DOI QR코드

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Wavelet operator for multiscale modeling of a nuclear reactor

  • 투고 : 2017.04.19
  • 심사 : 2018.02.07
  • 발행 : 2018.06.25

초록

This article introduces a methodology of designing a wavelet operator suitable for multiscale modeling. The operator matrix transforms states of a multivariable system onto projection space. In addition, it imposes a specific structure on the system matrix in a multiscale environment. To be specific, the article deals with a diagonalizing transform that is useful for decoupled control of a system. It establishes that there exists a definite relationship between the model in the measurement space and that in the projection space. Methodology for deriving the multirate perfect reconstruction filter bank, associated with the wavelet operator, is presented. The efficacy of the proposed technique is demonstrated by modeling the point kinetics nuclear reactor. The outcome of the multiscale modeling approach is compared with that in the single-scale approach to bring out the advantage of the proposed method.

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참고문헌

  1. P.V. Kokotovic, R.E. O'Malley, P. Sannuti, Singular perturbations and order reduction in control theory: an overview, Automatica 12 (1976) 123-132. https://doi.org/10.1016/0005-1098(76)90076-5
  2. R.G. Phillips, Reduced order modeling and control of two-time-scale discrete systems, Int. J. Control 31 (1980) 765-780. https://doi.org/10.1080/00207178008961081
  3. D.S. Naidu, Singular perturbations and time scales in control theory and applications, Dyn. Contin.Discret. Impuls Sys. Ser. B: Appl. Algorithms 9 (2002) 233-278. https://doi.org/10.3934/dcds.2003.9.233
  4. S.R. Shimjith, A.P. Tiwari, B. Bandyopadhyay, A three-timescale approach for design of linear state regulator for spatial control of advanced heavy water reactor, IEEE Trans. Nuclear Sci. 58 (3) (2011) 1264-1276. https://doi.org/10.1109/TNS.2011.2114674
  5. M. Boroushaki, M.B. Ghofrani, C. Lucas, M.J. Yazdanpanah, Identification and control of a nuclear reactor core (VVER) using recurrent neural networks and fuzzy systems, IEEE Trans. Nuclear Sci. 50 (1) (Feb 2003) 159-174. https://doi.org/10.1109/TNS.2002.807856
  6. C. Shiguo, Z. Ruanyu, W. Peng, L. Taihua, Enhance accuracy in pole identification of system by wavelet transform de-noising, IEEE Trans. Nuclear Sci. 51 (1) (Feb. 2004) 250-255. https://doi.org/10.1109/TNS.2004.825098
  7. F. Previdi, S.M. Savaresi, P. Guazzoni, L. Zetta, Detection and clustering of light charged particles via system-identification techniques, Int. J. Adapt. Control Signal Process. 21 (2007) 375-390. https://doi.org/10.1002/acs.927
  8. S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Machine Intell. 11 (7) (1989) 674-693. https://doi.org/10.1109/34.192463
  9. K.C. Chou, A.S. Willsky, A. Benveniste, Multiscale recursive estimation, data fusion, and regularization, IEEE Trans. Autom. Control 39 (3) (1994) 464-478. https://doi.org/10.1109/9.280746
  10. D. Coca, S.A. Billings, Non-linear system identification using wavelet multiresolution models, Int. J. Control 74 (18) (2001) 1718-1736. https://doi.org/10.1080/00207170110089743
  11. X.W. Chang, L. Qu, Wavelet estimation of partially linear models, Comput. Stat. Data Anal. 47 (1) (2004) 31-38. https://doi.org/10.1016/j.csda.2003.10.018
  12. N.V. Troung, L. Wang, P.C. Young, Non-linear system modelling based on nonparametric identification and linear wavelet estimation of SDP models, In. J. Control 80 (5) (2007) 774-788. https://doi.org/10.1080/00207170601185996
