RBF principal manifolds for process monitoring

IEEE Transactions on Neural Networks

Volumn 10, Issue 6, 1999, Pages 1424-1434

  Wilson, David J H ^b   Irwin, George W ^a,b   Lightbody, Gordon ^a,b  

^a IEEE

^b QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TRANSFORMATIONS; OPTIMIZATION; PROCESS CONTROL; SENSORS; STATISTICAL METHODS;

PRINCIPAL COMPONENT ANALYSIS (PCA); RADIAL BASIS FUNCTION (RBF) NETWORKS;

NEURAL NETWORKS;

EID: 0033310095     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.809087     Document Type: Article

References (30)

1. P. Bekker and J. de Leeuw, "Relations between variants of nonlinear principal components analysis," in Component and Correspondent Analysis, Dimension Reduction by Function Approximation, J. L. A. van Rijckesvorsel and J. de Leeuw, Eds. New York: Wiley, 1988, pp. 1-31.
2. C. M. Bishop, "Curvature-driven smoothing in backpropagation neural networks," Proc. IEEE Int. Conf. Neural Networks, 1990, pp. 749-753.
3. C. L. Chen, W. C. Chen, and F. W. Chang, "Hybrid learning algorithm for Gaussian potential function networks," Proc. Inst. Elect. Eng. Control Theory Applicat., vol. 140, Part D, no. 6, pp. 442-448, 1993.
4. D. Dong and T. J. McAvoy, "Nonlinear principal component analysis-based on principal curves and neural networks," Comput. Chem. Eng., vol. 20, no. 1, pp. 65-78, 1996.
5. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization. San Diego, CA: Academic, 1981.
6. F. Girosi, M. Jones, and T. Poggio, "Regulariztion theory and neural networks architectures," Neural Comput., vol. 7, pp. 219-269, 1995.
7. T. Hastie and W. Stuetzle, "Principal curves," J. Amer. Statist. Assoc., vol. 84, no. 406, pp. 502-516, 1989.
8. J. E. Jackson, A User's Guide to Principal Components. New York: Wiley, 1991.
9. J. Karhunen and J. Joutsensalo, "Generalizations of principal component analysis, optimization problems, and neural networks," Neural Networks, vol. 8, no. 4, pp. 549-562, 1995.
10. B. Kegl, A. Krzyzak, T. Linder, and K. Zeger, "A polygonal line algorithm for constructing principal curves," in Proc. Neural Inform. Processing Syst., 1999.
11. T. Kohonen, Self-Organization and Associative Memory. Berlin, Germany: Springer-Verlag, 1984.
12. T. Kourti and J. F. MacGregor, "Process analysis, monitoring and diagnosis, using multivariate projection methods," Chemometrics Intell. Lab. Syst., vol. 28, pp. 3-21, 1995.
13. T. Kourti, P. Nomikos, and J. F. MacGregor, "Analysis, monitoring and fault diagnosis of batch processes using multiblock and multiway PLS," J. Process Contr., vol. 5, no. 4, pp. 277-284, 1995.
14. M. A. Kramer, "Nonlinear principal component analysis using autoassociative neural networks," AIChE J., vol. 37, no. 2, pp. 233-243, 1991.
15. M. LeBlanc and R. Tibshirani, "Adaptive principal surfaces," J. Amer. Statist. Assoc., vol. 89, no. 425, pp. 53-65, 1994.
16. D. Lowe, "The radial basis function network - Techniques, principles, and hints," RSRE Malvern, U.K., 1992.
17. _, "Nonlocal radial basis functions for forecasting and density estimation," in Proc. IEEE Int. Conf. Neural Networks, vol. 2, pp. 1197-1198, 1994.
18. E. B. Martin and A. J. Morris, "Nonparametric confidence bounds for process performance monitoring charts," J. Proc. Contr., vol. 6, no. 6, pp. 349-358, 1996.
19. S. McLoone, M. D. Brown, G. W. Irwin, and G. Lightbody, "A hybrid linear/nonlinear training algorithm for feedforward neural networks," IEEE Trans. Neural Networks, vol. 9, pp. 669-684, 1998.
20. W. H. Press, S. A. Teukolsky, W. T. Vetterlmg, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. New York: Cambridge Univ. Press, 1992.
21. B. Scholkopf, A. Smola, and K.-R. Muller, "Nonlinear component analysis as a kernel eigenvalue problem," Neural Comput., vol. 10, pp. 1299-1319, 1998.
22. A. J. Smola, S. Mika, and B. Scholkopf, "Quantization functionals and regularized principal manifolds," Tech. Rep. NC2-TR-1998-028, NeuroCOLT2 Tech. Rep. Series, 1998.
23. G. W. Stewart, Introduction to Matrix Computations. London, U.K.: Academic, 1973.
24. A. R. Webb, "An approach to nonlinear principal components analysis using radially symmetric kernel functions," Statist. Comput., vol. 6, pp. 159-168, 1996.
25. D. J. H. Wilson, G. W. Irwin, and G. Lightbody, "Fault detection in an overheads condenser using multivariate SPC," in Proc. UKACC Int. Conf. Contr. '96, Inst. Elect. Eng. Conf. Pub. 427, vol. 1, pp. 293-298.
26. _, "Nonlinear PLS modeling using radial basis functions," in Proc. Inst. Measurement Contr., vol. 19, 1997, pp. 211-220.
27. D. J. H. Wilson and G. W. Irwin, "Multivariate SPC using radial basis functions," in Proc. UKACC Int. Conf. Contr. 98, vol. 1, 1-4 Sept. 1998, p. 479-484.
28. B. M. Wise and N. L. Ricker, "Recent advances in multivariate statis tical process control improving robustness and stability," Proc. IFAC Symp. ADCHEM '91, pp. 125-130.
29. B. M. Wise and N. B. Gallagher, "The process chemometrics approach to process monitoring and fault detection," J. Proc. Control, vol. 6, no. 6, pp. 329-348, 1996.
30. L. Xu, E. Oja, and C. Y. Suen, "Modified hebbian learning for curve and surface fitting," Neural Networks, vol. 5, no. 3, pp. 441-457, 1992.