概率PCA多元统计方法在过程监控中的应用研究
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摘要
在长期的运行中,生产过程不可避免会发生一些变化,可能影响产品质量,甚至造成重大事故,完全依靠人力的传统监控方法已不足以解决复杂的质量控制问题。统计过程监控方法不需要复杂的机理模型,通过统计方法提取过程数据的重要信息,并将其量化为几个统计监控指标便可实现对过程的监控,充分利用过程的已有信息,可实现性强,历经三十多年的发展,统计过程监控方法已经取得了一系列令人瞩目的成果,并在现代过程工业中得到了广泛的应用。
概率主元分析(PPCA)通过期望最大化(EM)算法建立过程的生成模型,确定主元和误差的概率函数,能实现有效的故障检测和故障识别,得到工业界和学术界的广泛关注。但是基于PPCA的监控方法的应用前提是过程变量之间满足线性关系,并且不存在自相关,然而大多数实际工业过程往往无法满足这些条件,使基于PPCA的监控方法得不到理想的效果。
本文针对基于PPCA过程监控的缺点,主要做了以下几方面的工作:
1.提出基于PPCA的改进监控方法,直接对所有过程变量白化值的范数进行监控,并通过对每个过程变量的白化值监控实现在线故障识别,减少了监控量。将其应用于化工吸附分离过程,与基于PCA的监控的方法作了比较。
2.解决具有较强动态特性的工业生产过程的监控问题,提出了动态概率主元分析法,对经过时间序列扩展后的变量数据阵,通过EM算法建立生成模型,从而将静态PPCA推广到动态多变量过程,有效消除了过程变量的自相关关系。
3.在非线性过程的监控方面,提出基于动态核概率主元分析法,利用核函数将经过压缩的动态增广数据阵映射到高维空间,然后利用PPCA方法对满足线性关系的过程变量进行处理,通过连续重整加热炉系统的应用研究表明该方法有好的监控性能。
After long time running, there are some changes in any producing system, which will unavoidably influence the quality of products and even result in great accidents. Therefore, the traditional methods entirely based on manpower are outdated and can not satisfy the complicated desire of quality control. Having no use of complex mechanism model, multivariable statistical process monitoring method can monitor process through extracting important information from raw data using statistical method and then transforming them into several significative indices. The method not only takes sufficient use of the existing information and is well realizable, but also greatly reduces the procedure of process monitoring system, which has been developed more than thirty years, in which lots of research results have been acquired and applied widely.
Probabilistic principal component analysis(PPCA) firstly assume the distribution of latent variables and error vector, secondly evaluate the generative model by the expectation and maximization (EM) algorithm, so it can detect fault effectively and performs on-line fault identification, which make it attractive both in industry and academia. However PPCA is a linear way, the preconditions of its application are that process are normally distributed and no auto-correlation among them. But most of industrial process are complicated and always violate the preconditions, so the PPCA-based method behaves unsatisfactorily.
Aiming at the disadvantages of the PPCA-based method, the main contributions are as follows:
1. The dissertation proposes an improved monitoring way which monitors the norm of whiten measurement variables and perform on-line fault identification by monitoring every whiten variable, so the load of monitoring is reduced. At last PCA and PPCA are compared in monitoring process of chemical separation.
2. Aiming at the strong dynamic characteristic of the industrial process, using EM algorithm, the dynamic PPCA model is built to cope with the data matrix extend by time series. According to the technique, static PPCA can be extended to monitor dynamic multivariate process, and auto-correlation among process variables is effectively eliminated.
3. On the monitoring of nonlinear process. The dissertation propose a dynamic kernel PPCA, it maps the compressed data matrix extended by time series into high-dimensional space by kernel function, then PPCA can be used to monitor the linear mapped value or process variables. The method is used in the continuous and reforming heating stove system process, and the results verify its effectiveness.
