摘要
本文主要研究了运用多向主元分析法和核函数法概率密度估计相结合的多元统计过程监控技术对间歇生产过程进行实时的状态监测与故障诊断。用核函数法概率密度估计对间歇生产过程进行实时状态监测的主要优点是它属于非参数法概率密度估计的一种，不需要数据总体的任何先验知识或是假设而直接基于实测数据样本求出总体的概率分布密度函数，摆脱了对不可靠的先验知识的依赖。本文从这一背景出发，重点是对用核函数法概率估计对间歇生产过程实时状态监测的方法进行较广泛、深入的研究。
在传统的实时监测方法中缺乏合适的统计量能够反映间歇生产过程中主元空间的实时变化。针对这一缺点，本文首次提出用KDE提取主元的概率密度函数用作为实时状态监测图，应用于对间歇生产过程主元空间实时状态监测的问题上。
另外，本文也尝试用主元PDF对间歇生产过程的故障批次进行检测，取得了较好的效果，从而为今后间歇生产过程批次检测的问题提供了一个新的选择。
This paper investigates the application of the multivariate statistical process monitoring and control technology, which employs both Multiway Principal Component Analysis (MPCA) and Kernel Density Estimation (KDE), to real time status monitoring and fault diagnosis of batch production processes. KDE is a non-parametric method which is capable of extracting the population's Probability Density Function (PDF) based on data sample only without any a prior knowledge about the statistic properties of the data regime. In this thesis, it is conducted the implementation of the KDE for monitoring the performance of batch production processes.
The conventional real-time monitoring method does not use the non-parametrical PDF of the principal components, which are capable of indicating the real-time changes of batch production processes. To improve the monitoring sensitivity, it is for the first time to propose the utilization of the PDF of the principal components in real-time to monitor batch production process.
Besides the above-mentioned efforts, this thesis also applies the PDF of the principal components to detect the faulty batches of the batch process and the result is encouraging, which provides a new option for process inspection.
引文
[1]．胡遵素；切尔诺贝利事故及其影响与教训：辐射防护；第14卷第5期G(1994-9)
[2]．胡昌华，许化龙；控制系统故障珍断与容错控制的分析和设计；北京：国防工业出版社，2001
[3]. Brisk, M. L.; Process control: Theories and Profits. IFAC Congress, Perth, Australia.: 1993
[4]．陈前；关于工程大系统的状态监测与故障诊断；振动、测试与诊断：2002，Vol．22，No．3
[5]. Isermann. R.; Process Fault Detection Based on Modeling and Estimation Methods-A surrey; Automatic; 1984, Vol.20, pp387-404
[6]. Moor, R.L., M.A.Kramer; Expert systems in on-line process control; Chemical Process Control Ⅲ, Asilomer, USA, 1986, pp839-867
[7]. Zhang, J., P.D.Roberts, J.E.Eltis; Fault diagnosis of a. mixing process based on qualitative representation of physical behaviours; Journal of Intelligent and Robotic Systems; 1990, Vol3, No.2, pp103-115
[8]. Zhang, J., P.D.Roberts, and J.E.Ellis; A self-learning fault diagnosis system; Transactions of the Institute of Measurement and Control; 1991, Vol13, No.1,pp29-35
[9]. Zhang, J., P.D.Roberts; Process fault diagnosis with diagnostic rules based structural decomposition; Journal of Process Control; 1991, 1., pp259-269
[10]. Venkatasubramanian, V. and K.Chan; A neural network methodology for process fault diagnosis; AIChE J. 1989, 35, pp1993-2002
[11]. Watanabe, K., I.Matsura, M.Abe, M.Kubota, and D.M.Himmelblau; Incipient fault diagnosis of chemical process via artificial neural networks; AIChE J.. 1989.35. pp1803-1812
[12]. Zhang, J. and P.D.Roberts; Process fault diagnosis with diagnostic rules based structural decomposition; Journal of Process Control; 1991, 1, pp259-269