  13. Y. Li, H.L. Wei, S.A. Billings, Identification of time-varying systems using multiwavelet basis functions, IEEE Trans. Control Sys. Technol. 19 (3) (2011) 656-663. https://doi.org/10.1109/TCST.2010.2052257
  14. F. He, H.L. Wei, S.A. Billings, Identification and frequency domain analysis of non-stationary and nonlinear systems using time-varying NARMAX models, Int. J. Sys. Sci. 46 (11) (2015) 2087-2100. https://doi.org/10.1080/00207721.2013.860202
  15. G. Heo, S.S. Choi, S.H. Chang, Thermal power estimation by fouling phenomena compensation using wavelet and principal component analysis, Nuclear Eng. Design 199 (2000) 31-40. https://doi.org/10.1016/S0029-5493(00)00249-1
  16. G.Y. Park, J. Park, P.Y. Seong, Application of wavelets noise-reduction technique to water-level controller, Nuclear Technol. 145 (2004) 177-188. https://doi.org/10.13182/NT04-A3468
  17. V.Vajpayee, S.Mukhopadhyay, A.P. Tiwari, Subspace-basedwaveletpreprocessed data-driven predictive control, INCOSE Int. Symp. 26 (s1) (2016) 357-371. https://doi.org/10.1002/j.2334-5837.2016.00337.x
  18. G. Espinosa-Paredes, A. Nunez-Carrera, A. Prieto-Guerrero, M. Cecenas, Wavelet approach for analysis of neutronic power using data of ringhals stability benchmark, Nuclear Eng. Design 237 (2007) 1009-1015. https://doi.org/10.1016/j.nucengdes.2006.01.020
  19. A. Prieto-Guerrero, G. Espinosa-Paredes, Decay ratio estimation of bwr signals based on wavelet ridges, Nuclear Sci. Eng. 160 (3) (2008) 302-317. https://doi.org/10.13182/NSE160-302
  20. M. Antonopoulos-Domis, T. Tambouratzis, System identification during a transient via wavelet multiresolution analysis followed by spectral techniques, Ann. Nuclear Energy 25 (6) (1998) 465-480. https://doi.org/10.1016/S0306-4549(97)00070-4
  21. T. Tambouratzis, M. Antonopoulos-Domis, Parameter estimation during a transient application to BW Rstability, Ann. Nuclear Energy 31 (18) (2004) 2077-2092. https://doi.org/10.1016/j.anucene.2004.07.006
  22. S. Mukhopadhyay, A.P. Tiwari, Consistent output estimate with wavelets: an alternative solution of least squares minimization problem for identification of the LZC system of a large PHWR, Ann. Nuclear Energy 37 (2010) 974-984. https://doi.org/10.1016/j.anucene.2010.03.006
  23. V. Vajpayee, S. Mukhopadhyay, A.P. Tiwari, Multiscale subspace identification of nuclear reactor using wavelet basis function, Ann. Nuclear Energy 111 (2018) 280-292. https://doi.org/10.1016/j.anucene.2017.09.001
  24. A. Gabor, C. Fazekas, G. Szederkenyi, K.M. Hangos, Modeling and identification of a nuclear reactor with temperature effects and xenon poisoning, Eur. J. Control 17 (1) (2011) 104-115. https://doi.org/10.3166/ejc.17.104-115
  25. L. Hong, G. Cheng, C.K. Chui, A filter-bank-based kalman filtering technique for wavelet estimation and decomposition of random signals, IEEE Trans. Circuits Sys. II: Analog Digit. Signal Process. 45 (2) (1998) 237-241. https://doi.org/10.1109/82.661660
  26. H.M. Nounou, M.N. Nounou, Multiscale fuzzy kalman filtering, Eng. Appl. Artif. Intell. 19 (5) (2006) 439-450. https://doi.org/10.1016/j.engappai.2005.11.001
  27. E.G. Gilbert, Controllability and observability in multivariable control systems, J. SIAM Control 1 (2) (1963) 128-151.
  28. B. Friedland, Control Systems Design: an Introduction to State-space Methods, McGraw-Hill Higher Education, 1985.
  29. L. Ljung, System Identification: Theory for the User, second ed., Prentice Hall, Upper Saddle River, NJ, 1999.