概率主元分析(PPCA)通过期望最大化(EM)算法建立过程的生成模型,确定主元和误差的概率函数,能实现有效的故障检测和故障识别,得到工业界和学术界的广泛关注。但是基于PPCA的监控方法的应用前提是过程变量之间满足线性关系,并且不存在自相关,然而大多数实际工业过程往往无法满足这些条件,使基于PPCA的监控方法得不到理想的效果。
本文针对基于PPCA过程监控的缺点,主要做了以下几方面的工作:
1.提出基于PPCA的改进监控方法,直接对所有过程变量白化值的范数进行监控,并通过对每个过程变量的白化值监控实现在线故障识别,减少了监控量。将其应用于化工吸附分离过程,与基于PCA的监控的方法作了比较。
2.解决具有较强动态特性的工业生产过程的监控问题,提出了动态概率主元分析法,对经过时间序列扩展后的变量数据阵,通过EM算法建立生成模型,从而将静态PPCA推广到动态多变量过程,有效消除了过程变量的自相关关系。
3.在非线性过程的监控方面,提出基于动态核概率主元分析法,利用核函数将经过压缩的动态增广数据阵映射到高维空间,然后利用PPCA方法对满足线性关系的过程变量进行处理,通过连续重整加热炉系统的应用研究表明该方法有好的监控性能。
After long time running, there are some changes in any producing system, which will unavoidably influence the quality of products and even result in great accidents. Therefore, the traditional methods entirely based on manpower are outdated and can not satisfy the complicated desire of quality control. Having no use of complex mechanism model, multivariable statistical process monitoring method can monitor process through extracting important information from raw data using statistical method and then transforming them into several significative indices. The method not only takes sufficient use of the existing information and is well realizable, but also greatly reduces the procedure of process monitoring system, which has been developed more than thirty years, in which lots of research results have been acquired and applied widely.
Probabilistic principal component analysis(PPCA) firstly assume the distribution of latent variables and error vector, secondly evaluate the generative model by the expectation and maximization (EM) algorithm, so it can detect fault effectively and performs on-line fault identification, which make it attractive both in industry and academia. However PPCA is a linear way, the preconditions of its application are that process are normally distributed and no auto-correlation among them. But most of industrial process are complicated and always violate the preconditions, so the PPCA-based method behaves unsatisfactorily.
Aiming at the disadvantages of the PPCA-based method, the main contributions are as follows:
1. The dissertation proposes an improved monitoring way which monitors the norm of whiten measurement variables and perform on-line fault identification by monitoring every whiten variable, so the load of monitoring is reduced. At last PCA and PPCA are compared in monitoring process of chemical separation.
2. Aiming at the strong dynamic characteristic of the industrial process, using EM algorithm, the dynamic PPCA model is built to cope with the data matrix extend by time series. According to the technique, static PPCA can be extended to monitor dynamic multivariate process, and auto-correlation among process variables is effectively eliminated.
3. On the monitoring of nonlinear process. The dissertation propose a dynamic kernel PPCA, it maps the compressed data matrix extended by time series into high-dimensional space by kernel function, then PPCA can be used to monitor the linear mapped value or process variables. The method is used in the continuous and reforming heating stove system process, and the results verify its effectiveness.
引文
1.邵裕森.过程控制及仪表[M].上海:交通大学出版社,1997
2.胡峰,孙国基.过程监控技术及其应用[M].国防工业出版社,2001
3.杨叔子,郑晓军.人工智能与诊断专家系统[M].西安交通大学出版社,1990
4.吴今培,肖健华.智能故障诊断与专家系统[M].科学出版社,1997
5. Raich A C,Cinar A.Statistical process monitoring and disturbance diagnosis in multivariable continuous processes[J].AIChE J, 1996, 42(4):995-1009
6. Frank, P M.Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy-a survey and some new results [J].Automatica,1990, 26 (3):459-474
