基于响应传递率的非白随机激励仅输出结构模态参数辨识

Output-only structural modal parameter estimation under non-white excitations based on response transmissibility

在对工作状态的航天器等结构进行仅输出模态参数辨识时,激励非白造成了无法剔除谐波引起的虚假模态。为解决此问题,该研究对最新的基于结构响应传递率的模态参数辨识方法进行了改进,提出了一种改进的基于多参考点响应传递率的仅输出模态参数辨识方法。首先,推导了多参考点的结构响应传递率表达式,建立了其左矩阵分式多项式的参数化模型,进而给出了辨识问题的最小二乘估计,利用正则方程Jacobi矩阵的分块性质对最小二乘问题矩阵形式完成了缩减,降低了计算量;然后,通过高维伴随矩阵方法解决了矩阵多项式的特征值求解问题,即多参考多输出的模态参数求解问题,以及通过矩阵伪逆解决了现有方法中载荷工况数与响应点数和参考点数的约束问题;最后,通过两个数值算例对所提方法进行了验证,辨识结果表明:辨识方法能够很好的辨识出结构的模态频率、阻尼比和模态振型,且能够很好的避免激励中含有的谐波分量对辨识结果造成的影响,解决了传统仅输出模态参数辨识中激励非白对辨识结果造成的影响问题。

In cases of output-only modal parameter estimation for operational engineering structures,such as aerospace structures,the non-white excitations lead to non-physical modes being not able to be identified. For these cases,the recently developed response transmissibility-based methods of modal parameter estimation were studied and an improved poly-reference response transmissibility-based output-only approach of modal parameter estimation was proposed.Firstly,the parametric model of the poly-reference response transmissibility was introduced,it was presented by the left matrix fraction polynomials,the formulations of the least square estimation for unknown parameters were proposed,and the normal equation of the least square estimation was reduced by using the block property of the corresponding Jacobian matrix,it largely decreases the computational costs. Secondly,based on the high-dimensional accompany matrix method,the eigenvalue problem of the matrix polynomials was solved,it led to the solution to the modal parameters. In addition,the original constraints between the number of loading conditions and the number of references were removed by using the pseudo inverse of matrix. Finally,two numerical examples validated the proposed method. The results illustrated that the proposed method can be used to estimate the modal parameters very well and has the advantage of avoiding the influence of harmonics,so the problem due to non-white excitations is solved.