辛几何模态分解方法及其分解能力研究  

Symplectic geometry mode decomposition method and its decomposition ability

作　　者：程正阳 王荣吉[1] 潘海洋[2] CHENG Zhengyang;WANG Rongji;PAN Haiyang(College of Mechanical and Electrical Engineering,Central South University of Forestry and Technology,Changsha 410004,China;College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410082,China)

机构地区：[1]中南林业科技大学机电工程学院,长沙410004 [2]湖南大学机械与运载工程学院,长沙410082

出　　处：《振动与冲击》2020年第13期27-35,共9页Journal of Vibration and Shock

基　　金：国家重点研发计划项目(2016YFF0203400);国家自然科学基金(51575168,51875183)。

摘　　要：针对经验模态分解(Empirical Mode Decomposition,EMD)、集合经验模态分解(Ensemble Empirical Mode Decomposition,EEMD)、局部特征尺度分解(Local Characteristic scale Decomposition,LCD)等方法的不足,提出了一种新的分析方法--辛几何模态分解(Symplectic Geometry Mode Decomposition,SGMD)方法,该方法采用辛矩阵相似变换求解Hamilton矩阵的特征值,并利用其对应的特征向量重构辛几何分量(Symplectic Geometry Component,SGC),从而对复杂信号去噪的同时进行自适应分解,得到若干个SGC。通过仿真信号模型,研究了SGMD方法的分解性能、噪声鲁棒性,分析了分量信号的频率比、幅值比和初相位差对SGMD方法分解能力的影响。将SGMD方法应用于齿轮故障实验数据分析,结果表明SGMD方法能够有效地对待分解信号完成分解并剔除噪声信号。Aiming at shortcomings of the empirical mode decomposition(EMD),the ensemble empirical mode decomposition(EEMD)and the local characteristic scale decomposition(LCD),a new analysis method called the symplectic geometry mode decomposition(SGMD)was proposed here.Firstly,the symplectic matrix similarity transformation was used to solve eigenvalues of a Hamiltonian matrix and the corresponding eigenvectors were used to reconstruct symplectic geometry components(SGCs).So,a complicated signal was de-noised and meanwhile adaptively decomposed into some SGCs.Then,using a simulation signal model,the decomposition performance and noise robustness of SGMD method were studied.Effects of frequency ratio,amplitude ratio,and initial phase difference of the components on decomposition ability of SGMD were analyzed.Finally,the proposed method was applied in gear fault test data analysis.The results showed that SGMD method can effectively decompose signals to be decomposed and eliminate noise signals.

关 键 词：辛几何模态分解(SGMD) 辛矩阵相似变换 辛几何分量(SGC) 分解能力 

分 类 号：TH113[机械工程—机械设计及理论]