《AR与Prony法的时变系统模态参数识别》

本文研究基于AR和Prony法的线性时变振动系统的模态参数识别。在经典Prony法的基础上，提出了可以处理非平稳信号的时变Prony法。采用递推最小二乘算法估计模型参数，并讨论了基函数的选择，其中以时间多项式基、离散长球面基以及离散余弦基下所识别的效果较好。为验证本文方法的有效性，进行了数字仿真和附加质量随时间连续变化的悬臂梁的模态分析试验，试验结果和理论结果比较表明了本文提出的线性时变系统的模态参数识别方法有效、可行。

Modal Parameter Identification of a Time-Varying System by Autoregressive Modelling and Prony Analysis

Modal parameter identification of a time-variant linear vibration system by autoregressive modeling and Prony analysis is studied in this paper. Based on the classical Prony analysis, an improved method to process nonstationary signals is presented. The recursive least squares is adopted to estimate model parameters, and the choice of the basis functions are discussed. It shows that some basis functions such as time polynomial, discrete long spherical and discrete cosine are more suitable to modal parameter identification than other ones. To validate the proposed method, digital simulation and a test of a cantilever beam with an adjustable mass are completed. The comparison between identification results and theoretical results indicates that the proposed method is effective and feasible to identify modal parameters of time-variant linear system.