基于加速度响应连续小波变换的线性时变结构瞬时频率识别

Instantaneous frequencies identification of a linear time-varying structure using continuous wavelet transformation of free decay acceleration response

推导了函数积分运算的连续小波变换计算方法。借助此法,假设线性时变结构的质量系数为时不变常数,或者其随时间变化的规律已被经验掌握,仅利用线性时变结构自由振动的加速度响应信号,就可以计算出速度响应和位移响应信号的连续小波变换值。将一小段时刻点的线性代数方程组构造成最小二乘问题,求解最小二乘解识别出结构的时变阻尼和时变刚度,从而确定时变结构的瞬时频率。通过对5层剪切梁楼房模型和3自由度密集模态时变结构瞬时频率的识别,验证了识别方法的正确性、有效性和抗噪声能力。

A deduction of continuous wavelet transformation（CWT） of an arbitrary function＇s integration was presented.Based on this algorithm,assuming a linear time-varying structure＇s mass coefficients are constants or known in advance,the CWT values of the velocities and displacements responses of a linear time-varying structure were estimated only by using its free decay acceleration response.Consequently,the time-dependent physical parameters（stiffness and damping） at different instance could be determined by solving a least square problem from a group of linear algebraic equations of a short time.Subsequently,a five-story shear-beam building model and a 3-DOF structure with closely spaced modes were investigated and their instantaneous frequencies were identified with the proposed method.Numerical results showed that the proposed identification method has good accuracy and effectiveness,and an improved anti-noise capability.