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

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (20) : 166-171.

论文

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

许鑫1，2，史治宇1，Wieslaw J. Staszewski2, 龙双丽1

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Instantaneous frequencies identification for linear time-varying structures using continuous wavelet transform of free decay acceleration response

XU Xin1, 2, SHI Zhi-yu1, Wieslaw J. Staszewski 2, Long Shuang-li1

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摘要

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.

Abstract

This paper presents a deduction on continuous wavelet transform of an arbitrarily function’s integration. Based on this algorithm, assuming the linear time-varying structural mass coefficients are constants or known in advance, the CWT values of the velocities and displacements response of a linear time-varying structure can be estimated only by using free decay acceleration response. Consequently the time dependent physical parameters (stiffness and damping) at different instance can be determined by solving least square problem from simple linear equations of a short time. Subsequently a five-story shear-beam building model and a three degree-of-freedom structure with closely spaced modes are investigated and their instantaneous frequencies are identified by the proposed method. Numerical results validate the proposed identification method with good accuracy, effectiveness and improved anti-noise capability.

导出引用

许鑫;史治宇;Wieslaw J. Staszewski;龙双丽. 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[J]. 振动与冲击, 2012, 31(20): 166-171

XU Xin;;SHI Zhi-yu;Wieslaw J. Staszewski;Long Shuang-li. Instantaneous frequencies identification for linear time-varying structures using continuous wavelet transform of free decay acceleration response[J]. Journal of Vibration and Shock, 2012, 31(20): 166-171