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基于堆叠降噪自编码器的神经–符号模型及在晶圆表面缺陷识别

刘国梁 余建波

刘国梁, 余建波. 基于堆叠降噪自编码器的神经–符号模型及在晶圆表面缺陷识别. 自动化学报, 2022, 48(11): 2688−2702 doi: 10.16383/j.aas.c190857
引用本文: 刘国梁, 余建波. 基于堆叠降噪自编码器的神经–符号模型及在晶圆表面缺陷识别. 自动化学报, 2022, 48(11): 2688−2702 doi: 10.16383/j.aas.c190857
Liu Guo-Liang, Yu Jian-Bo. Application of neural-symbol model based on stacked denoising auto-encoders in wafer map defect recognition. Acta Automatica Sinica, 2022, 48(11): 2688−2702 doi: 10.16383/j.aas.c190857
Citation: Liu Guo-Liang, Yu Jian-Bo. Application of neural-symbol model based on stacked denoising auto-encoders in wafer map defect recognition. Acta Automatica Sinica, 2022, 48(11): 2688−2702 doi: 10.16383/j.aas.c190857

基于堆叠降噪自编码器的神经–符号模型及在晶圆表面缺陷识别

doi: 10.16383/j.aas.c190857
基金项目: 国家自然科学基金(71771173)资助
详细信息
    作者简介:

    刘国梁:同济大学机械与能源工程学院硕士研究生. 2018年获上海大学学士学位. 主要研究方向为机器学习, 深度学习和智能质量管控. E-mail: guoliangliutt@163.com

    余建波:同济大学机械与能源工程学院教授. 2009年获上海交通大学博士学位. 主要研究方向为机器学习, 深度学习, 智能质量管控, 过程控制, 视觉检测与识别. 本文通信作者.E-mail: jbyu@tongji.edu.cn

Application of Neural-symbol Model Based on Stacked Denoising Auto-encoders in Wafer Map Defect Recognition

Funds: Supported by National Natural Science Foundation of China (71771173)
More Information
    Author Bio:

    LIU Guo-Liang Master student at the School of Mechanical and Energy Engineering, Tongji University. He received his bachelor degree from Shanghai University in 2018. His research interest covers machine learning, deep learning and intelligent quality control

    YU Jian-Bo Professor at the School of Mechanical and Energy Engineering, Tongji University. He received his Ph.D. degree from Shanghai Jiaotong University in 2009. His research interest covers machine learning, deep learning, intelligent quality control, process control, visual inspection and identification. Corresponding author of this paper

  • 摘要: 深度神经网络是具有复杂结构和多个非线性处理单元的模型, 通过模块化的方式分层从数据提取代表性特征, 已经在晶圆缺陷识别领域得到了较为广泛的应用. 但是, 深度神经网络在应用过程中本身存在“黑箱”和过度依赖数据的问题, 显著地影响深度神经网络在晶圆缺陷识别的工业可应用性. 提出一种基于堆叠降噪自编码器的神经–符号模型. 首先, 根据堆叠降噪自编码器的网络特点采用了一套符号规则系统, 规则形式和组成结构使其可与深度神经网络有效融合. 其次, 根据 网络和符号规则之间的关联性提出完整的知识抽取与插入算法, 实现了深度网络和规则之间的知识转换. 在实际工业晶圆表面图像数据集WM-811K上的试验结果表明, 基于堆叠降噪自编码器的神经–符号模型不仅取得了较好的缺陷探测与识别性能, 而且可有效提取规则并通过规则有效描述深度神经网络内部计算逻辑, 综合性能优于目前经典的深度神经网络.
  • 图  1  堆叠降噪自编码器

    Fig.  1  Stacked denoising autoencoder

    图  2  堆叠降噪自编码器的神经–符号模型

    Fig.  2  Stacked denoising autoencoder based neural-symbolic model

    图  3  置信度规则初始化网络过程示意图

    Fig.  3  The process of network initialization base on confidence rule

    图  4  MofN规则初始化网络过程示意图

    Fig.  4  The process of network initialization based on MofN rules

    图  5  基于KBSDAE的晶圆表面缺陷识别系统

    Fig.  5  Wafer surface defect recognition system based on KBSDAE

    图  6  晶圆缺陷探测与识别流程

    Fig.  6  The process of defect detecting and identifying on wafer

    图  7  正常模式与8种缺陷模式的晶圆图

    Fig.  7  Normal pattern and eight defect patterns of wafer

    图  8  WM-811K中晶圆图数据构成

    Fig.  8  Data Structure of wafer map in WM-811K

    图  9  基于原始数据的控制图

    Fig.  9  Control chart based on raw data

    图  11  基于KBSDAE提取特征的控制图

    Fig.  11  Control chart based on feature extracted by KBSDAE

    图  10  基于SDAE提取特征的控制图

    Fig.  10  Control chart based on feature extracted by SDAE

    图  12  SDAE和相应的符号规则的晶圆表面缺陷识别率对比

    Fig.  12  Comparison of wafer defect recognition rates between SDAE and corresponding rules

