基于边界判别多流形分析的故障数据集降维方法  

Dimension reduction method of fault data set based on BDMA

作　　者：常书源 赵荣珍[1] 陈博[1] 何天经[1] 石明宽 CHANG Shuyuan;ZHAO Rongzhen;CHEN Bo;HE Tianjing;SHI Mingkuan(School of Mechanical and Electronical Engineering,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学机电工程学院,兰州730050

出　　处：《振动与冲击》2021年第23期120-126,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(51675253);兰州理工大学红柳一流学科建设项目。

摘　　要：针对现有多流形学习方法未考虑流形间边界信息而导致降维后数据不易于分类的问题,提出一种新的边界判别多流形分析(margin discriminant multi-manifold analysis,MDMA)方法。该方法同时考虑数据的类内相似性、类间差异性、同类流形结构和异类流形结构,并且为避免降维过程中出现小样本问题,在构造目标函数时将这4点归结为指数化迹商优化结构。通过两个转子系统试验数据集进行验证。结果表明,与其他几种典型降维方法对比,该方法能更有效地提取出蕴含在数据中的判别信息,在故障辨识中表现出更好的分类性能。Here,aiming at the problem of existing multi-manifold learning methods without considering information of boundary between manifolds to make data after dimension reduction difficult to classify,a new boundary margin discriminant multi-manifold analysis(MDMA)method was proposed.It was shown that MDMA simultaneously considers intra-class similarity,inter-class difference,homogeneous manifold structure and heterogeneous manifold structure of data.In order to avoid the small sample problem in process of dimension reduction,these four points were summarized as the exponential trace quotient optimization structure when constructing an objective function.This new method was verified with test data set of 2 rotor systems.The results showed that compared with several other typical dimension reduction methods,the proposed method can more effectively extract the discrimination information contained in data;it can have better classification performance in fault recognition.

关 键 词：故障诊断 维数约简 小样本问题 边界判别多流形分析(MDMA) 

分 类 号：TH165.3[机械工程—机械制造及自动化] TP18[自动化与计算机技术—控制理论与控制工程]