7. Venkatasubramanian V, Rengaswamy R, Yin K, et al.A review of process fault detection and diagnosis Part I:Quantitative model-based methods[J].Computers and Chemical Engineering, 2003, 27(3):293-311
8. Jiang B, Fahmida N C.Parameter fault detection and estimation of a class of nonlinear systems using observers[J].Journal of the Franklin Institute, 2005, 342(7): 725-736
9. Frank K, Anselm S. Isermann, R.Fault detection for modern diesel engines using signal and process model-based methods[J].Control Engineering Practice.2005,13(2):189- 203
10. Kinnaert M, Vrancic D, Denolin E,et al.Model-based fault detection and isolation for a gas-liquid separation unit[J].Control Engineering Practice,2000,8(11):1273-1283
11. Gertler J.Analytical redundancy methods in fault detection and isolation[C].In Proceeding of IFAC/IAMCS symposium on safe process,1991:91-96
12. Gertler J.Fault detection and isolation using parity relation[J].Control Engineering Practice,1997,5(5):653-661
13. Isermann R.Fault diagnosis of machines via parameter estimation and knowledge processing–tutorial paper[J].Automatica,1993, 29(4): 815-835
14.闻新,张洪钺,周露.控制系统的故障诊断和容错控制[M].北京:机械工业出版社,1998
15. Balle P.Fuzzy-model-based parity equations for fault isolation[J].Control engineering practice,1999,7(2):261-270
16. Balle P,Fuessel D.Closed-loop fault diagnosis based on a nonlinear process model and automatic fuzzy rule generation[J].Engineering Application of Artificial Intelligence.2000, 13(6):695-704
17. Venkatasubramanian V,Rengaswamy R,Yin K,et al.A review of process fault detection and diagnosis Part II: Qualitative models and search strategies[J].Computers and Chemical Engineering, 2003, 27(3):313-326
18. Palshikar G K, Khemani D.Diagnosing dynamic systems using trace patterns[J].Pattern Recognition letters,1999,20(7):741-753
19.陈玉东,施颂椒,翁正新.动态系统的故障诊断方法综述[J].化工自动化及仪表,2001,28(3):1-14
20.高桂革,顾幸生.小波变换在分布参数系统控制中的应用[J].清华大学学报,2007,47(S2):1862-1865
21. Kumamaru K,Hu J,Inoue K,et al.Robust fault detection using index of kullback discrimination information[C].Proceeding of IFAC world congress,San Francisco,USA,1996: 205-210
22. Venkatasubramanian V,Rengaswamy R,Yin K,et al.A review of process fault detection and diagnosis part III:process history based methods[J].Computers and Chemical Engineering, 2003,27(3):327-346
23. Chiang L H,Russell E L,Braatz R D.Fault Detection and Diagnosis in Industrial System[M].Springer-Verlag,London,2001
24. Raich A C,Cinar A.Multivariate statistical methods for monitoring continuous processes: assessment of discrimination power of disturbance models and diagnosis of multiple disturbances[J].Chemometrics and Intelligent Laboratory Systems,1995,30:37-48
25. MacGregor J F.Using on-line process data to improve quality: challenges for statisticians [J].Int.Stat.Rev,1997,65(3):309-323
26. Bakshi B R.Multiscale PCA with application to multivariate statistical process monitoring [J].AIChE J,1998,44(7):1596-1610
27. Negiz A,Cinar A.Statistical monitoring of multivariable dynamic processes with state-space models[J].AIChE J,1997, 43(8):2002-2020
28.孙静.接近零不合格过程质量的质量控制[M].清华大学出版社,2001
29. Box G,Luceno A.Statistical control by monitoring and feedback adjustment -- A Discussion[J].Technology,1985,17(4):176-209
30.张杰,阳宪惠.多变量统计过程控制[M].北京:化学工业出版社,2000
31. Jackson J E.Principal components and factor analysis: partⅠ- principal components [J]. J. Qual.Tech,1980,12(4):201-213
32. Jose C,Jesus P.Online monitoring of batch processes using multi-phase principal component analysis.Journal of Process Control, 2006, 16(10):1021-1035
33. Eitle D,Gunkel S,Gundy K V.Cumulative exposure to stressful life events and male gang membership[J].Journal of Criminal Justice,2004,32(2):95-111
