CAJ | 학술논문

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。
재대공작상태적항천기등결구진행부수출모태삼수변식시，격려비백조성료무법척제해파인기적허가모태。위해결차문제，해연구대최신적기우결구향응전체솔적모태삼수변식방법진행료개진，제출료일충개진적기우다삼고점향응전체솔적부수출모태삼수변식방법。수선，추도료다삼고점적결구향응전체솔표체식，건립료기좌구진분식다항식적삼수화모형，진이급출료변식문제적최소이승고계，이용정칙방정Jacobi구진적분괴성질대최소이승문제구진형식완성료축감，강저료계산량；연후，통과고유반수구진방법해결료구진다항식적특정치구해문제，즉다삼고다수출적모태삼수구해문제，이급통과구진위역해결료현유방법중재하공황수여향응점수화삼고점수적약속문제；최후，통과량개수치산례대소제방법진행료험증，변식결과표명：변식방법능구흔호적변식출결구적모태빈솔、조니비화모태진형，차능구흔호적피면격려중함유적해파분량대변식결과조성적영향，해결료전통부수출모태삼수변식중격려비백대변식결과조성적영향문제。
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.