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http://dx.doi.org/10.1016/j.net.2018.02.003

Wavelet operator for multiscale modeling of a nuclear reactor  

Vajpayee, Vineet (Homi Bhabha National Institute)
Mukhopadhyay, Siddhartha (Homi Bhabha National Institute)
Tiwari, Akhilanand Pati (Homi Bhabha National Institute)
Publication Information
Nuclear Engineering and Technology / v.50, no.5, 2018 , pp. 698-708 More about this Journal
Abstract
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.
Keywords
Diagonalizing Transform; Filter Bank; Multiscale Modeling; Nuclear Reactor; Wavelets;
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1 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.   DOI
2 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.   DOI
3 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.   DOI
4 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.   DOI
5 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.   DOI
6 S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Machine Intell. 11 (7) (1989) 674-693.   DOI
7 K.C. Chou, A.S. Willsky, A. Benveniste, Multiscale recursive estimation, data fusion, and regularization, IEEE Trans. Autom. Control 39 (3) (1994) 464-478.   DOI
8 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.   DOI
9 D. Coca, S.A. Billings, Non-linear system identification using wavelet multiresolution models, Int. J. Control 74 (18) (2001) 1718-1736.   DOI
10 X.W. Chang, L. Qu, Wavelet estimation of partially linear models, Comput. Stat. Data Anal. 47 (1) (2004) 31-38.   DOI
11 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.   DOI
12 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.   DOI
13 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.   DOI
14 G.Y. Park, J. Park, P.Y. Seong, Application of wavelets noise-reduction technique to water-level controller, Nuclear Technol. 145 (2004) 177-188.   DOI
15 T. Tambouratzis, M. Antonopoulos-Domis, Parameter estimation during a transient application to BW Rstability, Ann. Nuclear Energy 31 (18) (2004) 2077-2092.   DOI
16 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.   DOI
17 A. Prieto-Guerrero, G. Espinosa-Paredes, Decay ratio estimation of bwr signals based on wavelet ridges, Nuclear Sci. Eng. 160 (3) (2008) 302-317.   DOI
18 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.   DOI
19 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.   DOI
20 V. Vajpayee, S. Mukhopadhyay, A.P. Tiwari, Multiscale subspace identification of nuclear reactor using wavelet basis function, Ann. Nuclear Energy 111 (2018) 280-292.   DOI
21 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.   DOI
22 V.Vajpayee, S.Mukhopadhyay, A.P. Tiwari, Subspace-basedwaveletpreprocessed data-driven predictive control, INCOSE Int. Symp. 26 (s1) (2016) 357-371.   DOI
23 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.   DOI
24 L. Ljung, System Identification: Theory for the User, second ed., Prentice Hall, Upper Saddle River, NJ, 1999.
25 H.M. Nounou, M.N. Nounou, Multiscale fuzzy kalman filtering, Eng. Appl. Artif. Intell. 19 (5) (2006) 439-450.   DOI
26 E.G. Gilbert, Controllability and observability in multivariable control systems, J. SIAM Control 1 (2) (1963) 128-151.
27 B. Friedland, Control Systems Design: an Introduction to State-space Methods, McGraw-Hill Higher Education, 1985.
28 R.G. Phillips, Reduced order modeling and control of two-time-scale discrete systems, Int. J. Control 31 (1980) 765-780.   DOI
29 P.V. Kokotovic, R.E. O'Malley, P. Sannuti, Singular perturbations and order reduction in control theory: an overview, Automatica 12 (1976) 123-132.   DOI