您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (1): 27-34.doi: 10.6040/j.issn.1671-9352.0.2023.035

•   • 上一篇    下一篇

基于非负CP分解的图像数据监控方法

范金宇1,2(),邹杨1,2,熊健3,古勇毅1,2,*()   

  1. 1. 广东财经大学统计与数学学院, 广东 广州 510320
    2. 广东财经大学大数据与教育统计实验室, 广东 广州 510320
    3. 广州大学经济与统计学院, 广东 广州 510320
  • 收稿日期:2023-01-13 出版日期:2024-01-20 发布日期:2024-01-19
  • 通讯作者: 古勇毅 E-mail:jinyufan@gdufe.edu.cn;gdguyongyi@163.com
  • 作者简介:范金宇(1988—), 女, 讲师, 博士, 研究方向为统计过程控制、高维数据分析, E-mail: jinyufan@gdufe.edu.cn
  • 基金资助:
    国家自然科学基金面上资助项目(12271111);广州市科技计划项目(202102020419);全国统计科学研究项目(2021LY014)

Imagedata control chart based on nonnegative CP tensor decomposition

Jin-yu FAN1,2(),Yang ZOU1,2,Jian XIONG3,Yongyi GU1,2,*()   

  1. 1. School of Statistics and Mathematics, Guangdong University of Finance & Economics, Guangzhou 510320, Guangdong, China
    2. Big data and Educational Statistical Application Laboratory, Guangdong University of Finance & Economics, Guangzhou 510320, Guangdong, China
    3. School of Economics and Statistics, Guangzhou University, Guangzhou 510320, Guangdong, China
  • Received:2023-01-13 Online:2024-01-20 Published:2024-01-19
  • Contact: Yongyi GU E-mail:jinyufan@gdufe.edu.cn;gdguyongyi@163.com

RichHTML

2

PDF (PC)

200

摘要：

非负张量分解不仅能有效提取图像数据特征, 而且不破坏图像数据的内部结构。因此, 本文基于非负CANDECOMP/PARAFAC(CP)分解建立无需额外参数设置和调优的图像数据控制图, 并基于仿真模拟分析该控制图在不同偏移情形下的监控性能。仿真结果显示, 该控制图对图像的位置偏移、面积变化、形状变化和颜色变化都能做出快速预警。为了比较所建立的控制图的性能优劣, 通过一个实际的工业生产中的无纺布图像, 基于相同的参数设置, 将所提出的非负CP分解控制图与广义似然比(generalized likelihood ratio, GLR)时空控制图、区域增长的指数加权移动平均(exponentially weighted moving average, EWMA)时空控制图和基于实时对比(real time contrasts, RTC)控制图进行比较。模拟结果显示, 当偏移量大于2的时候, 非负CP分解控制图的检测性能媲美现有的检测方法; 当偏移量不超过2时, 非负CP分解控制图能更快速地检测出异常。

关键词: 图像数据, 非负张量分解, 特征提取, 控制图

Abstract:

Nonnegative tensor decomposition is well known for extracting the features of image data effectively and do not destroy the internal structure features of the data at the same time. This paper establishes a control chart for image data based on nonnegative tensor decomposition without any additional parameters. The monitoring performance of the proposed chart is verified by simulation under location changes, area changes, shape changes and color changes of images. Meanwhile, through a real industrial nonwoven fabric image, comparisons of the proposed control chart, the GLR-based spatiotemporal chart, the EWMA and region growing based chart and the RTC chart are conducted with the same parameter settings. The results show that our proposed method is superior to the other methods when shift size is less than or equal to 2 and performs similarly with the other method when the shift size is large than 2.

Key words: image data, nonnegative tensor decomposition, feature extraction, control chart

中图分类号: 

  • O213

图1

受控图像样本和失控图像样本"

图2

非负CP分解控制图对位置偏移、区域变化、形状变化和颜色变化的ARL1和MRL1"

图3

非织物纺织原始图像和其名义图像"

表1

MRL0=150, 偏移区域10×10和偏移中心(125, 125)时，GLR时空控制图，EWMA时空控制图，RTC方法控制图和非负CP分解控制图的MRL1"

δ GLR时空控制图[10] EWMA时空控制图[15] RTC方法控制图[16] 非负CP分解控制图
-10 2.0 3.0 6.5 4.0
-5 8.0 6.0 10.0 8.0
-3 31.0 12.0 22.0 16.0
-2 78.0 30.0 49.0 29.0
-1 141.5 101.0 107.5 72.0
1 134.5 85.5 112.0 65.0
2 81.0 29.0 47.5 27.0
3 29.0 12.0 23.0 16.0
5 7.0 6.0 9.0 8.0
10 2.0 3.0 7.0 4.0

表2

偏移范围10×10时，不同区域划分及偏移中心下非负CP控制图的ARL1和MRL1"