34. Dong D,McAvoy T J.Nonlinear principal component analysis based on principal curvesand neural networks[J].Comput Chem Eng,1996,20(1): 65-78
35. Misra M,Yue H H,Qin S J,et al.Multivariate process monitoring and fault diagnosis by multi-scale PCA[J].Computers and Chemical Engineering 2002,26(9):1281–1293
36. Wenfu K,Storer R H,Georgakis C.Disturbance detection and isolation by dynamic principal component analysis[J].Chemometrics and intelligent lab system,1995,30:179-196
37. Cho J H,Lee J M ,Choi S W,et al.Fault identification for process monitoring using kernel principal component analysis[J].Chemical Engineering Science,2005,60(1):279– 288
38. Choi S W,Lee C,Lee J M,et al.Fault detection and identification of nonlinear processes based on kernel PCA[J].Chemometrics and Intelligent Laboratory Systems,2005,75:55– 67
39. Kim D,Lee I B.Process monitoring based on probabilistic PCA[J].Chemometrics and Intelligent Laboratory Systems,2003,67:109–123
40. Lee J M,Yoo C K,Lee I B.Fault detection of batch processes using multi-way kernel principal component analysis[J].Computers and Chemical Engineering,2004,28(9): 1837–1847
41. Tipping M E,Bishop C M.Probabilistic Principal Component Analysis[J].Journal of the Royal Statistical Society,Series B 61,1997:611-622 (part 3)
42.赵忠盖,刘飞.工业过程核概率主元模型建立及监控指标[J].华东理工大学学报,2006, 32(7):864-867
43. Kresta J V,Marlin T E,MacGregor J F.Multivariable statistical monitoring of process operating performance[J].Can. J. of Chem.Eng,69,1991:35-47
44. Roweis S.EM algorithms for PCA and SPCA[J].Advances in Neural Information Processing System,1998(10):626-632
45.王惠文.偏最小二乘回归方法及其应用[M].北京:国防工业出版社,1999
46. McLachlan G,Krishnan T.The EM algorithm and extensions[M].Wiley series in probability and statistics,John Wiley & Sons,1997
47. Liu F,Zhao Z G.Chemical Separation Process Monitoring Based on Nonlinear Principal Component Analysis[C].Lecture notes in computer science,Springer,2004,v3173,798-803
48.刘直芳,游志胜,王运琼.基于概率主成分分析的人脸识别[J].红外与激光工程,2004,33(1):71-75
49. Chen J, Liu K C.On-line batch process monitoring using dynamic PCA and dynamic PLS models[J].Chemical Engineering Science,2002,57(1):63-75
50. Treasure R J,Kruger U,Cooper J E.Dynamic multivariate statistical process control using subspace identification[J].Journal of Process Control,2004,14(3): 279-292
51. Hyvarinen A.New approximations of differential entropy for independent component analysis and projection pursuit[J].In Advances in Neural Information Processing Systems,1998,10:273-279
52. Downs J J,Vogel E F.A plant-wide industrial-process control problem[J].Computers & Chemical Engineering,1993,17(3):245-255
53.赵忠盖,刘飞.因子分析及其在过程监控中的应用[J].化工学报, 2007,58(4):970-974
54. Sch?lkopf B,Smola A J,Müller K.Nonlinear component analysis as a kernel eigvalue problem[J].Neural Computation,1998,10(5):1000-1016
55. Wu J N,Wang J,Liu L.Feature extraction via KPCA for classification of gait patterns[J].Human Movement Science,2007,26(3):393-411
56. Lee J M,Yoo C K,Choi S W,et al.Nonlinear process monitoring using kernel principal component analysis[J].Chemical Engineering Science,2004,59(1):223-234
57. Krammer M A.Nonlinear principal component analysis using autoassociative neural networks[J].AIChE Journal,1991,37(2):233-243
58. Michael E T.Sparse kernel principal component analysis[J].Advances in Neural Information Processing Systems,2000:633-639
59. Harris T J,Ross W H.Statistical process control procedures for correlated observations[J]. The Canadian Journal of Chemical Engineering ,1991,69(2):48-57
60.沈倩,刘育明,梁军.基于DPCA方法的故障检测与诊断分析[J].制造业自动化2005,27(6):51-54
61.沈复,李阳初.石油加工单元过程原理(上册)[M].北京:中国石化出版社,1996.