    图  13  KBSDAE和SDAE训练过程的均方误差变化对比

    Fig.  13  Comparison of mean square errors of KBSDAE and SDAE training processes

    图  14  Local和Edge-local模式的晶圆图

    Fig.  14  Wafer maps in Local and Edge-local patterns

    图  15  不同微调训练步数的SDAE与KBSDAE分类性能比较

    Fig.  15  Comparison of classification performances between SDAE and KBSDAE with different fine-tuning steps

    图  16  不同训练数据量下的 KBSDAE 与 SDAE 识别性能比较

    Fig.  16  Comparison of classification performances between KBSDAE and SDAE with different training data volumes

    图  17  仿真数据集中晶圆图构成示意图

    Fig.  17  Data structure of wafer map in simulation dataset

    表  1  晶圆图像特征集

    Table  1  Wafer map feature set

    特征类别特征集
    几何特征区域特征、线性特征、Hu 不变矩
    灰度特征平均值、方差、歪斜度、峰值、能量、熵
    纹理特征能力、对比度、相关性、均匀度、熵
    投影特征峰值、平均幅值、均方根幅值、投影波形特性、
    投影峰值、投影脉冲
    下载: 导出CSV

    表  2  3种控制图的缺陷探测率 (%)

    Table  2  Defect detection capabilities of three control charts (%)

    模式原始数据SDAEKBSDAE
    Random62.9010097.54
    Center99.4099.9097.20
    Local58.0281.4888.58
    Edge-local85.0310098.75
    Scratch99.2798.5486.86
    Near-full0.000.00100
    Donut7.4197.5381.48
    Edge-ring91.1067.1990.86
    平均值70.8980.5893.52
    下载: 导出CSV

    表  3  部分置信度符号规则

    Table  3  Part of Confidence Rule

    DAE置信度规则
    DAE 1$\begin{aligned} & {\rm{0} }{\rm{.55} }:h_{ 2}^1 \Leftrightarrow {x_{\rm{1} } } \wedge \neg {x_{\rm{2} } } \wedge \neg {x_4} \wedge {x_5} \wedge \cdots \wedge {x_{21} } \wedge \neg {x_{22} } \wedge {x_{23} } \wedge \neg {x_{25} } \wedge \cdots \wedge \neg {x_{ {\rm{49} } } } \wedge {x_{50} } \wedge \neg {x_{51} } \\ & 0.65:h_{42}^1 \Leftrightarrow \neg {x_{\rm{1} } } \wedge \neg {x_{\rm{2} } } \wedge \neg {x_3} \wedge {x_4} \wedge \neg {x_5} \wedge \cdots \wedge \neg {x_{24} } \wedge {x_{25} } \wedge \cdots \wedge \neg {x_{ {\rm{49} } } } \wedge \neg {x_{50} } \wedge {x_{51} } \\ & {\rm{0} }{\rm{.56} }:h_{79}^1 \Leftrightarrow {x_{\rm{1} } } \wedge {x_3} \wedge \neg {x_4} \wedge \cdots \wedge {x_{21} } \wedge {x_{22} } \wedge {x_{23} } \wedge \neg {x_{24} } \wedge \neg {x_{25} } \wedge \cdots \wedge {x_{ {\rm{49} } } } \wedge {x_{50} } \wedge {x_{51} } \\ \end{aligned}$
    DAE 2$0.72:h_9^2 \Leftrightarrow \neg h_{\rm{2}}^1 \wedge \neg h_5^1 \wedge h_{\rm{7}}^1 \wedge \neg h_{10}^1 \wedge \neg h_{11}^1 \wedge \neg h_{12}^1 \wedge \cdots \wedge \neg h_{41}^1 \wedge h_{42}^1 \wedge \cdots \wedge \neg h_{77}^1 \wedge \neg h_{78}^1 \wedge \neg h_{{\rm{79}}}^1$
    下载: 导出CSV