[13]. Zhang, J. and A.J.Morris; On-line process fault diagnosis using fuzzy neural networks; Intelligent Systems Engineering; 1994, 3, pp37-47
[14]．张杰，阳宪惠；多变量统计过程控制；化学工业出版社：ISBN 7-5025-2881-4：2000
[15]. Kowalski B., Gerlach R., Wold H., et al; Chemical Systems under Indirect Observation; 1982, North-Holland, AmSterdam, pp191-209
[16]. Wold H. Research papers in statistics; David F Eds, New York; Wiley, 1966
[17]. Wold H. Multivariate analysis; Krishnaiah P Eds; New York; Academic Press, 1966
[18]. MacGregor, J. F; Kourti, T; Statistical Process Control of Multivariate Processes, Control Engineering Prac.; 1995, Vol.3, No.3, pp403-414
[19]. Morud T E. Multivariate statistical process control; example from the chemical process industry; Journal of Chemometrics; 1996, Vol. 10, pp669-675
[20]．杜元虎，陈迪，黄文虎；系统状态监测的人工智能方法，东北林业大学学报，1998，Vol．26 No．6，pp49-52
[21]. Kourti T, MacGregor J F.; Process analysis, monitoring and diagnosis using multivariate projection methods; Chemometrics and Intelligent Laboratory Systems; 1995, Vol.28, pp3-21
[22]. Wise B M, Gallagher N B, MacGregor J F. The process chemometrics approach to process monitoring and fault detection. Newcastle: Preprints of the IFAC Workshop on On-line Fault Detection and Supervision in the Chemical Process Industries, 1995
[23]. Jackson, J.E.; Principal Components and Factor Analysis: Part 1, Principal Analysis; J.Qual.Technol. 12, 1980, pp201-pp213
[24]．任若恩，王惠文；多元统计数据分析，国防工业出版社，ISBN 7-118-01678-0，1997
[25]．方开泰：实用多元统计分析，华东师范大学出版社，1989
[26]．项静恬，史久恩：非线性系统中数据处理的统计方法；科学出版社；ISBN7-03-005640-X：1987
[27]．常宾宝，王树青；分批生产过程的监测与评价；自动化与仪表；2002(3)；pp29-31
[28]. Wold.S, K.Esbensen, P.Geladi; Principal component analysis; Chemometrics andIntelligent Laboratory Systems; 1987, 2(1～3): pp37-pp52
[29]. Fang L. G., Chen Q., Yang J., et al; Application of principal component analysis and kernel density estimation on structural damage detection; Proceedings of COMADEM, Birmingham, UK, 2002
[30]. Svante Wold; Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models; 1978, Vol.20, No.4, pp397-pp405
[31]. W.J.Krzanowski; Cross-Validation in Principal Component Analysis; 1987, Brometrics 43, pp575-pp584
[32]．成成，黄道；IPCA在故障检测与分离中的应用，化东理工大学学报，Vol．26，No．5，2000，pp502-505
[33]．王纲，赵立杰，辛小宁；基于多方向主元分析方法的间歇生产过程性能监视和故障诊断；沈阳化工学报；1999，Vol．13，No．3，pp190-196
[34]. Chen Q, Wynne R, Sandoz D J; Application of Principal Component Analysis and Kernel Density Estimation to Enhance Process Monitoring; Control Engineering Practise; 2002, 8 (5) , pp531-543
[35]．冯雄峰，阳宪惠，徐用懋：多元统计过程监控方示的平方预测误差分析：清华大学学报；1999，Vol．52，No．6，pp471-475
[36]．赵立杰，王纲等；非线性PCA方法在间歇生产过程性能监视和故障诊断中的应用；沈阳化工学院学报；2000；Vol．14，No．1，pp62-68
[37]. Barry M.Wise, Neal B. Gallagher; The Process Chemometrics Approach to Process Monitoring and Fault Detection; J. Proc. Cont., 1996, Vol.6, No.6, pp329-pp348
[38]. Robert L. Mason, Youn-Min Chou, John C. Young; Applying Hotelling T~2 Statistic to Batch Processes; Journal of Quality Technology; 2001, Vol.33, No.4, pp466-479