2.胡峰,孙国基.过程监控技术及其应用[M].国防工业出版社,2001
3.杨叔子,郑晓军.人工智能与诊断专家系统[M].西安交通大学出版社,1990
4.吴今培,肖健华.智能故障诊断与专家系统[M].科学出版社,1997
5. Raich A C,Cinar A.Statistical process monitoring and disturbance diagnosis in multivariable continuous processes[J].AIChE J, 1996, 42(4):995-1009
6. Frank, P M.Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy-a survey and some new results [J].Automatica,1990, 26 (3):459-474
7. Venkatasubramanian V, Rengaswamy R, Yin K, et al.A review of process fault detection and diagnosis Part I:Quantitative model-based methods[J].Computers and Chemical Engineering, 2003, 27(3):293-311
8. Jiang B, Fahmida N C.Parameter fault detection and estimation of a class of nonlinear systems using observers[J].Journal of the Franklin Institute, 2005, 342(7): 725-736
9. Frank K, Anselm S. Isermann, R.Fault detection for modern diesel engines using signal and process model-based methods[J].Control Engineering Practice.2005,13(2):189- 203
10. Kinnaert M, Vrancic D, Denolin E,et al.Model-based fault detection and isolation for a gas-liquid separation unit[J].Control Engineering Practice,2000,8(11):1273-1283
11. Gertler J.Analytical redundancy methods in fault detection and isolation[C].In Proceeding of IFAC/IAMCS symposium on safe process,1991:91-96
12. Gertler J.Fault detection and isolation using parity relation[J].Control Engineering Practice,1997,5(5):653-661
13. Isermann R.Fault diagnosis of machines via parameter estimation and knowledge processing–tutorial paper[J].Automatica,1993, 29(4): 815-835
14.闻新,张洪钺,周露.控制系统的故障诊断和容错控制[M].北京:机械工业出版社,1998
15. Balle P.Fuzzy-model-based parity equations for fault isolation[J].Control engineering practice,1999,7(2):261-270
16. Balle P,Fuessel D.Closed-loop fault diagnosis based on a nonlinear process model and automatic fuzzy rule generation[J].Engineering Application of Artificial Intelligence.2000, 13(6):695-704
17. Venkatasubramanian V,Rengaswamy R,Yin K,et al.A review of process fault detection and diagnosis Part II: Qualitative models and search strategies[J].Computers and Chemical Engineering, 2003, 27(3):313-326
18. Palshikar G K, Khemani D.Diagnosing dynamic systems using trace patterns[J].Pattern Recognition letters,1999,20(7):741-753
19.陈玉东,施颂椒,翁正新.动态系统的故障诊断方法综述[J].化工自动化及仪表,2001,28(3):1-14
20.高桂革,顾幸生.小波变换在分布参数系统控制中的应用[J].清华大学学报,2007,47(S2):1862-1865
21. Kumamaru K,Hu J,Inoue K,et al.Robust fault detection using index of kullback discrimination information[C].Proceeding of IFAC world congress,San Francisco,USA,1996: 205-210
22. Venkatasubramanian V,Rengaswamy R,Yin K,et al.A review of process fault detection and diagnosis part III:process history based methods[J].Computers and Chemical Engineering, 2003,27(3):327-346
23. Chiang L H,Russell E L,Braatz R D.Fault Detection and Diagnosis in Industrial System[M].Springer-Verlag,London,2001
24. Raich A C,Cinar A.Multivariate statistical methods for monitoring continuous processes: assessment of discrimination power of disturbance models and diagnosis of multiple disturbances[J].Chemometrics and Intelligent Laboratory Systems,1995,30:37-48
25. MacGregor J F.Using on-line process data to improve quality: challenges for statisticians [J].Int.Stat.Rev,1997,65(3):309-323
26. Bakshi B R.Multiscale PCA with application to multivariate statistical process monitoring [J].AIChE J,1998,44(7):1596-1610
27. Negiz A,Cinar A.Statistical monitoring of multivariable dynamic processes with state-space models[J].AIChE J,1997, 43(8):2002-2020
28.孙静.接近零不合格过程质量的质量控制[M].清华大学出版社,2001
29. Box G,Luceno A.Statistical control by monitoring and feedback adjustment -- A Discussion[J].Technology,1985,17(4):176-209
30.张杰,阳宪惠.多变量统计过程控制[M].北京:化学工业出版社,2000
31. Jackson J E.Principal components and factor analysis: partⅠ- principal components [J]. J. Qual.Tech,1980,12(4):201-213
