#### 期刊菜单

Process Control of Mixed Data Based on Support Vector Machine
DOI: 10.12677/DSC.2022.111001, PDF, HTML, XML, 下载: 307  浏览: 898  国家自然科学基金支持

Abstract: Recently, as manufacturing system is becoming increasingly automated and intelligent, the data obtained from manufacturing system also presents the characteristics of diversified data sources, large data volumes, and mixed data types. In this paper, it is discussed on process control and diagnoses of mixed data in order to handle both measurable data and attribute data simultaneously. Support Vector Machine (SVM) is applied to realize the process control and diagnosis for multivariate mixed data when the process mean out of control. From multivariate normal data to mixed data, the accuracy of SVM is studied from the viewpoints of the shift, subgroup size, and the change of correlations to make comparison among four different kernels, and then C-SVM and M-SVM are provided to monitor the process in control or not and identify which parameter(s) to be out of control. Furthermore, compared SVM with Hotelling’s multivariate control chart, it is concluded that SVM has excellent performance on monitoring the process in control or not when it is applied to mixed data.

1. 引言

2. 基于SVM的计量数据的过程控制与诊断

2.1. 基于二分类SVM的过程控制

Table 1. Determination of 2-dimensional normal data

$n=10$$\rho =0.3$ 时均值偏移量变化的分析结果如表2所示。对比四种核函数的结果可见，Sigmoid核函数与线性核函数表现不佳，而且均使用了几乎所有的数据作为支持向量；多项式核函数和RBF核函数的准确率则较高，其中多项式使用的支持向量个数更少。使用同一种核函数时，对比不同均值偏移量的分析结果可见，异常样本的均值偏移量越大，SVM准确率越高。

Table 2. Results of 2-dimensional normal data when the shift of process mean is changed ( n = 10 , ρ = 0.3 )

$n=10$ 、均值偏移量 $\Delta \mu$ 为1个标准差时相关系数变化的分析结果如表3所示。对比四种核函数的结果可见，不论变量间的相关关系是正相关还是负相关、是强相关还是弱相关，Sigmoid核函数与线性核函数都表现不佳，而且均使用了几乎所有的数据作为支持向量。对于表现较好的多项式核函数和RBF核函数，则变量间相关性越强，SVM准确率越高；正相关还是负相关的影响不大。

Table 3. Results of 2-dimensional normal data when the correlation is changed ( n = 10 , Δ μ : 1σ)

$\rho =0.3$，均值偏移量 $\Delta \mu$ 为1个标准差时子组大小变化的分析结果如表4所示。对比四种核函数的结果可见，不论子组大小n为5、10、20，Sigmoid核函数与线性核函数都表现不佳，而且均使用了几乎所有的数据作为支持向量。对于表现较好的多项式核函数和RBF核函数，则随着子组大小的减少，SVM准确率会降低，所需的支持向量数增加。

Table 4. Results of 2-dimensional normal data when the subgroup size is changed ( ρ = 0.3 , Δ μ : 1σ)

2.2. 基于多分类M-SVM的过程诊断

Table 5. Results of diagnosis based on M-SVM when the shift of process mean is changed ( ρ = 0.3 , n = 10 )

3. 基于SVM的混杂数据的过程控制与诊断

3.1. 基于二分类SVM的混杂数据的过程控制

Table 6. Determination of 3-dimensional mixed data

$\mu =0,p=0.2,\lambda =3$。本文期望对正态近似效果较差的混杂数据进行研究，故数据的分布参数以及子组大小的选定尽量远离正态近似的条件，n取10。

${R}_{1}=\left[\begin{array}{ccc}1& 0.3& 0.3\\ 0.3& 1& 0.3\\ 0.3& 0.3& 1\end{array}\right],{R}_{2}=\left[\begin{array}{ccc}1& 0.7& 0.7\\ 0.7& 1& 0.7\\ 0.7& 0.7& 1\end{array}\right]$

m取1000。共生成14000个子组，其中：受控子组和失控子组各7000组。基于二分类SVM的混杂数据分析结果如表7所示。

Table 7. Results of C-SVM for mixed data

3.2. 基于多分类M-SVM的混杂数据的过程诊断

Table 8. The accuracy of diagnosis based on M-SVM for mixed data

4. 与Hotelling多元控制图的性能对比

4.1. 性能对比的设计

$Accuracy\left(0\right)=1-\alpha =1-1/\text{ARL}\left(0\right)$ (1)

$Accuracy\left(1\right)=1-\beta =1/\text{ARL}\left(1\right)$ (2)

4.2. 正态数据的控制性能对比

Table 9. Comparison of process control performance for normal data ( ρ = 0.7 , n = 10 , Δ μ : 1σ)

4.3. 混杂数据的控制性能对比

Table 10. Comparison of process control performance for mixed data (correlation matrix: R 2 )

5. 结论

1) 相比于线性核函数和Sigmoid核函数，利用基于多项式polynomial核函数和径向基RBF核函数的支持向量机进行控制，均有较高的准确率。子组大小越大、变量间相关性越强以及均值偏移量越大，则准确率越高。

2) 对比二分类SVM的准确率与多分类M-SVM的总准确率可见，二分类SVM优于M-SVM。故而，当需要在受控状态与失控状态之间进行控制时，二分类SVM的控制方法更为有效；当需要进一步对不同的失控状态进行诊断时，建议使用基于M-SVM的诊断。在利用M-SVM进行诊断时，对核函数的考虑需要特别审慎，建议同时尝试多项式polynomial核函数和径向基RBF核函数。

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