Bearing Fault Recognition and Classification Method based on EWT and Multiscale Fuzzy Entropy and VPMCD
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摘要: 针对振动信号提取轴承故障特征及识别分类的研究方式，提出了一种结合EWT-多尺度模糊熵-VPMCD的方法。首先，运用经验小波变换提取振动信号的模态分量。其次，引入信息论中的模糊熵算法，并加以多尺度粗粒度划分得到多尺度模糊熵特征描述。然后，用VPMCD对特征向量进行自适应选择预测模型训练。最终通过实验表明：模态分量多尺度模糊熵能够有效描述故障特征；VPMCD在少训练样本情况下获得了最低90%的分类准确率，相较一些常用的分类方法有着更好的性能表现。Abstract: Aiming at the research methods of extracting bearing fault characteristics, identifying and classifying vibration signals, a new method combining EWT、multi-scale fuzzy entropy and VPMCD algorithms is proposed in the thesis. Firstly, the modal components of the vibration signal are extracted by the empirical wavelet transform (EWT). Secondly, the fuzzy entropy algorithm in information theory is introduced, and multi-scale coarse-grained partitioning method is used to obtain the multi-scale fuzzy entropy feature description. Then, VPMCD algorithm is used to train the model by adaptively selecting prediction model. The experiments show that multi-scale fuzzy entropy of modal components can effectively describe the fault features. VPMCD achieves a minimum classification accuracy of 90% with a small number of training samples, which has better performance than some common classification methods.
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Key words:
- vibration signals /
- fault characteristics /
- EWT /
- multi-scale fuzzy entropy /
- VPMCD
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表 1 模型表达式
模型 预测特征值${f_i}$表达式 QI ${f_i} = {b_0} + \displaystyle \sum\limits_{j = 1}^{p - 1} {b_j^{(1)}{f_n}} + \displaystyle \sum\limits_{t = 1}^{p - 1} {b_j^{(2)}f_{{n_t}}^2 + }$${\displaystyle \sum\limits_{l = 1}^{p - 2} {\displaystyle \sum\limits_{t = l + 1}^{p - 1} {{b_{tl}}{f_{{n_t}}}} } } {f_{{n_l}}}\quad n,{n_t},{n_l} \ne i,n,{n_t},{n_l} \in [1,p] $ Q ${f_i} = {b_0} + \displaystyle \sum\limits_{j = 1}^{p - 1} {b_j^{(1)}{f_n}} + \displaystyle \sum\limits_{t = 1}^{p - 1} {b_j^{(2)}f_{{n_t}}^2} \quad n,{n_t} \ne i,n,{n_t} \in [1,p] $ LI ${f_i} = {b_0} + \displaystyle \sum\limits_{j = 1}^{p - 1} {{b_j}{f_n}} + \displaystyle \sum\limits_{l = 1}^{p - 2} {\displaystyle \sum\limits_{t = l + 1}^{p - 1} {{b_{tl}}{f_{{n_t}}}{f_{{n_l}}}} } \quad n,{n_t},{n_l} \ne i,n,{n_t},{n_l} \in [1,p] $ L ${f_i} = {b_0} + \displaystyle \sum\limits_{j = 1}^{p - 1} {{b_j}{f_n}} \quad n \ne i,n \in [1,p]$ 
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表 2 不同故障的模态分量模糊熵示例
故障
类型IMF1
模糊熵IMF2
模糊熵IMF3
模糊熵IMF4
模糊熵IMF5
模糊熵正常 0.249 0.273 0.248 0.223 0.077 滚子故障 0.126 0.307 0.212 0.185 0.133 内圈故障 0.171 0.283 0.240 0.215 0.174 外圈故障 0.257 0.268 0.295 0.166 0.157
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表 3 内圈故障VPM系数及模型类别
系数（列） 模态分量（行） IMF1 IMF2 IMF3 IMF4 IMF5 $ {C}_{1} $ 0.649 0.200 1.413 −1.570 −0.383 $ {C}_{2} $ 0.363 2.732 12.820 −8.682 −1.238 $ {C}_{3} $ −0.460 −1.585 −8.048 0.576 −1.801 $ {C}_{4} $ 1.721 −0.790 3.207 −6.847 −5.942 $ {C}_{5} $ −0.701 1.237 −1.481 11.351 6.232 $ {C}_{6} $ 0.612 −0.754 4.852 −4.391 0.651 $ {C}_{7} $ 0.228 0.050 −6.364 2.894 0.107 $ {C}_{8} $ 5.891 4.123 −11.020 0.899 2.815 $ {C}_{9} $ −4.092 −0.056 1.278 1.683 −0.510 $ {C}_{10} $ 0.227 3.931 −1.977 −18.970 −2.766 $ {C}_{11} $ −3.874 −1.733 1.922 2.281 8.196 $ {C}_{12} $ 5.367 1.090 25.518 31.895 3.525 $ {C}_{13} $ 1.485 2.157 9.924 −6.138 −7.819 $ {C}_{14} $ −0.923 −7.421 −6.590 −23.886 −6.006 $ {C}_{15} $ 0.771 −0.567 6.054 −1.610 1.795 模型类别 QI QI QI QI QI
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表 4 输出结果示例
特征向量(列) 样本类型（行） 正常
样本滚子故障
样本内圈故障
样本外圈故障
样本正常 0.0253 1.5615 1.2281 0.5184 滚子故障 0.2736 0.0045 0.1846 0.4627 内圈故障 1.0799 0.2244 0.0221 0.1114 外圈故障 0.2029 0.0101 0.1063 0.0329 输出结果 正常 滚子故障 内圈故障 外圈故障 分类结果 正确 正确 正确 正确
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