ARL0=200(MRL0=150) 偏移量δ
-10 -5 -3 -2 -1 1 2 3 5 10
区域大小 偏移中心(125, 125)
10×10 4.0(4) 9.1(8) 18.6(16) 36.0(29) 98.4(72) 90.0(65) 33.6(27) 18.3(16) 8.5(8) 3.8(4)
15×15 3.9(4) 8.8(8) 18.3(16) 36.0(29) 96.5(68) 95.1(67) 35.0(28) 18.0(15) 8.8(8) 3.8(4)
20×20 3.9(4) 8.8(8) 19.3(16) 36.0(28) 103.2(75) 90.0(65) 34.1(27) 18.4(15.5) 8.6(8) 3.9(4)
区域大小 偏移中心(188, 206)
10×10 4.0(4) 8.8(8) 18.9(17) 38.1(29) 97.5(70.5) 96.1(67) 34.5(27) 18.3(16) 8.7(8) 3.8(4)
15×15 4.0(4) 9.2(8) 18.7(15.5) 35.2(27) 100.8(72) 94.1(66) 35.0(27) 18.6(16) 8.9(8) 3.9(4)
20×20 3.9(4) 9.1(8) 18.6(16) 34.9(28) 99.1(70) 93.4(66.5) 36.3(27) 18.3(16) 8.7(8) 3.9(4)
区域大小 偏移中心(158, 78)
10×10 4.0(4) 9.0(8) 18.5(16) 34.7(27) 99.2(71) 95.7(68) 33.4(26) 18.2(16) 8.9(8) 3.9(4)
15×15 4.0(4) 9.1(8) 18.8(16) 35.1(27) 97.0(72) 90.1(65) 33.4(26) 17.6(15) 9.0(8) 3.9(4)
20×20 4.0(4) 9.0(8) 18.5(16) 34.7(27) 99.2(71) 95.6(68) 33.4(26) 18.2(16) 8.9(8) 3.9(4)
1 MEOLA C . Infrared thermography of masonry structures[J]. Infrared Physics and Technology, 2007, 49 (3): 228- 233.
doi: 10.1016/j.infrared.2006.06.010
2 SEO J J , YOON H , HA H , et al. Infrared thermographic diagnosis mechnism for fault detection of ball bearing under dynamic loading conditions[J]. Advanced Materials Research, 2011, (295/296/297): 1544- 1547.
3 PASTOR M L , BALANDRAUD X , GRÉDIAC M , et al. Applying infrared thermography to study the heating of 2024-T3 aluminium specimens under fatigue loading[J]. Infrared Physics & Technology, 2008, 51 (6): 505- 515.
4 VELLVEHI M , PERPIÑÀ X , LAURO G L , et al. Irradiance-based emissivity correction in infrared thermography for electronic applications[J]. Review of Scientific Instruments, 2011, 82 (11): 114901.
doi: 10.1063/1.3657154
5 NEOGI N , MOHANTA D K , DUTTA P K . Review of vision-based steel surface inspection systems[J]. EURASIP Journal on Image and Video Processing, 2014, 2014 (1): 1- 19.
doi: 10.1186/1687-5281-2014-1
6 YAN H , PAYNABAR K , SHI J J . Image-based process monitoring using low-rank tensor decomposition[J]. IEEE Transactions on Automation Science and Engineering, 2015, 12 (1): 216- 227.
doi: 10.1109/TASE.2014.2327029
7 HORST R L , NEGIN M . Vision system for high-resolution dimensional measurements and on-line SPC: web process application[J]. IEEE Transactions on Industry Applications, 1992, 28 (4): 993- 997.
doi: 10.1109/28.148468
8 TAN J , CHANG Z , HSIEH F . Implementation of an automated real-time statistical process controller[J]. Journal of Food Process Engineering, 1996, 19 (1): 49- 61.
doi: 10.1111/j.1745-4530.1996.tb00380.x
9 LYU J J , CHEN M N . Automated visual inspection expert system for multivariate statistical process control chart[J]. Expert Systems With Applications, 2009, 36 (3): 5113- 5118.
doi: 10.1016/j.eswa.2008.06.047
10 MEGAHED F M , WELLS L J , CAMELIO J A , et al. A spatiotemporal method for the monitoring of image data[J]. Quality and Reliability Engineering International, 2012, 28 (8): 967- 980.
doi: 10.1002/qre.1287
11 HE Z , ZUO L , ZHANG M , et al. An image-based multivariate generalized likelihood ratio control chart for detecting and diagnosing multiple faults in manufactured products[J]. International Journal of Production Research, 2016, 54 (6): 1771- 1784.
