基于子结构的参数化模型降阶方法  

A component-based parametric model order reduction method

作　　者：刘营 李鸿光[1] 李韵[1] 杜环宇 LIU Ying;LI Hongguang;LI Yun;DU Huanyu(Institute of Vibration,Shock and Noise,State Key Laboratory of Mechanical System and Vibration,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学机械系统与振动国家重点实验室振动、冲击、噪声研究所,上海200240

出　　处：《振动与冲击》2020年第16期148-154,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(11427801)。

摘　　要：针对参数化模型降阶方法在多维参数维度的情况下面临采样点过多、离线构建降阶模型数据库时间长等问题,提出了一种基于子结构的参数化模型降阶方法。在固定界面模态综合法的基础上,设置标准模态矩阵,利用不同参数主模态矩阵之间的Frobenius范数最小准则确定了转换矩阵,推导了子结构降阶矩阵各元素的变换公式,对其进行坐标转换;对参数空间上的采样点重复整个计算过程生成了坐标兼容的离线数据库。并以电磁振动台动圈为例,采用该方法对均布采样样本点展开了仿真研究。结果表明,此方法能大幅减少采样点的个数及模型生成与计算时间,提高降阶模型离线训练效率;所构建的参数化降阶模型具备很高的在线计算效率及计算准确度。A parametric model order reduction(PMOR)method may suffer from the curse of dimensionality in the case of multi-dimensional parameter domains,for which the number of samples required to cover the parameter domain increases exponentially with the dimension.Thus a component-based PMOR method was proposed in this paper.Based on the fixed interface component modal synthesis method,the transformation matrices were deduced according to the minimum Frobenius norm criteria between different normal modes.Then the reduced substructure matrices of discrete distributed sample parameter points were all transformed to the compatible coordinate to establish offline database.The proposed method was subsequently applied to the moving coil of electrical-dynamic shakers.The proposed method was used to perform simulation for the uniformly distributed sample points.The results show that the proposed method can significantly reduce the sample points'number and improve calculation efficiency.The resulting parametric reduced model possesses high online calculation efficiency and accuracy.

关 键 词：参数化模型降阶(PMOR) 模态综合法 电磁振动台 动圈 

分 类 号：O327[理学—一般力学与力学基础] O39[理学—力学]