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Regularization of Ill-Posed Surveillance and Diagnostic Measurements

  • Andrei V. Gribok
  • J. Wesley Hines
  • Aleksey Urmanov
  • Robert E. Uhrig
Chapter
Part of the Power Systems book series (POWSYS)

Abstract

Most data-based predictive modeling techniques have an inherent weakness in that they may give unstable or inconsistent results when the predictor data is highly correlated. Predictive modeling problems of this design are usually under constrained and are termed ill-posed. This paper presents several examples of ill-posed diagnostic problems and regularization methods necessary for getting accurate and consistent prediction results. The examples include plant-wide sensor calibration monitoring and the inferential sensing of nuclear power plant feedwater flow using neural networks, and non-linear partial least squares techniques, and linear regularization techniques implementing ridge regression and informational complexity measures.

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References

  1. Akaike H (1973) Information theory and an extension of the maximum likelihood principle, in 2nd International Symposium on Information Theory, Ed. B.N. Petrov and F. Csaki, pp. 267–281. Budapest: Akademiai KiadoGoogle Scholar
  2. Belsley DA, Kuh E, Welsch RE (1980) Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, John Wiley @ Sons, New YorkzbMATHCrossRefGoogle Scholar
  3. Bozdogan H (1996) Informational complexity criteria for regression models, Information Theory and Statistics Section on Bayesian Stat. Science. ASA Annual Meeting, Chicago, IL, Aug. 4–8Google Scholar
  4. Golub GH, Heath M, Wahba G (1979) “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics, 21, No. 2, pp. 215–223MathSciNetzbMATHCrossRefGoogle Scholar
  5. Gribok AV, Hines JW, Uhrig RE(2000) “Use of Kernel Based Techniques for Sensor Validation in Nuclear Power Plants,” American Nuclear Society International Topical Meeting on Nuclear Plant Instrumentation, Controls, and Human-Machine Interface Technologies ( NPIC HMIT 2000 ), Washington, DC, NovemberGoogle Scholar
  6. Gribok AV, Attieh I, Hines JW, Uhrig RE (2001) “Regularization of Feedwater Flow Rate Evaluation for Venturi Meter Fouling Problems in Nuclear Power Plants,” Nuclear Technology, 134 pp.3–14 Google Scholar
  7. Gross KC, Singer RM, Wegerich SW, Herzog JP, Van Alstine R, Bockhorst FK (1997) “Application of a Model-based Fault Detection System to Nuclear Plant Signals,” Proc. of the Intl. Conf. on Intelligent System Application to Power Systems, Seoul, Korea. pp. 60–65Google Scholar
  8. Hansen PC (1989) Regularization, GSVD and Truncated GSVD,BIT 29, pp. 491–504Google Scholar
  9. Hansen PC (1992) “Analysis of discrete ill-posed problems by means of the L-curve,” SIAM Review, Vol. 34, No. 4, pp. 561–580MathSciNetzbMATHCrossRefGoogle Scholar
  10. Hines JW, Uhrig RE, Black C, Xu X (1997) “An Evaluation of Instrument Calibration Monitoring Using Artificial Neural Networks,” published in the proceedings of the 1997 American Nuclear Society Winter Meeting, Albuquerque, NM, November 16–20Google Scholar
  11. Hines JW, Uhrig, RE, Wrest DJ (1998) “Use of Autoassociative Neural Networks for Signal Validation,” Journal of Intelligent and Robotic Systems. 21: 143–154CrossRefGoogle Scholar
  12. Hines JW, Gribok AV, Attieh I, Uhrig RE (1999) “Regularization Methods for Inferential Sensing in Nuclear Power Plants,” Fuzzy Systems and Soft Computing in Nuclear Engineering, Ed. Da Ruan, Springer, 1999Google Scholar
  13. Hines JW, Gribok AV, Attieh I, Uhrig RE (2000) “Neural Network Regularization Techniques for a Sensor Validation System,” American Nuclear Society Annual Meeting, San Diego, California, June 4–8, 2000Google Scholar
  14. Hines JW, Rasmussen B (2001) “On-Line Sensor Calibration Verification: A Survey,” Proceedings of the 14th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management, Manchester, England, September, 2001Google Scholar
  15. Hoerl AE, Kennard RW (1970) “Ridge regression: biased estimation for nonorthogonal problems,” Technometrics, 12, pp. 55–67zbMATHCrossRefGoogle Scholar
  16. Konishi S, Kitagawa G (1996) “Generalized information criteria in model selection,” Biometrika, 83, No. 4, pp. 875–890MathSciNetzbMATHCrossRefGoogle Scholar
