A Method of Dimension Reduction of Rotor Faults Data Set Based on Fusion of Global and Local Discriminant Information
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摘要: 针对传统的数据降维方法无法兼顾保持全局特征信息与局部判别信息的问题，提出一种核主元分析（Kernel principal component analysis，KPCA）和正交化局部敏感判别分析（Orthogonal locality sensitive discriminant analysis，OLSDA）相结合的转子故障数据集降维方法.该方法首先利用KPCA算法有效降低数据集的相关性、消除冗余属性，由此实现了最大程度地保留原始数据全局非线性信息的作用；然后利用OLSDA算法充分挖掘出数据的局部流形结构信息，达到了提取出具有高判别力低维本质特征的目的.上述方法的特点是通过同时进行的正交化处理可避免局部子空间结构发生失真，采用三维图直观显示出低维结果，以低维特征子集输入最近邻分类器（K-nearest neighbor，KNN）的识别率和聚类分析之类间距Sb、类内距Sw作为衡量降维效果的指标.实验表明该方法能够全面地提取出全局与局部判别信息，使故障分类更清晰，相应地识别准确率得到了明显提升.该研究可为解决高维和非线性机械故障数据集的可视化与分类问题，提供理论参考依据.
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关键词:
- 故障诊断 /
- 数据可视化 /
- 数据降维 /
- 核主元分析 /
- 正交化局部敏感判别分析
Abstract: Aimed at the problem that traditional dimension reduction methods cannot juggle global feature information and local discriminant information, a method of dimension reduction of the rotor fault dataset based on kernel principal component analysis (KPCA) and orthogonal locality sensitive discriminant analysis (OLSDA) is proposed. Firstly, the KPCA algorithm can reduce the correlation and redundant attributes of datasets and retain maximized original data information of global nonlinearity. Then, the OLSDA algorithm is used to fully excavate local manifold structure information of the data so as to extract the low-dimension essential feature with high discrimination. The method avoids distortion of local subspace structure by using a simultaneous orthogonalization process, and shows low dimensional results intuitively with 3-dimensional figure. Finally, the indexes to measure the dimension reduction effect are the recognition rate at which low-dimensional feature subset is input into KNN (K-nearest neighbor), the between-class scatter Sb and within-class scatter Sw of clustering analysis. Rotor experiment shows that this method can comprehensively extract global and local discriminant information, which makes classification of faults more clear and corresponding recognition accuracy rate significantly improved. This study provides a theoretical base for solving the visualization and classification problem of high-dimensional and nonlinear mechanical fault dataset.1) 本文责任编委 胡昌华 -
图 1 融合全局与局部判别信息的故障数据集降维方法
Fig. 1 The method of dimension reduction of fault data set of the integrated global and local discriminant information
图 2 测试样本基于不同方法的降维结果
Fig. 2 The results of test sample based on different methods of dimension reduction
图 3 各类降维方法的测试样本类间距、类内距及其比值
Fig. 3 The test samples' between-class scatter, within-class scatter and their ratio of all kinds of dimension reduction methods
图 4 不同训练样本数对应的平均识别准确率
Fig. 4 The average recognition accuracy based on the different number of training samples
图 5 不同随机噪声干扰下的6种算法的平均识别准确率
Fig. 5 The average recognition accuracy of six kinds of algorithms under different random noise interference
表 1 各通道故障特征参数
Table 1 Fault characteristic parameters of each channel
序号 特征名称 序号 特征名称 1 均方幅值 10 裕度指标 2 方根幅值 11 频率均值 3 平均幅值 12 频率中心 4 最大值 13 标准差频率 5 峰峰值 14 峭度频率 6 峭度 15 均方根频率 7 波形指标 16 ~ 23 前4层IMF分量 8 峰值指标 的能量特征及对应 9 脉冲指标 的4层复杂度特征 
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表 2 各降维方法的识别准确率 (%)
Table 2 Methods of dimension reduction of recognition accuracy (%)
故障类型 各降维方法的故障诊断准确率 A1 A2 A3 A4 A5 A6 松动 1 0.667 1 1 1 1 碰磨 1 0.8 0.833 1 0.967 1 不对中 0.72 0.933 1 1 1 1 不平衡 0.62 1 0.867 0.8 1 1 识别准确率 0.835 0.85 0.925 0.95 0.992 1
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表 3 算法的时间复杂度
Table 3 Time complexity of all the algorithms
降维算法 时间复杂度 PCA $O(d^3)+{\rm O}(nd)$ KPCA ${\rm O}(d^3)+{\rm O}(nd)+{\rm O}(d^3)$ OLSDA ${\rm O}(dn \log n)+{\rm O}(n^2)+{\rm O}(pn^2)$ PCA-KOLSDA ${\rm O}(d^3)+{\rm O}(nd)+{\rm O}(dn \log n)+{\rm O}(n^2)+{\rm O}(pn^2)$ KPCA-OLPP ${\rm O}(d^3)+{\rm O}(nd)+{\rm O}(d^3)+ {\rm O}(dn \log n)+{\rm O}(n^2)$ KPCA-LSDA ${\rm O}(d^3)+{\rm O}(nd)+{\rm O}(d^3)+ {\rm O}(dn \log n)+{\rm O}(n^2)$ KPCA-OLSDA ${\rm O}(d^3)+{\rm O}(nd)+{\rm O}(d^3)+ {\rm O}(dn \log n)+{\rm O}(n^2)$
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表 4 算法的特征提取时间 (s)
Table 4 Feature extraction time (s) for algorithms
降维数目 A1 A2 A3 A4 A5 A6 3 0.210 1.300 0.527 5.306 3.323 3.541 10 0.848 1.132 0.366 4.715 3.350 3.441 20 0.939 1.136 0.448 4.767 3.443 3.371 40 0.947 1.168 0.380 5.667 3.801 3.407 60 0.704 1.312 0.388 5.632 3.564 3.331 80 0.654 1.236 0.381 6.013 3.708 3.430
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