Research on Fault Diagnosis of Improved Kernel Fisher Based on Mahalanobis Distance in the Field of Chemical Industry
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摘要: 针对化工故障诊断数据存在非线性分布、 数据类别复杂、数据量大且故障特征不易区分等问题, 本文提出一种基于马氏距离的改进核Fisher故障诊断方法(Mahalanobis distance-based kernel Fisher discrimination, MKFD). 首先, 针对数据非线性分布的特点, 本文将核Fisher判别分析算法改进, 改进后的算法可以有效解决原始样本在投影后出现的因类间距离差异过大、类内距离不够紧凑造成的样本混叠现象. 除此之外, 利用Euclidean距离对类间距做加权处理时, 用组平均距离取代质心距离, 提升了运算效率, 降低了时间复杂度; 其次, 根据高斯径向基核函数(Radial basis function, RBF)在MKFD中所呈现出的诊断精度的规律, 本文采用一种新的核参数选择方法: 区间三分法, 用以取代在实际应用中依靠经验的交叉验证法; 最后, 本文采用马氏距离对故障进行分类, 基于田纳西伊—斯特曼过程(Tennessee-Eastman, TE)数据将本方法与其他改进核Fisher算法进行仿真验证对比. 结果表明新提出MKFD算法不仅可以提高故障诊断的运算效率, 也能有效提高诊断的精度.Abstract: Aiming at the problems of the non-linear distribution, complex category, large amount of fault diagnosis data in chemical industry and the difficulty of distinguishing fault features, a improved kernel Fisher fault diagnosis method based on Mahalanobis distance is proposed in this paper. Firstly, due to the data with non-linear property, a new improved kernel Fisher discriminant analysis method is proposed, which can effectively solve the sample aliasing phenomenon caused by large difference between classes and insufficient compact distance between classes after projection of original samples. In addition, using the Euclidean distance in class spacing, the group average distance is used to replace the center of mass distance, which improves the efficiency of operation and reduces the time complexity. Secondly, according to the rule of diagnostic accuracy presented by the (RBF) in Fisher discriminant analysis (MKFD), a new method, interval “three-point method”, of selecting nuclear parameters is proposed in this paper, which is used to replace the cross-validation method relying on experience in practical application. Finally, faults are classified based on Mahalanobis distance using Tennessee-Sterman process. The proposed method is compared with other improved kernel Fisher algorithm. The results show that (MKFD) can not only improve the calculation efficiency of fault diagnosis, but also improve the accuracy of diagnosis.
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Key words:
- Kernel Fisher /
- fault diagnosis /
- interval three-point method /
- Tennessee-Sterman process /
- optimization
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图 3 故障诊断准确率与核参数取值折线图
Fig. 3 Line diagram of the fault diagnosis accuracy and kernel parameter
图 4 故障诊断准确率与核参数取值折线图
Fig. 4 Line diagram of the fault diagnosis accuracy and kernel parameter
表 1 故障类型描述
Table 1 Description of the selected fault sample sets
Fault Number Fault description Fault type 3 物料 D 的温度的异变 阶跃 4 反应器冷却水入口温度的异变 阶跃 5 泠凝器冷却水入口温度的异变 阶跃 7 物料 C 压力下降 阶跃 
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表 2 选取不同核参数σ下故障诊断的准确率 (KFD)
Table 2 The fault diagnosis accuracy based on different kernel parameter σ(KFD)
The value of the parameter σ Test accuracy (%) The value of the parameter σ Test accuracy (%) 0.1 25 30 81.25 0.2 30.31 40 80.94 0.8 50 70 53.13 2 66.88 90 51.56 4 75.63 100 45 8 78.44 160 43.75 10 79.38 180 33.44
