频响函数曲线拟合与模态分析精细化  

Refinement of FRFs curve fitting and modal analysis

作　　者：董磊[1] 宋汉文[2] 郑铁生[1] 

机构地区：[1]复旦大学力学与工程科学系,上海200433 [2]同济大学航空航天与力学学院,上海200092

出　　处：《振动与冲击》2016年第2期69-75,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(11272235)

摘　　要：由于Vector Fitting(VF)将有理分式函数直接分解为部分分式和的叠加,极点(模态频率)获取顺序依模态贡献量由大到小排列,可保证拟合误差随拟合阶次增大迅速收敛,故对VF方法用于模态参数辨识的可行性进行论证,优化拟合精度与计算规模,并对曲线拟合算法误差、参数稳定性、模型定阶详细讨论,实现频响函数曲线拟合的精细化。利用已有文献数据进行考核,并与商业算法比较。In conventional orthogonal polynomial algorithms which are most widely used in modal analysis, the best model order is usually defined with the consideration of the existence of the noise modes. Unfortunately, the minimum error could not be well achieved simultaneously. Considering the numerical instability and the computation difficulty due to the increase of model order, the demand of dividing the frequency range into several sub-bands comes up. The vector fitting （VF） algorithm was introduced to decompose the rational function by taking common set of partial fractions as basis functions, and the acquisition order of the modes was arranged according to the modal energy, to ensure the fast convergence of VF algorithm. Then, the parametric stability of the partial fractions and the numerical stability can be attained with the increase of the model order. In the paper, a brief review of VF was presented and the feasibility of VF in modal analysis was demonstrated. The refinement of the FRFs curve fitting was completed through a fine disposal of deviation analysis, parametric stability and order selection. An aerospace case study was carried out to verify the effectiveness of the algorithm and the results were compared with those by another algorithm.

关 键 词：模态分析 参数辨识 频率响应函数 曲线拟合 精细化 

分 类 号：O321[理学—一般力学与力学基础] O327[理学—力学]