中国管理科学 ›› 2024, Vol. 32 ›› Issue (3): 299-312.doi: 10.16381/j.cnki.issn1003-207x.2023.0396cstr: 32146.14.j.cnki.issn1003-207x.2023.0396
收稿日期:
2023-03-11
修回日期:
2023-06-21
出版日期:
2024-03-25
发布日期:
2024-03-25
通讯作者:
方兴华
E-mail:xinghuafang@cjlu.edu.cn
基金资助:
Huiwen Lu,Xinghua Fang(),Mingshun Song,Yujia Deng,Jia Huang
Received:
2023-03-11
Revised:
2023-06-21
Online:
2024-03-25
Published:
2024-03-25
Contact:
Xinghua Fang
E-mail:xinghuafang@cjlu.edu.cn
摘要:
连续大规模生产不仅要求企业能更准确高效地识别生产过程状态,还需要识别生产过程中潜在的质量问题,从而提前规避质量风险。现有控制图方法能监测短期内生产过程是否处于异常状态,但难以对长期生产过程潜在的质量问题进行识别和分析。为了突破这一局限,本文提出在过程控制中运用基于相对熵的方法对质量数据分布形态进行识别,通过识别质量异常模式来分析潜在的质量问题。首先,通过仿真生成五种分布模式训练集和测试集;其次,将测试集样本质量特性值的概率分布或经核密度估计拟合后的概率密度作为模型输入;最后,通过构建的相对熵函数来量化抽样样本分布与各典型质量异常模式分布的相似性和差异性,输出生产状态分类指标,并通过两个质量模式判断准则完成模式识别。仿真结果表明,本文提出的方法在质量特性值为离散和连续情况下均能对质量异常分布模式进行有效识别。通过与同类方法进行对比,发现本文方法具有更高的识别精度,可以更有效地监控和识别生产过程的质量异常。
中图分类号:
鲁惠文,方兴华,宋明顺,邓钰佳,黄佳. 基于相对熵的质量异常模式识别研究[J]. 中国管理科学, 2024, 32(3): 299-312.
Huiwen Lu,Xinghua Fang,Mingshun Song,Yujia Deng,Jia Huang. Quality Abnormal Pattern Recognition Based on Relative Entropy[J]. Chinese Journal of Management Science, 2024, 32(3): 299-312.
表1
离散情况下各异常分布模式概率分布"
组号 | 区间 | |||||
---|---|---|---|---|---|---|
1 | (663.65,663.75] | 0.025 | 0.075 | 0.025 | 0.1125 | 0.025 |
2 | (663.75,663.85] | 0.0625 | 0.1 | 0.05 | 0.175 | 0.0375 |
3 | (663.85,663.95] | 0.1125 | 0.1125 | 0.0875 | 0.2125 | 0.05 |
4 | (663.95,664.05] | 0.1875 | 0.1375 | 0.125 | 0.1875 | 0.075 |
5 | (664.05,664.15] | 0.225 | 0.15 | 0.1625 | 0.125 | 0.125 |
6 | (664.15,664.25] | 0.1875 | 0.1375 | 0.1125 | 0.075 | 0.1875 |
7 | (664.25,664.35] | 0.1125 | 0.1125 | 0.1375 | 0.05 | 0.2125 |
8 | (664.35,664.45] | 0.0625 | 0.1 | 0.175 | 0.0375 | 0.175 |
9 | (664.45,664.55] | 0.025 | 0.075 | 0.125 | 0.025 | 0.1125 |
表2
各生产状态下抽样样本概率分布"
组号 | 区间 | 正常型样本 | 平顶型样本 | 双峰型样本 | 偏左峰型样本 | 偏右峰型样本 |
---|---|---|---|---|---|---|
1 | (663.65,663.75] | 0.025 | 0.0875 | 0.025 | 0.1 | 0.025 |
2 | (663.75,663.85] | 0.05 | 0.1 | 0.0375 | 0.1625 | 0.0375 |
3 | (663.85,663.95] | 0.125 | 0.1125 | 0.0875 | 0.225 | 0.05 |
4 | (663.95,664.05] | 0.175 | 0.125 | 0.125 | 0.175 | 0.075 |
5 | (664.05,664.15] | 0.225 | 0.15 | 0.225 | 0.1375 | 0.1125 |