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表 3 利用区间三分法求解最优核参数σ对应的故障诊断的准确率 (KFD)
Table 3 The accuracy of fault diagnosis of optimal kernel parameter by using the interval three-part method (KFD)
迭代次数 对应区间 三分点 1 三分点 2 三分点 3 三分点 4 ${X_1}$ $D({X_1})$ ${X_2}$ $D({X_2})$ ${X_3}$ $D({X_3})$ ${X_3}$ $D({X_4})$ 1 [1, 100] 1 50 % 34 79 % 67 51 % 100 45 % 2 [1, 67] 1 50 % 23 80 % 45 73.8 % 67 51 % 3 [1, 45] 1 50 % 15.7 79.4 % 30.3 81.25 % 45 73.8 % 4 [15.7, 45] 15.7 79.4 % 25.5 80 % 35.2 78.8 % 45 73.8 % 5 [15.7, 35.2] 15.7 79.4 % 22.2 80.3 % 28.7 80.4 % 35.2 78.8 % 6 [22.2, 35.2] 22.2 80.3 % 26.5 80 % 30.9 81.25 % 35.2 78.8 %
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表 4 KFD算法和MKFD算法中不同核参数的故障诊断结果
Table 4 The fault diagnosis with different kernel parameters in KFD algorithm and MKFD algorithm
The value of the
parameter σ in KFDTrain
accuracy (%)Test
accuracy (%)The value of the
parameter σ in MKFDTrain
accuracy (%)Test
accuracy (%)0.1 100 25 0.1 100 25 1 100 50 1 100 50 10 99.8 79.4 4 100 76.9 30 99.8 81.3 8 100 99.69 60 70.5 44.7 12 99.9 92.5 90 27.7 25.3 16 99.9 80.6
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表 5 选取不同核参数σ下故障诊断的准确率(按照区间三分法做纵向表)
Table 5 The fault diagnosis accuracy based on different kernel parameters σ (Make the longitudinal table according to the interval three-part method)
Ionosphere Breast cancer The value of the parameter σ Test accuracy (%) The value of the parameter σ Test accuracy (%) 1 78.9 1 31.7 34 91.6 149 95.1 49 92 223 94.9 56 92.4 248 95.4 59 92.8 297 95.4 63 92.8 334 95.4 67 92.4 346 95.4 68 92 445 94.6 78 90.8 667 94 100 86.1 1000 93.2
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表 6 区间三分法迭代求解最优核参数σ (MKFD)
Table 6 The iterative solution of the optimal kernel parameters σ using interval partition method
迭代次数 对应区间 三分点 1 三分点 2 三分点 3 三分点 4 ${X_1}$ $D({X_1})$ ${X_2}$ $D({X_2})$ ${X_3}$ $D({X_3})$ ${X_3}$ $D({X_4})$ 1 [1, 100] 1 50.9 % 34 60.6 % 67 57.5 % 100 58.1 % 2 [1, 67] 1 50.9 % 23 76.6 % 45 58.1 % 67 57.5 % 3 [1, 45] 1 50 % 15.7 96.3 % 30.3 63.8 % 45 58.1 % 4 [1, 30.3] 1 50 % 10.8 99.69 % 20.5 84.69 % 30.3 63.8 % 5 [1, 20.5] 1 50 % 7.5 99.38 % 14 97.81 % 20.5 84.69 % 6 [1, 14] 1 50 % 5.3 81.56 % 9.7 99.69 % 14 97.81 %
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表 7 交叉验证法选取不同核参数σ下故障诊断的准确率(FDGLPP)
Table 7 The fault diagnosis accuracy based on different kernel parameters σ by cross validation method
The value of the
parameter σTest
accuracy (%)The value of the
parameter σTest
accuracy (%)The value of the
parameter σTest
accuracy (%)0.1 25 0.5 68.13 3 55.31 1 52.19 5 75.31 6 79.38 50 28.44 25 25.0 9 99.69 100 41.25 50 28.44 12 25.0 500 39.06 75 34.69 15 55.94 1000 38.75 95 40.0 18 25.0
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表 8 四种模型的故障诊断结果与运行时间
Table 8 Fault diagnosis results and running time of the four models
Model Optimal value of parameter σ Test accuracy (%) Test time (s) KFD 30 81.25 3.90072 CKFD 8 97.81 4.14769 FDGLPP 10 99.69 9.30612 MKFD 9 99.69 3.86806
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