doi: 10.1080/00207543.2015.1062569
12 何桢, 左玲, 张敏. 基于广义似然比的图像数据监控方法[J]. 系统工程学报, 2016, 31 (1): 127- 134.
HE Zhen , ZUO Ling , ZHANG Min . Image data process control based on generalized likelihoodratio[J]. Journal of Systems Engineering, 2016, 31 (1): 127- 134.
13 BUI A T , APLEY D W . A monitoring and diagnostic approach for stochastic textured surfaces[J]. Technometrics, 2018, 60 (1): 1- 13.
doi: 10.1080/00401706.2017.1302362
14 BUI A T , APLEY D W . Monitoring for changes in the nature of stochastic textured surfaces[J]. Journal of Quality Technology, 2018, 50 (4): 363- 378.
doi: 10.1080/00224065.2018.1507559
15 ZUO L , HE Z , ZHANG M . An EWMA and region growing based control chart for monitoring image data[J]. Quality Technology and Quantitative Management, 2020, 17 (4): 470- 485.
doi: 10.1080/16843703.2019.1682751
16 郭晓晓, 李涛. 基于RTC方法的图像数据监控研究[J]. 甘肃科学学报, 2019, 31 (1): 134- 139.
GUO Xiaoxiao , LI Tao . Image data monitoring based on RTC method[J]. Journal of Gansu Sciences, 2019, 31 (1): 134- 139.
17 KAZEMI S , NIAKI S T A . Monitoring image-based processes using a PCA-based control chart and a classification technique[J]. Decision Science Letters, 2021, 10 (1): 39- 52.
18 LOWRY C A , MONTGOMERY D C . A review of multivariate control charts[J]. IIE Transactions, 1995, 27 (6): 800- 810.
doi: 10.1080/07408179508936797
19 王兆军, 巩震, 邹长亮. ARL计算方法综述[J]. 数理统计与管理, 2011, 30 (3): 467- 497.
WANG Zhaojun , GONG Zhen , ZOU Changliang . The calculation of average run length: a review[J]. Application of Statistics and Management, 2011, 30 (3): 467- 497.
20 STEINER S H , JONES M . Risk-adjusted survival time monitoring with an updating exponentially weighted moving average (EWMA) control chart[J]. Statistics in Medicine, 2009, 29 (4): 444- 454.
[1] 高琦,戴洪帅,武艳华. 基于MPEWMA控制图的串联排队网络的监测与控制[J]. 《山东大学学报(理学版)》, 2023, 58(8): 104-110, 117.
[2] 苏自鹏,袁磊,刘鹏,陈兴蜀,罗永刚,陈良国. 高速网络流实时处理模型研究与实现[J]. 《山东大学学报(理学版)》, 2022, 57(9): 25-32.
[3] 董哲瑾,王健,钱凌飞,林鸿飞. 一种用户成长性画像的建模方法[J]. 《山东大学学报(理学版)》, 2019, 54(3): 38-45.
[4] 陈鑫,薛云,卢昕,李万理,赵洪雅,胡晓晖. 基于保序子矩阵和频繁序列模式挖掘的文本情感特征提取方法[J]. 山东大学学报（理学版）, 2018, 53(3): 36-45.
[5] 徐也,徐蔚然. 基于语义特征扩展的知识库增量引文推荐算法[J]. 山东大学学报（理学版）, 2016, 51(11): 26-32.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 王刚,许信顺*. 一种新的基于多示例学习的场景分类方法[J]. J4, 2010, 45(7): 108 -113 .
[2] 陆玮洁,主沉浮,宋 翠,杨艳丽 . 中药郁金中无机离子的毛细管电泳法测定[J]. J4, 2007, 42(7): 13 -18 .
[3] 孙小婷1,靳岚2*. DOSY在寡糖混合物分析中的应用[J]. J4, 2013, 48(1): 43 -45 .
[4] 任敏1,2,张光辉1. 右半直线上依分布收敛独立随机环境中随机游动的吸收概率[J]. J4, 2013, 48(1): 93 -99 .
[5] 徐俊峰. 关于复代数微分方程亚纯解的增长级[J]. J4, 2010, 45(6): 91 -93 .
[6] 张丽,许玉铭 . σ1-空间及其性质[J]. J4, 2006, 41(5): 30 -32 .
[7] 解树涛,宋晓妍,石梅,陈秀兰,孙彩云,张玉忠* . 康宁木霉（Trichoderma koningii）SMF2分泌的peptaibols类抗菌肽Trichokonins抑菌活性研究[J]. J4, 2006, 41(6): 140 -144 .
[8] 刘保仓,史开泉 . S-粗集的信度特征[J]. J4, 2006, 41(5): 26 -29 .
[9] 王红妹,肖敏*,李正义,李玉梅,钱新民 . 转糖基β-半乳糖苷酶产生菌筛选和鉴定及酶催化生成低聚半乳糖[J]. J4, 2006, 41(1): 133 -139 .
[10] 张佳丽,苗连英,宋文耀. 最大度为8不含相邻4-圈的1-平面图边色数[J]. 山东大学学报（理学版）, 2014, 49(04): 18 -23 .
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发