工程振动信号微积分敏感性及其应用研究

工程施工监测中常常需要监测振动速度信号或振动加速度信号，振动速度信号和振动加速度信号的频谱特性差别很大，进而影响后续分析.本文采用傅立叶变换的时域微积分性来分析工程振动信号频谱的微积分敏感性，并通过拉普拉斯变换求取结构振动傅立叶谱，自功率谱，频响函数，并分析它们微积分敏感性.通过频响函数分析了其微分敏感性的物理意义.通过对背景工程中高层建筑实测自然激励的振动信号，验证了频谱微积分敏感性，并分析了频谱微积分敏感性对于振动信号分析的影响.研究结果表明：工程振动信号在数学上由于傅立叶变换的时域微积分性质，使得傅立叶谱峰值的频率分布具有微积分敏感性，随着振动信号微分阶次的升高，高频成分逐渐升高，低频成分逐渐降低；由不同信号的频响函数表达式，对结构动刚度、阻抗、动质量的频率分布规律进行了阐述；不同监测信号对于高、低频成分的识别精度不同，对于结构物高、阶模态的识别精度亦不同，对于高阶的频率成分的识别建议进行振动加速度信号监测，对于低阶频率的识别建议采用振动速度信号监测.

Differential Sensitivity of Engineering Vibration Signal and its Application

In engineering construction monitoring, it is often necessary to monitor the vibration velocity signal or vibration acceleration signal. The spectrum characteristics of vibration velocity signal and vibration acceleration signal are very different, which will affect the subsequent analysis. In this paper, the time-domain calculus of Fourier transform is adopted to analyze the sensitivity of the spectrum of engineering vibration signal. The Fourier spectrum, self-power spectrum and frequency response function of structural vibration are obtained by Laplace transform, and their sensitivity is analyzed. The physical significance of its differential sensitivity is analyzed by frequency response function. The vibration signal of measured natural excitation in middle and high buildings in the background engineering is verified, and the influence of the sensitivity of spectrum calculus on the vibration signal analysis is analyzed. The results show that:In terms of mathematics, the frequency distribution of the peak of Fourier spectrum is sensitive to calculus due to the time-domain calculus nature of Fourier transform. With the increase of the differential order of vibration signal, the high-frequency component increases gradually and the low-frequency component decreases gradually;The frequency distribution of dynamic stiffness, impedance and dynamic mass of the structure is described by the frequency response function expression of different signals;Different monitoring signals have different recognition accuracy for high and low frequency components, as well as high order modal recognition accuracy for structures. Vibration acceleration signal monitoring is recommended for identification of high order frequency components, and vibration velocity signal monitoring is recommended for identification of low order frequency.