利用加速度响应连续小波变换的时变系统物理参数识别

摘要

基于小波理论,推导了函数积分运算的连续小波变换计算方法,应用此方法仅用线性时变结构的振动加速度响应信号,就可计算出速度和位移响应信号的连续小波变换值,并将振动微分方程组转换成用小波表示的线性方程组,求解不同时刻的线性代数方程组识别出时变结构的物理参数(质量、刚度和阻尼).以5自由度时变结构为仿真算例,利用添加噪声的采集信号,识别了突变、线性变化和周期变化3种不同类型的时变物理参数,算例验证了识别方法的正确性、有效性和抗噪声能力.最后还研究了多尺度分析对参数识别的影响,给出了尺度参数区间选取和离散的依据.%Based on wavelet theory, continuous wavelet transform algorithm of a function's integration is deduced in this paper. The CWT values of velocity and displacement response signals can be estimated via the above algorithm and by which only the acceleration response of a linear time-varying system is used, and the vibration differential equations can be transformed into linear equations with wavelet expression. Therefore the physical parameters (mass, stiffness and damping) of an arbitrarily time-varying system can be directly determined by solving the linear equations at each moment. Subsequently, a 5 degrees-of-freedom time-varying model is simulated. With three different kinds of time-varying cases (abruptly, smoothly and periodically) , systemic physical parameters are identified by the proposed identification method using the data with noise. The accuracy, effectiveness and the anti-noise ability of the proposed method are validated by the numerical results. At last, the influence of the resolution analysis to the identification results and how to choose the scale parameters are studied.