高维空间可分性指标在转子诊断系统优化中的应用

摘要/Abstract

摘要： 二叉树相关向量机系统中正负类样本的选取往往通过方差进行可分性度量。常用的高斯核函数是在高维空间中完成分类，由于高维空间中数据点存在度量集中现象，欧氏距离往往并不能较好地度量样本点的可分性。分数范数计算出的高维空间距离差异性更大，故构造了一种基于分数范数的样本点距离度量指标。基于该指标优化各层分类器样本选取，通过实验1验证了基于高维可分性指标优化后的系统相较于欧氏距离优化后的系统在分类精度上有了较为显著的提高；实验2表明优化后的系统与智能诊断算法相比，在分类精度和耗时方面也具有优势。

关键词: 高斯核空间, 度量集中, 分数范数, 系统优化

Abstract: The selection of positive and negative samples in the related vector machine multi-fault classification system based on binary tree was often measured by the Euclidean distance. Traditional Euclidean distance couldn't reflect the separability of sample points properly because of the measurement concentration of data points in high-dimensional spaces. As the differences of high-dimensional space distance calculated by fractional norm were greater, an index of high-dimensional space sample point distances was proposed based on fractional norm. Optimizing sample selection of classifiers at different levels based on this index, the results of experiment 1 prove that the optimized system based on high-dimensional space separability index has a significant improvement in classification accuracy than the optimized system based on Euclidean distance. The results of experiment 2 show that compared with intelligent diagnosis algorithm, the normal binary tree structure has advantages in classification efficiency and time consuming.

Key words: Gauss kernel space, measurement concentration, fractional norm, system optimization

中图分类号:

TM41

徐搏超. 高维空间可分性指标在转子诊断系统优化中的应用[J]. 中国机械工程.

XU Bochao. Applications of Separability Index of High-dimensional Space in Rotor Diagnosis System Optimization[J]. China Mechanical Engineering.

参考文献

[1]张龙, 张磊, 熊国良,等. 二叉树型多分类器融合的轴承故障诊断方法[J]. 计算机工程与应用, 2015, 51(21):243-249.
ZHANG Long, ZHANG Lei, XIONG Guoliang, et al. Method of Binary Tree Structure Based Multiple Classifier Fusion in Bearing Fault Diagnosis[J]. Computer Engineering and Application, 2015, 51(21):243-249.
[2]LIU Xiaofeng, BO Lin. Identification of Resonance States of Rotor-bearing System Using RQA and Optimal Binary Tree SVM[J]. Neurocomputering, 2015, 152:36-44.
[3]陈星, 严华. 二叉树SVM算法在小样本故障诊断中的优化[J]. 计算机测量与控制, 2015, 23(3):689-692.
CHEN Xing, YAN Hua. Optimization of BT-SVM for Small Sample Fault Diagnosis[J]. Computer Measurement & Control,2015, 23(3):689-692.
[4]曹苏群, 王士同, 陈晓峰. 基于后验概率的不平衡数据集特征选择算法[J]. 计算机工程, 2008, 34(19):1-3.
CAO Suqun,WANG Shitong, CHEN Xiaofeng. Posterior-probability-based Feature Selection Algorithm for Imbalanced Datasets[J]. Computer Engineering, 2008, 34(19):1-3.
[5]袁广林, 薛模根, 韩裕生,等. 基于自适应多特征融合的mean shift目标跟踪[J]. 计算机研究与发展, 2010, 47(9):1663-1671.
YUAN Guanglin, XUE Mogen, HAN Yusheng, et al. Mean Shift Object Tracking Based on Adaptive Multi-features Fusion[J]. Journal of Computer Research and Development, 2010, 47(9):1663-1671.
[6]张秋余, 赵付清, 王静,等. C-SVM在不同类别样本数目不均衡下的优化[J]. 兰州理工大学学报, 2007, 33(4):90-92.
ZHANG Qiuyu, ZHAO Fuqing, WANG Jing, et al. Optimization of C-SVM in Case of Samples with Unequal Numbers in Their Different Varieties[J]. Journal of Lanzhou University of Technology, 2007, 33(4):90-92.
[7]刘涌, 李海潮, 赵鞭. 一种基于二叉树的测控设备故障诊断方法[J]. 电讯技术, 2016, 56(8):928-933.
LIU Yong, LI Haichao, ZHAO Bian. A Fault Diagnosis Method for TT&C Equipment Based on Binary Tree[J]. Telecommunication Engineering, 2016, 56(8):928-933.
[8]冯育强, 董佳华. 无穷维空间中有界闭凸集的一个反例[J]. 高师理科学刊, 2017, 37(2):4-5.
FENG Yuqiang, DONG Jiahua. A Counterexample of Bounded Closed Convex Set in Infinite Dimensional Space[J]. Journal of Science of Teachers' College and University, 2017, 37(2):4-5.
[9]DURRANT R J. When Is ‘Nearest Neighbour' Meaningful: a Converse Theorem and Implications[J]. Journal of Complexity, 2009, 25(4):385-397.
[10]MIL'MAN V D. New Proof of the Theorem of A. Dvoretzky on Intersection of Convex Bodies[J]. Function Analysis and Its Application, 1971,5(4):288-295.
[11]FRANOIS D, WERTZ V, VERLEYSEN M. Non-Euclidean Metrics for Similarity Search in Noisy Datasets[C]//The 13th European Symposium on Artificial Neural Networks. Bruges, 2005: 339-344.
[12]HSU C M, CHEN M S. On the Design and Applicability of Distance Functions in High-dimensional Data Space[J]. IEEE Transactions on Knowledge & Data Engineering, 2009, 21(4):523-536.
[13]HINNEBURG A, AGGARWAL C C, KEIM D A. What Is the Nearest Neighbor in High Dimensional Spaces?[C]//The 26th VLDB Conference. Cario, 2000:506-515.
[14]AGGARWAL C C, HINNEBURG A，KEIM D A. On the Surprising Behavior of Distance Metrics in High Dimensional Spaces[C]//The 8th International Conference on Database Theory. London, 2001:420-434.
[15]赵莹. 支持向量机中高斯核函数的研究[D]. 上海：华东师范大学, 2007.
ZHAO Ying. The Study on Gauss Kernel Function in Support Vector Machine[D]. Shanghai: East China Normal University, 2007.
[16]李状, 柳亦兵, 滕伟,等. 基于粒子群优化KFCM的风电齿轮箱故障诊断[J]. 振动、测试与诊断, 2017, 37(3):484-488.
LI Zhuang，LIU Yibing，TENG Wei，et al. Fault Diagnosis of Wind Turbine Gearbox Based on KFCM Optimized by Particle Swarm Optimization[J]. Journal of Vibration Measurement & Diagnosis, 2017, 37(3):484-488.
[17]郑波, 高峰. 基于S-PSO分类算法的故障诊断方法[J]. 航空学报, 2015, 36(11):3640-3651.
ZHENG Bo, GAO Feng. Fault Diagnosis Method Based on S-PSO Classification Algorithm[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(11):3640-3651.