基于二次调频小波变换的时变系统物理参数识别

Physical Parameter Identification of Time-varying Systems Based on Quadratic Chirplet Transform

基于二次调频小波理论,提出函数积分运算的二次调频小波变换计算方法。应用此方法,仅利用时变结构的加速度响应信号就可以重构出速度和位移响应信号并将振动微分方程转换为线性方程。为解决随机激励下参数识别问题,进一步结合分数阶模糊函数推导二次调频信号的自相关性理论,得出相关系数与时变物理参数的线性表达式进而识别各时刻的物理参数。以一个4自由度时变结构为仿真算例,识别线性变化、周期变化、二次函数变化、快速突变4种不同类型的时变物理参数,验证了识别方法的正确性。

Based on the theory of quadratic chirplet,a method of the quadratic chirplet transform with function integral operation is proposed,by which,the acceleration response signal of the time-varying structure is merely used to reconstruct the speed and displacement response signal and to transform vibration differential equation into linear one.To solve the problem of parameter identification under random excitation,by further combining with the fractional ambiguity,the autocorrelation theory of the quadratic frequency modulation signal is derived to abtain the linear expression of correlation coefficient and time-varying physical parameters,so as to identify the physical parameters of each time.With a 4-iDOF time-varying structure as a simulation example,four different types of time-varying physical parameters such as linear change,periodic change,quadratic function change and rapid mutation are identified,which verifies the correctness of the identification method.