32. Jose C,Jesus P.Online monitoring of batch processes using multi-phase principal component analysis.Journal of Process Control, 2006, 16(10):1021-1035
33. Eitle D,Gunkel S,Gundy K V.Cumulative exposure to stressful life events and male gang membership[J].Journal of Criminal Justice,2004,32(2):95-111
34. Dong D,McAvoy T J.Nonlinear principal component analysis based on principal curvesand neural networks[J].Comput Chem Eng,1996,20(1): 65-78
35. Misra M,Yue H H,Qin S J,et al.Multivariate process monitoring and fault diagnosis by multi-scale PCA[J].Computers and Chemical Engineering 2002,26(9):1281–1293
36. Wenfu K,Storer R H,Georgakis C.Disturbance detection and isolation by dynamic principal component analysis[J].Chemometrics and intelligent lab system,1995,30:179-196
37. Cho J H,Lee J M ,Choi S W,et al.Fault identification for process monitoring using kernel principal component analysis[J].Chemical Engineering Science,2005,60(1):279– 288
38. Choi S W,Lee C,Lee J M,et al.Fault detection and identification of nonlinear processes based on kernel PCA[J].Chemometrics and Intelligent Laboratory Systems,2005,75:55– 67
39. Kim D,Lee I B.Process monitoring based on probabilistic PCA[J].Chemometrics and Intelligent Laboratory Systems,2003,67:109–123
40. Lee J M,Yoo C K,Lee I B.Fault detection of batch processes using multi-way kernel principal component analysis[J].Computers and Chemical Engineering,2004,28(9): 1837–1847
41. Tipping M E,Bishop C M.Probabilistic Principal Component Analysis[J].Journal of the Royal Statistical Society,Series B 61,1997:611-622 (part 3)
42.赵忠盖,刘飞.工业过程核概率主元模型建立及监控指标[J].华东理工大学学报,2006, 32(7):864-867
43. Kresta J V,Marlin T E,MacGregor J F.Multivariable statistical monitoring of process operating performance[J].Can. J. of Chem.Eng,69,1991:35-47
44. Roweis S.EM algorithms for PCA and SPCA[J].Advances in Neural Information Processing System,1998(10):626-632
45.王惠文.偏最小二乘回归方法及其应用[M].北京:国防工业出版社,1999
46. McLachlan G,Krishnan T.The EM algorithm and extensions[M].Wiley series in probability and statistics,John Wiley & Sons,1997
47. Liu F,Zhao Z G.Chemical Separation Process Monitoring Based on Nonlinear Principal Component Analysis[C].Lecture notes in computer science,Springer,2004,v3173,798-803
48.刘直芳,游志胜,王运琼.基于概率主成分分析的人脸识别[J].红外与激光工程,2004,33(1):71-75
49. Chen J, Liu K C.On-line batch process monitoring using dynamic PCA and dynamic PLS models[J].Chemical Engineering Science,2002,57(1):63-75
50. Treasure R J,Kruger U,Cooper J E.Dynamic multivariate statistical process control using subspace identification[J].Journal of Process Control,2004,14(3): 279-292
51. Hyvarinen A.New approximations of differential entropy for independent component analysis and projection pursuit[J].In Advances in Neural Information Processing Systems,1998,10:273-279
52. Downs J J,Vogel E F.A plant-wide industrial-process control problem[J].Computers & Chemical Engineering,1993,17(3):245-255
53.赵忠盖,刘飞.因子分析及其在过程监控中的应用[J].化工学报, 2007,58(4):970-974
54. Sch?lkopf B,Smola A J,Müller K.Nonlinear component analysis as a kernel eigvalue problem[J].Neural Computation,1998,10(5):1000-1016
55. Wu J N,Wang J,Liu L.Feature extraction via KPCA for classification of gait patterns[J].Human Movement Science,2007,26(3):393-411
56. Lee J M,Yoo C K,Choi S W,et al.Nonlinear process monitoring using kernel principal component analysis[J].Chemical Engineering Science,2004,59(1):223-234
57. Krammer M A.Nonlinear principal component analysis using autoassociative neural networks[J].AIChE Journal,1991,37(2):233-243
58. Michael E T.Sparse kernel principal component analysis[J].Advances in Neural Information Processing Systems,2000:633-639
59. Harris T J,Ross W H.Statistical process control procedures for correlated observations[J]. The Canadian Journal of Chemical Engineering ,1991,69(2):48-57
60.沈倩,刘育明,梁军.基于DPCA方法的故障检测与诊断分析[J].制造业自动化2005,27(6):51-54
61.沈复,李阳初.石油加工单元过程原理(上册)[M].北京:中国石化出版社,1996.