向真值靠拢，任何相邻两估计值之间的逼近程度远远小于噪声的上界。在有界噪声出现的情况下，该算法的鲁棒性可以通过在参数修正方程中引入死区的方法来增强。最后用理论上的仿真算例和弹簧-质量-阻尼系统的振动响应来验证两方法的有效性和可行性。

Application of recursive approach in parameters identification of linear regression model

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.