6 | (664.15,664.25] | 0.175 | 0.125 | 0.15 | 0.0875 | 0.2 |
7 | (664.25,664.35] | 0.125 | 0.1125 | 0.1 | 0.05 | 0.225 |
8 | (664.35,664.45] | 0.0625 | 0.1 | 0.2 | 0.0375 | 0.1625 |
9 | (664.45,664.55] | 0.0375 | 0.0875 | 0.05 | 0.025 | 0.1125 |
表4
连续情况下本文方法质量异常模式识别结果(前三组数据)"
实际 生产状态 | 组别 | 各异常分布模式下参考概率密度函数 | |||||
---|---|---|---|---|---|---|---|
正常型 | 1 | 0.1471 | 3.0491 | 0.5426 | 0.7555 | 0.5717 | |
2 | 0.0676 | 3.5682 | 0.4536 | 0.9082 | 0.6138 | ||
3 | 0.6173 | 3.2701 | 0.8085 | 1.9990 | 0.3854 | ||
平顶型 | 1 | 10.9016 | 0.4409 | 8.1541 | 5.9751 | 4.5511 | |
2 | 6.9010 | 0.1209 | 4.9365 | 3.9987 | 3.2251 | ||
3 | 6.9487 | 0.1534 | 5.4575 | 4.0236 | 2.5367 | ||
双峰型 | 1 | 12.8379 | 4.4870 | 0.0592 | 2.5017 | 2.2468 | |
2 | 12.5993 | 4.2614 | 0.0616 | 2.5801 | 2.1333 | ||
3 | 15.2103 | 4.3650 | 0.1749 | 2.7952 | 2.8101 | ||
偏左峰型 | 1 | 1.1832 | 3.6800 | 1.2999 | 0.5131 | 2.1266 | |
2 | 1.3484 | 3.8035 | 1.4694 | 0.6042 | 2.3609 | ||
3 | 0.9237 | 4.6595 | 1.1970 | 0.4783 | 2.0006 | ||
偏右峰型 | 1 | 0.9931 | 2.3243 | 1.3585 | 2.1843 | 0.3822 | |
2 | 1.2937 | 2.3823 | 1.1193 | 2.6115 | 0.4612 | ||
3 | 0.7496 | 4.3715 | 0.9244 | 2.6061 | 0.3126 |
表6
离散情况下各对比方法的质量异常模式识别结果"
典型实际生产状态 | 对比方法 | ||||||
---|---|---|---|---|---|---|---|
正常型 | 相关系数 | 0.9899 | 0.9710 | 0.4943 | 0.2696 | 0.3411 | |
余弦相似度 | 0.9970 | 0.9462 | 0.8884 | 0.8090 | 0.8276 | ||
欧式距离 | 0.0306 | 0.1287 | 0.1794 | 0.2398 | 0.2278 | ||
平顶型 | 相关系数 | 0.9742 | 0.9687 | 0.4873 | 0.2921 | 0.2921 | |
余弦相似度 | 0.9215 | 0.9974 | 0.9408 | 0.8750 | 0.8750 | ||
欧式距离 | 0.1551 | 0.0250 | 0.1225 | 0.1871 | 0.1871 | ||
双峰型 | 相关系数 | 0.6885 | 0.7208 | 0.8289 | -0.1686 | 0.5839 | |
余弦相似度 | 0.9144 | 0.9188 | 0.9559 | 0.6962 | 0.8918 | ||
欧式距离 | 0.1620 | 0.1541 | 0.1146 | 0.3021 | 0.1803 | ||
偏左峰型 | 相关系数 | 0.3826 | 0.4019 | -0.3754 | 0.9877 | -0.6469 | |
余弦相似度 | 0.8337 | 0.8876 | 0.7241 | 0.9969 | 0.5807 | ||
欧式距离 | 0.2250 | 0.1777 | 0.2784 | 0.0306 | 0.3536 | ||
偏右峰型 | 相关系数 | 0.2955 | 0.3125 | 0.6811 | -0.6993 | 0.9929 | |
余弦相似度 | 0.8041 | 0.8684 | 0.9244 | 0.5518 | 0.9980 | ||
欧式距离 | 0.2456 | 0.1936 | 0.1490 | 0.3678 | 0.0250 |
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