有理分式正交多项式频响函数模态参数识别

 讨论一种多输入的频域模态参数识别方法。该方法将频响函数表示为具有矩阵系数的有理分式,利用Forsythe 正交多项式减少方程的病态并解耦系统矩阵,随后运用特征值与奇异值分解求解系统的极点与留数。使用欧洲国家航空界广泛使用的GARTEUR 飞机模型进行仿真计算。结果表明:该方法在30 %噪声下仍具有对严重耦合模态的识别能力;振型识别较为准确;适当提高分母阶次能取得更好的识别结果。

Modal Identification with Frequency Response Function Based on Rational Fraction Orthogonal Polynomials

This paper discusses a multiple input modal identification method in the freque ncy domain. The frequency response function (FRF) is expressed as a rational fra ction formulation with matrix coefficients. The Forsytihe orthogonal polynomial is exploited to reduce the ill conditioning of the equations and to decouple th e system matrix. Taking use of the eigenvalue decomposition and singular value d ecomposition, the poles and residues of the system are solved. An aircraft model called GARTEUR, which is widely used in European aerospace community, is taken to test this algorithm. It was proved that this method is good for heavily coupl ed modes even polluted by high noise levels (up to 30%). Good modal identificati on results are obtained, which can be further improved while higher order of the denominator polynomials is used.