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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, 2021, x(x): 1−15 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, 2021, x(x): 1−15 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, 2021, x(x): 1−15 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, 2021, x(x): 1−15 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(No. 71777173), 上海科委“科技创新行动计划”高新技术领域项目(No.19511106303), 中央高校基本业务经费项目
详细信息
    作者简介:

    刘国梁:同济大学机械与能源工程学院研究生. 2018年获上海大学机械工程及其自动化学院学士学位. 主要研究方向为机器学习, 深度学习, 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年获上海交通大学机械工程学院博士学位. 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. 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 P. R. China (No. 71777173), High and New Technology Field Project of "Action Plan for Scientific and Technological Innovation" of Shanghai Science and Technology Committee (No.19511106303), Funds for Basic Business of Central Universities
  • 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(Wafer map pattern recognition, WMPR)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. 本文提出了一种基于堆叠降噪自编码器(Stacked denoising auto-encoders, SDAE)的神经-符号模型. 首先, 根据SDAE的网络特点设计了一套全新的符号规则系统, 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SDAE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 base on classification rule

    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  正常晶圆图模式与8种缺陷模式

    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wafer缺陷识别率(%)对比, (a)train/test = 8/2, (b)train/test =2/8

    Fig.  12  Comparison of wafer defect recognition rate (%) between SDAE and corresponding rules, (a) train/test = 8/2, (b) train/test = 2/8

    图  13  KBSDAE和SDAE训练过程的均方误差变化对比, (a)DAE训练过程(c)Fine-tuning训练阶段

    Fig.  13  Comparison of mean square error of KBSDAE and SDAE training process, (a) DAE training process (c) Fine-tuning process

    图  14  Local和Edge-local模式的晶圆图

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

    图  15  不同fine-tuning训练步数的SDAE与KBSDAE分类性能比较

    Fig.  15  Comparison of classification performance 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 performance between SDAE and KBSDAE with different training data volumes

    图  17  仿真数据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  三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
    Total70.8980.5893.52
    下载: 导出CSV

    表  3  部分置信度符号规则

    Table  3  Part of Confidence Rule

    DAEConfidence rule
    DAE1$\begin{gathered} {\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{gathered} $
    DAE2$0.72:h_9^2 \Leftrightarrow \neg h_{\rm{2}}^1 \wedge \neg h_5^1 \wedge h_{\rm{7}}^1 \wedge \neg h_{10}^1 \wedge \neg h_{11}^1 \wedge \neg h_{12}^1 \wedge \cdots \wedge \neg h_{41}^1 \wedge h_{42}^1 \wedge \cdots \wedge \neg h_{77}^1 \wedge \neg h_{78}^1 \wedge \neg h_{{\rm{79}}}^1$
    下载: 导出CSV

    表  4  部分MofN规则

    Table  4  Part of MofN Rule

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

    表  5  KBSDAE的8种异常识别率(Random (P1), Center (P2), Local(P3), Edge-local (P4), Scratch (P5), Near-full (P6), Donut (P7) and Edge-ring (P8))

    Table  5  Recognition rate of defects in wafers base on KBSDAE (Random (P1), Center (P2), Local(P3), Edge-local (P4), Scratch (P5), Near-full (P6), Donut (P7) and Edge-ring (P8))

    P1P2P3P4P5P6P7P8
    P10.9100.0600000.03
    P20.010.99000000
    P30.010.010.8100.09000.08
    P400.0200.980000
    P5000.030.020.83000.12
    P6000.0100.250.8400
    P70000.13000.870
    P800000.02000.98
    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 rate (%) for various learning models

    数据集DBNSDAESSAEBPNNDenseNetResNetGoogleNetSVMGSYM-DBNINSS-KBANNJLNDAKBSDAE
    WM-811K80.8489.8786.680.7188.686.5374.3272.5485.6381.9690.491.14
    Simulation86.3491.2887.9689.2590.6991.8990.6378.8690.5892.7890.8495.28
    下载: 导出CSV
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  • 收稿日期:  2019-12-17
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