Abstract
This paper presents an analytical derivation and analysis of the uncertainty of the Multivariate State Estimation Technique (MSET). Like all other nonparametric techniques, MSET uncertainty consists of two parts: bias and variance. Bias is a systematic error in MSET inference and practically not computable and non-removable, but when properly regularized it is usually very small with respect to the variance when properly regularized. Variance, on the other hand, represents variability of the MSET estimate due to random noise in the data and can be estimated in real time. All the derivations and results are obtained for the inferential case. The MSET cost function is also derived which shows that MSET minimizes a weighted least squares cost function with weighting affected by the MSET memory matrix. The parallels between MSET and more traditional kernel techniques, namely kernel regression, are drawn and it is shown that MSET is a special type of kernel regression algorithm. The final section presents the results of the MSET uncertainty analysis for real world data obtained from a commercial nuclear power plant.
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Buckner, M. 2003. Learning from data with and localized regression and differential evolution. Ph.D. Dissertation, Nuclear Engineering Department, The University of Tennessee, Knoxville, USA.
Cherkassky, V., and Mulier, F. 1998. Learning From Data. New York: John Wiley & Sons, Inc.
Draper, N. R., and Smith, H. 1998. Applied Regression Analysis. New York: John Wiley & Sons, Inc.
Geman, S., Bienenstock, E., and Doursat, R. 1992. Neural networks and the bias/variance dilemma. Neural Computation 4(1): 1-58.
Girosi, F., Jones, M., and Poggio, T. 1995. Regularization theory and neural networks architectures. Neural Computation 7: 219-269.
Gribok, A. V., Hines, J. W., Attieh, I. K., and Uhrig, R. E. 2001. Regularization of feedwater flow rate evaluation for the Venturi meter fouling problems in nuclear power plants. Nuclear Technology 134(1): 3-14.
Gribok, A. V., Attieh, I. K., Hines, J. W., and Uhrig, R. E. 2001. Stochastic regularization of feedwater flow rate evaluation for the Venturi meter fouling problem in nuclear power plants. Inverse Problems in Engineering 9(6): 671-696.
Gribok, A. V., Hines, J. W., and Uhrig, R. E. 2000. Use of kernel based techniques for sensor validation in nuclear power plants. In The Third American Nuclear Society International Topical Meeting on Nuclear Plant Instrumentation and Control and Human-Machine Interface Technologies, Washington DC, November 13–17.
Gross, K. C. 1992. Spectrum-transformed sequential testing method for signal validation applications. In 8th Power Plant Dynamics, Control & Testing Symposium, Vol. 1, Knoxville, Tennessee, May, pp. 36.01-36.12.
Gross, K. C., Singer, R. M., Wegerich, S. W., Herzog, J. P., Alstine R. Van, and Bockhorst, F. 1997. Application of a model-based fault detection system to nuclear plant signals. In Proceedings, Intelligent System Applications to Power Systems, (ISAP). Seoul, Korea, July 6–10, pp. 66-70.
Gross, K. C., Wegerich, S. W., Singer, R. M., and Mott, J. E. 1998. Industrial Process Surveillance System, US Patent #5,764,509.
Hines, J. W., Wrest, D. J., and Uhrig, R. E. 1996. Plant wide sensor calibration monitoring. In Proceedings of the 1996 IEEE International Symposium on Intelligent Control. Dearborn, MI, September 15–18.
Hines, J. W., Gribok, A. V., Uhrig, R. E., and Attieh, I. K. 2000. Neural network regularization techniques for a sensor validation system. In Proceedings of American Nuclear Society Annual Meeting. San Diego, California, June 4–8.
Hines, J. W., Gribok, A. V., Attieh, I. K., and Uhrig, R. E. 2000. Improved methods for on-line sensor calibration verification. In Proceedings of 8th International Conference on Nuclear Engineering. Baltimore, MD, April 2–6.
Hines, J. W., Gribok, A. V., Attieh, I. K., and Uhrig, R. E. 1999. Regularization methods for inferential sensing in nuclear power plants. In Da Ruan (ed.), Fuzzy Systems and Soft Computing in Nuclear Engineering, Springer.
Hines, J. W., and Rasmussen, B. 2000. On-line sensor calibration verification: “a survey” Presented at the 14th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management, Manchester, England.
Mott, J. E., Young, R., and King, R. W. 1987. Pattern recognition software for plant surveillance. US DOE Report.
Pagan, A., and Ullah, A. 1999. Nonparametric Econometrics. Cambridge University Press.
Rasmussen, B., Hines, J. W., and Uhrig, R. E. 2000. Nonlinear partial least squares modeling for instrument surveillance and calibration verification. In Proceedings of the Maintenance and Reliability Conference (MARCON 2000). Knoxville, TN, May 7–10.
Schimek, M. G. 2000. Smoothing and Regression. Approaches, Computation, and Application. New York: John Wiley & Sons, Inc.
Singer, R. M., Gross, K. C., Herzog, J. P., King, R. W., and Wegerich, S. W. 1996. Model-based nuclear power plant monitoring and fault detection: theoretical foundations. In Proceedings of the 9th International Conference on Intelligent Systems Applications to Power Systems. Seoul, Korea.
Stone, C. J. 1982. Optimal global rates of convergence for nonparametric regression. Annals of Statistics 10: 1040-1053.
te Braake, H. A. B., van Can, H. J. L. V., and Verbruggen, H. B. 1998. Semi-mechanistic modeling of chemical processes with neural networks. Engineering Applications of Artificial Intelligence 11(4): 507-515.
Tikhonov, A. N., and Arsenin, V. Y. 1977. Solution of Ill-Posed Problems. Winston & Sons, Washington D.C.
Upadhyaya, B. R., and Eryurek, E. 1992. Application of neural networks for sensor validation and plant monitoring. Nuclear Technology 97: 170-176.
Vapnik, V. N. 1998. Statistical Learning Theory. New York: John Wiley & Sons, Inc.
Xu, Xiao, and Hines, J. W. 1998. On-line sensor calibration monitoring and fault detection for chemical processes. In Proceedings of the Maintenance and Reliability Conference (MARCON 98). Knoxville, TN, May 12–14.
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Gribok, A.V., Urmanov, A.M. & Hines, J.W. Uncertainty Analysis of Memory Based Sensor Validation Techniques. Real-Time Systems 27, 7–26 (2004). https://doi.org/10.1023/B:TIME.0000019124.24404.e9
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DOI: https://doi.org/10.1023/B:TIME.0000019124.24404.e9