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
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 Kiado
Belsley DA, Kuh E, Welsch RE (1980) Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, John Wiley @ Sons, New York
Bozdogan H (1996) Informational complexity criteria for regression models, Information Theory and Statistics Section on Bayesian Stat. Science. ASA Annual Meeting, Chicago, IL, Aug. 4–8
Golub GH, Heath M, Wahba G (1979) “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics, 21, No. 2, pp. 215–223
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, November
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
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. 60–65
Hansen PC (1989) Regularization, GSVD and Truncated GSVD,BIT 29, pp. 491–504
Hansen PC (1992) “Analysis of discrete ill-posed problems by means of the L-curve,” SIAM Review, Vol. 34, No. 4, pp. 561–580
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 16–20
Hines JW, Uhrig, RE, Wrest DJ (1998) “Use of Autoassociative Neural Networks for Signal Validation,” Journal of Intelligent and Robotic Systems. 21: 143–154
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, 1999
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, 2000
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, 2001
Hoerl AE, Kennard RW (1970) “Ridge regression: biased estimation for nonorthogonal problems,” Technometrics, 12, pp. 55–67
Konishi S, Kitagawa G (1996) “Generalized information criteria in model selection,” Biometrika, 83, No. 4, pp. 875–890
Kramer MA (1991) “Nonlinear Principal Component Analysis Using Autoassociative Neural Networks,” AIChE Journal, Vol. 37, No. 2, pp. 233–243
Li M, Vitanyi P (1997) An introduction to Kolmogorov complexity and its applications, Springer-Verlag New York, Inc.
Linhart H, Zucchini W (1986) Model Selection, Wiley Series in Probability and Mathematical Statistics, John Wiley Sons, Inc.
MacKay D (1992) “A practical Bayesian framework for backprop networks,” Neural Computation, 4: pp. 448–472
Mallows CL (1973) “Some comments on Ce,” Technometrics, 15, No. 4, pp. 661–675
Miller AJ (1990) Subset selection in regression, Monographs on Statistics and Applied Probability, Chapman and Hall
Morozov VA (1966) “On the solution of functional equations by the method of regularization,” Soviet Math. Dokl., 7, pp. 414–417
Qin SJ, McAvoy TJ (1992) “Nonlinear PLS Modeling Using Neural Networks,” Computers in Chemical Engineering, 16, No. 4, pp. 379–391
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 7–10
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, 2000
Reed RD, Marks RJ (1999) Neural Smithing, MIT Press, Cambridge MA, Chapter 7
Rissanen J (1989) Stochastic complexity in statistical inquiry, World Scientific Publishing Co. Pte. Ltd.
Schwaz R (1978) “Estimating the dimension of a model,” Ann. Statist. 6, 461–464
Uhrig RE (1991) “Potential Application of Neural Networks to the Operation of Nuclear Power Plants,” Nuclear Safety, 32, No. 1. pp 68–79
Upadhyaya BR (1985) “Sensor Failure Detection and Estimation,” Nuclear Safety
Upadhyaya BR, Holbert K (1989) “Development and Testing of an Integrated Signal Validation System for Nuclear Power Plants,” DOE Contract DE-ACO2–86NE37959, 1989
Upadhyaya BR, Eryurek E (1992) “Application of Neural Networks for Sensor Validation and Plant Monitoring,” Nuclear Technology, 97, 170–176
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 6–9
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, Amsterdam
Vapnik VN (1995) The nature of statistical learning theory, Springer-Verlag New York, Inc.
Wallace CS, Freeman PR (1987) “Estimation and inference by compact coding,” J.R.Statst. Soc. B, 49, pp. 240–252
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. 720–729
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Gribok, A.V., Hines, J.W., Urmanov, A., Uhrig, R.E. (2002). Regularization of Ill-Posed Surveillance and Diagnostic Measurements. In: Ruan, D., Fantoni, P.F. (eds) Power Plant Surveillance and Diagnostics. Power Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04945-7_20
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DOI: https://doi.org/10.1007/978-3-662-04945-7_20
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