[39]. MacGregor, J. F., Nomikos, P.; Monitoring Batch Processes, in Batch Processing Systems Engineering: Current Status and Future Directions (NATO ASI Series F), eds. Reklaitis, Rippin, Hortacso, and Sunol, Heidelberg: Springer-Verlag
[40]. Marsh, C. E., Tucker, T. W.; Application of SPC Techniques to Batch Units: ISA Transactions, 1991, Vol.30, pp39-47
[41]. MacGregor,J.F., C.Jaeckle, C.Kiparissides, and M.Houtoudi; Process monitoring and diagnosis by multiblock PLS methods; AIChE J. 1994, 40:pp826-pp838
[42]. Wise, B.M., N.B.Gallagher, S.W.Buler, 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; Journal of Chemometric; 1999, 13(.3～4), pp379-396
[43]. Louwerse, D.J. and A.K.Smilde; Multivariate statistical process control of batch processes based three-way models; Chemical Engineering Science; 2000, Vol.55, pp1225-1235
[44]. Tracy, N. D., Young, J. C., Mason, R. L.; Multivariate Control Charts for Individual Observations; Journal of Quality Technology; 1992, Vol.24; pp88-95
[45]. Seber, G. A. F; Multivariate Observations; John Wiley & Sons; New York, NY, 1984
[46]. B.W. Silverman; Density Estimation, Chapman & Hall Ltd. 1986
[47]. David W. Scott; Multivariate Density. Estimation-theory, practice and visualization, John Wiley & Sons, Inc. 1992
[48]. Peter Hall, Simon J.Sheather, etc.; On Optimal Data-Based Bandwidth Selection in Kernel Density Estimation; 1991, Vol.78, No.2, pp263-pp269
[49]. Paul Nomikos, John F.MacGregor; Multivariate SPC Charts for Monitoring Batch Processes; Techinometrics; 1995; vol.37, No. 1, pp41-59
[50]. Philip R.C.Nelson, Paul A.Taylor, John F.MacGregor; Missing Data Methods in PCA and PLS: Score Calculations with Incomplete Observations; Chemometrics and Intelligent Laboratory Systems 35. 1996, pp45-pp65
[51]. Lars Gregersen, Sten Bay Jorgensen; Supervision of fed-batch fermentations; Chemical Engineering Journal 75; 1999; pp69-76
[52]. Paul Nomikos, John F.MacGregor; Monitoring Batch Processes Using Multiway Principal Component Analysis; 1994. Vol.40, No.8, pp1361-pp1375
[53]. Johnson, R.A. and Wichern, D.W.; Applied Multivariate Statistical Analysis; Englewood Cliffs; NJ: Prentice-Hall: 1988
[54]. Chew, V.; Simultaneous Prediction Intervals; Technometrics; 1968, Vol.10,pp323-330
[55]. Hahn, G.J. and Cockrum. M.B.; Adapting Control Charts to Meet Practical Needs: A Chemical Processing Application; Journal of Applied Statistics; 1987, Vol.14, pp35-52
[56]. Martin. E B, Morris. A J: Non-parametric confidence bounds for process performance monitoring charts: Journal of Process Control; 1996, Vol.143, No.2,pp132-144
[57]. Julian J. Faraway, Myoungshic Jhun; Bootstrap Choice of Bandwidth for Density Estimation; Journal of the American Statistical Association; 1990, Vol.85, No.412, pp1119-pp1122
[58]. MacGregor, J. F.: Using On-Line Process Data to Improve Quality: Challenges for Statisticians; International Statistical Review; 1997, Vol.65, No.3, pp309-323
[59]. Karlene A. Kosanovich, Kenneth S.Dahl and Michael J.Piovoso; Improved Process Understanding Using Multiway Principal Component Analysis; Ind. Eng. Chem. Res; 1996, Vol.35, pp138-146
[60]．李春葆：C++程序设计导学；清华大学出版社；ISBN 7-302-05111-9／TP.2991；2002