摘要
针对间歇过程多模态、变量非线性、非高斯分布等特征,提出一种基于扩散K近邻距离的故障诊断方法.该方法首先在样本集完全图中应用马尔科夫随机游走定义带有分量权重的扩散距离,可以有效提取数据样本的关联信息和统计特征,然后应用K近邻规则方法对样本数据进行故障诊断.这种应用扩散距离替换传统K近邻规则欧式距离的统计方法,既可以提升对数据样本关联性信息的有效提取能力,又可以使得K近邻规则处理非线性、多模态检测问题的性能得以保持.通过在半导体蚀刻批次过程中的仿真应用,与传统线性、非线性方法的对比分析,实验结果验证了方法的有效性.
According to the multi-mode, variable nonlinear and non-Gaussian distribution characteristics of the batch process, we propose a new fault detection method based on diffusion K-nearest neighbor distance(FD–DDKNN). In this work, the diffusion distance with component weight which can effectively fetch correlation information and statistical characteristics in data samples is defined through Markovian random walk in complete graph of the samples set. Then, the adapted K-nearest neighbor rule(KNN) method is applied to data samples to detect faults. This method that replaces diffusion distance to conventional Euclidean distance in K-nearest neighbor rule, not only raises the ability of fetching relevance information in data samples, but also improves the performance of dealing with nonlinear and multi-mode characteristics based on KNN rule for detection problem. By the simulation application in the semiconductor etching batch process, compared with the traditional linear and nonlinear methods, the experimental results validate the effectiveness of the proposed method.
引文
[1]周东华,李钢,李元.数据驱动的工业过程故障诊断与预测技术–PCA与PLS的方法[M].北京:科学出版社,2011:22–30.(ZHOU Donghua,LI Gang,LI Yuan.Data Driven Industrial Process Fault Diagnosis Technology-Based on PCA and PLS Methods[M].Beijing:Science Press,2011:22–30.)
[2]李荣雨,荣冈.基于故障映射向量和结构化残差的主元分析(PCA)故障隔离[J].控制理论与应用,2008,25(6):1099–1104.(LI Rongyu,RONG Gang.Principal component analysis(PCA)of fault isolation based on fault mapping vector and structured residual[J].Control Theory&Applications,2008,25(6):1099–1104.)
[3]LI Y,ZHANG X M.Diffusion maps based k-nearest-neighbor rule technique for semiconductor manufacturing process fault detection[J].Chemometrics and Intelligent Laboratory Systems,2014,136(1):47–57.
[4]YU J B.Fault detection using principal components-based Gaussian mixture model for semiconductor manufacturing processes[J].IEEE Transactions on Semiconductor Manufacturing,2011,24(3):432–444.
[5]HUNG H,WU P S,TU I P,et al.On multilinear principal component analysis of order-two tensors[J].Biometrika,2012,99(3):569–583.
[6]GUNTHER J C,CONNER J S,SEBORG D E.Process monitoring and quality variable prediction utilizing PLS in industrial fed-batch cell culture[J].Journal of Process Control,2009,19(5):914–921.
[7]ZHAO S J,ZHANG J,XU Y M.Monitoring of processes with multiple operating modes through multiple principle component analysis models[J].Industrial&Engineering Chemistry Research,2004,43(22):7025–7035.
[8]CHOI S W,MARTIN E B,MORRIES A J,et al.Adaptive multivariate statistical process control for monitoring time-varying processes[J].Industrial&Engineering Chemistry Research,2006,45(9):3108–3118.
[9]DAYAL B S,MACGREGOR J F.Recursive exponentially weighted pls and its applications to adaptive control and prediction[J].Journal of Process Control,1997,7(3):169–179.
[10]LEE D S,VANROLLEGHEM P A.Adaptive consensus principal component analysis for on-line batch process monitoring[J].Environmental Monitoring and Assessment,2004,92(1/2/3):119–135.
[11]LI W H,YUE H H,VALLECERVANTES V,et al.Recursive PCA for adaptive process monitoring[J].Journal of Process Control,2000,10(5):471–486.
[12]WANG X,KRUGER U,LENNOX B.Recursive partial least squares algorithms for monitoring complex industrial processes[J].Control Engineering Practice,2003,11(6):613–632.
[13]张家良,曹建福,高峰,等.结合非线性频谱与核主元分析的复杂系统故障诊断方法[J].控制理论与应用,2012,29(12):1558–1564.(ZHANG Jialiang,CAO Jianfu,GAO Feng,et al.Fault diagnosis complex system based on nonlinear spectrum and kernel principal component analysis[J].Control Theory&Applications,2012,29(12):1558–1564.)
[14]SCHOLKOPF B,MIKA S,BURGES C J C,et al.Input space versus feature space in kernel based methods[J].IEEE Transactions on Neural Networks,1999,10(5):1000–1017.
[15]CUI P L,LI J H,WANG G Z.Improved kernel principal component analysis for fault detection[J].Expert Systems with Applications,2008,34(2):1210–1219.
[16]张成,李元.基于统计模量分析间歇过程故障检测方法研究[J].仪器仪表学报,2013,34(9):2103–2110.(ZHANG Cheng,LI Yuan.Study on the fault-detection method in batch process based on statistical pattern analysis[J].Chinese Journal of Scientific Instrument,2013,34(9):2103–2110.)
[17]HE Q P,WANG J.Fault detection using the k-nearest neighbor rule for semiconductor manufacturing processes[J].IEEE Transactions on Semiconductor Manufacturing,2007,20(4):345–354.
[18]HE Q P,WANG J.Principal component based k-nearest-neighbor rule for semiconductor process fault detection[C]//2008 American Control Conference.Seattle,WA:IEEE,2008:1606–1611.
[19]COIFMAN R R,LAFON S.Diffusion maps[J].Applied and Computational Harmonic Analysis,2006,21(1):5–30.
[20]COIFMAN R R,LAFON S,LEE A B,et al.Geometric diffusions as a tool for harmonic analysis and structure definition of data:Diffusion maps[J].Proceedings of the National Academy of Sciences of the United States of America,2005,102(21):7426–7431.
[21]SINGER A,WU H T.Vector diffusion maps and the connection Laplacian[J].Communications on Pure and Applied Mathematics,2012,65(8):1067–1144.
[22]HUANG Y,ZHA X F,LEE J,et al.Discriminant diffusion maps analysis:A robust manifold learner for dimensionality reduction and its applications in machine condition monitoring and fault diagnosis[J].Mechanical Systems and Signal Processing,2013,34(1):277–297.
[23]COIFMAN R R,KEVREKIDIS I G,LAFON S,et al.Diffusion maps,reduction coordinates,and low dimensional representation of stochastic systems[J].Multiscale Modeling&Simulation,2008,7(2):842–864.
[24]MAGGIONI M,MHASKAR H N.Diffusion polynomial frames on metric measure spaces[J].Applied and Computational Harmonic Analysis,2008,24(3):329–353.
[25]WISE B M,GALLAGHER N B,BUTLER S W,et al.A comparison of principal component analysis,multiway principal component analysis,trilinear decomposition and parallel factor analysis for fault detection in a semiconductor etch process[J].Journal of Chemometrics,1999,13(3-4):379–396.
[26]SINGH K P,MALIK A,BASANT N.Multi-way partial least squares modeling of water quality data[J].Analytica Chimical Acta,2007,584(2):385–396.
