基于小波方法的时变动力系统参数识别

Parameter Identification of Linear Time-Varying Dynamical System Based on Wavelet Method

针对离散时变动力学系统,运用Daubechies小波对其激励和系统响应信号作小波变换,将变换后的响应和激励代入微分方程,利用Daubechies小波尺度函数的正交性,将微分方程转换成简单的代数方程组,求解方程组,从而识别出时变系统的物理参数。推导了单自由度和多自由度线性时变系统的参数识别方程,介绍了小波系数的计算方法,阐述了系统时变参数的识别思路。通过对系统参数连续、周期和突变3种时变情况进行仿真研究,证明了方法的正确性和有效性。

An algorithm to identify the physical parameters of a linear time-varying(LTV) dynamical system is developed.First,the excitation and response signals of the system were decomposed using the Daubechies wavelet scaling function.Then,the differential equations of motion of the system were reduced to simple linear algebra equations based on the orthogonality of the scaling functions,from which the physical parameters can be directly identified.The parameter identification equations for both single-degree-of-freedom and multi-degree-of-freedom LTV systems are derived and the approach to compute the wavelet coefficients was also introduced.Numerical results demonstrate the validity of the method for the identification of smoothly,periodically and abruptly time-varying parameters.