  17. Kramer MA (1991) “Nonlinear Principal Component Analysis Using Autoassociative Neural Networks,” AIChE Journal, Vol. 37, No. 2, pp. 233–243CrossRefGoogle Scholar
  18. Li M, Vitanyi P (1997) An introduction to Kolmogorov complexity and its applications, Springer-Verlag New York, Inc.zbMATHGoogle Scholar
  19. Linhart H, Zucchini W (1986) Model Selection, Wiley Series in Probability and Mathematical Statistics, John Wiley Sons, Inc.zbMATHGoogle Scholar
  20. MacKay D (1992) “A practical Bayesian framework for backprop networks,” Neural Computation, 4: pp. 448–472CrossRefGoogle Scholar
  21. Mallows CL (1973) “Some comments on Ce,” Technometrics, 15, No. 4, pp. 661–675zbMATHGoogle Scholar
  22. Miller AJ (1990) Subset selection in regression, Monographs on Statistics and Applied Probability, Chapman and HallzbMATHGoogle Scholar
  23. Morozov VA (1966) “On the solution of functional equations by the method of regularization,” Soviet Math. Dokl., 7, pp. 414–417MathSciNetzbMATHGoogle Scholar
  24. Qin SJ, McAvoy TJ (1992) “Nonlinear PLS Modeling Using Neural Networks,” Computers in Chemical Engineering, 16, No. 4, pp. 379–391CrossRefGoogle Scholar
  25. Rasmussen B, Hines JW, Uhrig RE (2000a) “Nonlinear Partial Least Squares Modeling for Instrument Surveillance and Calibration Verification,” published in the proceedings of the Maintenance and Reliability Conference (MARCON 2000 ), Knoxville, TN, May 7–10Google Scholar
  26. Rasmussen B, Hines JW, Uhrig RE (2000b) “A Novel Approach to Process Modeling for Instrument Surveillance and Calibration Verification,” The Third American Nuclear Society International Topical Meeting on Nuclear Plant Instrumentation and Control and Human-Machine Interface Technologies, Washington DC, November 13–17, 2000Google Scholar
  27. Reed RD, Marks RJ (1999) Neural Smithing, MIT Press, Cambridge MA, Chapter 7Google Scholar
  28. Rissanen J (1989) Stochastic complexity in statistical inquiry, World Scientific Publishing Co. Pte. Ltd.Google Scholar
  29. Schwaz R (1978) “Estimating the dimension of a model,” Ann. Statist. 6, 461–464MathSciNetCrossRefGoogle Scholar
  30. Uhrig RE (1991) “Potential Application of Neural Networks to the Operation of Nuclear Power Plants,” Nuclear Safety, 32, No. 1. pp 68–79Google Scholar
  31. Upadhyaya BR (1985) “Sensor Failure Detection and Estimation,” Nuclear Safety Google Scholar
  32. Upadhyaya BR, Holbert K (1989) “Development and Testing of an Integrated Signal Validation System for Nuclear Power Plants,” DOE Contract DE-ACO2–86NE37959, 1989Google Scholar
  33. Upadhyaya BR, Eryurek E (1992) “Application of Neural Networks for Sensor Validation and Plant Monitoring,” Nuclear Technology, 97, 170–176Google Scholar
  34. Urmanov A, Gribok A, Hines JW, Rasmussen B (2001) “Application of Information Complexity in Principal Component Regression Modeling of the Venturi Meter Drift,” published in the proceedings of the Maintenance and Reliability Conference (MARCON 2000), Knoxville, TN, May 6–9Google Scholar
  35. Urmanov AM, Gribok AV, Hines JW, Uhrig RE (2000) “Complexity-penalized model selection for feedwater inferential measurements in nuclear power plants,” ANS International Topical Meeting on Nuclear Plant Instrumentation, Controls, and Human-Machine Interface Technologies (NPIC HMIT 2000), Washington, DC van Emden MH (1971) “An analysis of complexity,” Mathematical Centre Tracts, 35, AmsterdamGoogle Scholar
  36. Vapnik VN (1995) The nature of statistical learning theory, Springer-Verlag New York, Inc.zbMATHGoogle Scholar
  37. Wallace CS, Freeman PR (1987) “Estimation and inference by compact coding,” J.R.Statst. Soc. B, 49, pp. 240–252Google Scholar
  38. Zavaljevski N, Gross KC, Wegerich SW (1999) “Regularization Methods for the Multivariate State Estimation Technique (MSET),” Proc. of the Int. Conf. on Mathematics and Computations, Reactor Physics and Environmental Analysis in Nuclear Applications, September 27–30 1999, Madrid Spain, pp. 720–729Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Andrei V. Gribok
    • 1
  • J. Wesley Hines
    • 1
  • Aleksey Urmanov
    • 1
  • Robert E. Uhrig
    • 1
  1. 1.The University of TennesseeNuclear Engineering DepartmentKnoxvilleUSA

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