非平稳Gauss环境激励下模态参数识别的新方法

A New Modal Identification Method Under the Non-Stationary Gaussian Ambient Excitation

结合多元连续时间自回归模型,针对受均匀调制Gauss随机激励的线性时不变系统,提出了一种时域模态识别的新方法.该方法仅从响应数据就能够识别系统的物理参数.首先把结构动力学方程转化为一个3阶的连续时间自回归模型;接着基于在非常短的时间段内均匀调制函数接近于一个常数矩阵以及随机微分方程强解的性质,得到均匀调制函数的估计,并针对两种特殊情况进行讨论;然后利用Girsanov定理,对条件似然函数进行极大化,得到物理参数的精确极大似然估计.数值结果表明,该估计不仅具有极高的精度和稳健性,而且计算效率非常高.

Based on the multivariate continuous time autoregressive model, a new time-domain modal identification method of LTI system driven by the uniformly modulated Gaussian random excitation was presented. The method can identify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into the continuous time autoregressive model of order 3. Second, based on the assumption that the uniformly modulated function is approximately equal to a constant matrix in a very short time period and the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise, and two special situations are discussed too. Finally, by virtue of the Girsanov theorem, a likelihood function was introduced, which is just a conditional density function. Maximizing the likelihood function gives the exact maximum likelihood estimators of model parameters. Numerical results show that the method has high precision and computing efficiency.