    表  4  部分MofN规则

    Table  4  Part of MofN Rule

    分类MofN 规则
    类别 1$(C1)$${\rm{IF} }\;0.68\times{ {NumberTure}\; }({ {h} }_2^2,{ {h} }_3^2,{ {h} }_4^2,{ {h} }_5^2,{ {h} }_6^2,{ {h} }_7^2,{ {h} }_9^2,{ {h} }_{10}^2,{ {h} }_{12}^2,{ {h} }_{13}^2) - 1.35\times{ { {NumberTure} }\; }({ {h} }_1^2,{ {h} }_8^2,{ {h} }_{11}^2,{ {h} }_{14}^2,{ {h} }_{15}^2) > 0.75\;{ {{\rm{THEN}}} }\;{ {C} }1$
    类别 4$(C4)$${\rm{IF} }\;3.45\times{{NumberTure} \;}({ {h} }_5^2,{ {h} }_6^2,{ {h} }_7^2,{ {h} }_8^2) - 0.87\times{{NumberTure} \;}({ {h} }_1^2,{ {h} }_2^2,{ {h} }_3^2,{ {h} }_4^2,{ {h} }_9^2,{ {h} }_{10}^2,{ {h} }_{11}^2,{ {h} }_{12}^2,{ {h} }_{13}^2,{ {h} }_{14}^2,{ {h} }_{15}^2) > 4.73\;{\rm{THEN} }\;{ {C} }4$
    类别 5$(C5)$${\rm{IF} }\;0.85\times{ {NumberTure}\; }({ {h} }_2^2,{ {h} }_4^2,{ {h} }_5^2,{ {h} }_6^2,{ {h} }_7^2,{ {h} }_8^2,{ {h} }_9^2,{ {h} }_{10}^2,{ {h} }_{12}^2,{ {h} }_{15}^2) - 1.76\times{ { { {NumberTure} } }\; }({ {h} }_1^2,{ {h} }_3^2,{ {h} }_{11}^2,{ {h} }_{13}^2,{ {h} }_{14}^2,) > 1.44\;{\rm{THEN} }\;{{C} }5$
    下载: 导出CSV

    表  5  基于 KBSDAE 的晶圆缺陷识别率

    Table  5  Recognition rates of defects in wafers based on KBSDAE

    模式RandomCenterLocalEdge-localScratchNear-fullDonutEdge-ring
    Random0.9100.0600000.03
    Center0.010.99000000
    Local0.010.010.8100.09000.08
    Edge-local00.0200.980000
    Scratch000.030.020.83000.12
    Near-full000.0100.250.8400
    Donut0000.13000.870
    Edge-ring00000.02000.98
    下载: 导出CSV

    表  6  结构规则超参数敏感性分析

    Table  6  Model hyperparameter sensitivity analysis

    隐藏层数隐节点数置信度规则数分类规则数准确度 (%)
    120 + 51/2189.37
    1/288.70
    1/487.57
    1/3189.00
    1/288.80
    1/488.57
    1/5189.80
    1/288.97
    1/487.67
    280, 15 + 51/2186.27
    1/290.02
    1/489.00
    1/3190.00
    1/291.56
    1/489.78
    1/5190.00
    1/288.13
    1/488.90
    380, 30, 15 + 51/2184.23
    1/289.37
    1/489.20
    1/3183.47
    1/287.33
    1/488.07
    1/5184.23
    1/288.62
    1/489.05
    下载: 导出CSV

    表  7  各种学习模型的晶圆缺陷识别率 (%)

    Table  7  Wafer defect recognition rates for various learning models (%)

    数据集 WM-811K 仿真
    DBN 80.84 86.34
    SDAE 89.87 91.28
    SSAE 86.6 87.96
    BPNN 80.71 89.25
    DenseNet 88.6 90.69
    ResNet 86.53 91.89
    GoogleNet 74.32 90.63
    SVMG 72.54 78.86
    SYM-DBN 85.63 90.58
    INSS-KBANN 81.96 92.78
    JLNDA 90.4 90.84
    KBSDAE 91.14 95.28
    下载: 导出CSV
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  • 收稿日期:  2019-12-17
  • 录用日期:  2020-12-20
  • 修回日期:  2020-05-18
  • 网络出版日期:  2021-01-29
  • 刊出日期:  2022-11-22

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