Use of 3D-VAR and Kalman Filter Approaches for Neutronic State and Parameter Estimation in Nuclear Reactors

Abstract In this paper, data assimilation (DA) techniques that have proven to be efficient in the fields of meteorological forecast and oceanography are applied to neutronics problems. Two applications, the techniques of which can be used to enhance optimization, are presented: three-dimensional (3-D) neutronic field interpolation in online core monitoring, and parameter estimation in code qualification procedures. First, the main bases of DA theory are shortly presented. Calibration and estimation procedures that are in use today at Electricité de France (EDF) are then briefly introduced. We also analyze the main limitations of these procedures and the potential improvements that the use of various DA techniques can provide. We present the MANARA mock-up, which computes a 3-D field interpolation and has been implemented in PALM, a DA-dedicated coupling platform developed at the Centre Européen de Recerche et de Formation Avancée en Calcul Scientifique (CERFACS). Result validation and comparison with former interpolation procedure CAMARET are also presented. Next, the principles of the KAFEINE mock-up, based on an extended Kalman filter approach, are displayed. This application covers the field of optimal parameter calibration using the in-core measures. In conclusion, these first two applications to neutronics, carried out in partnership between CERFACS and EDF Research and Development, seem very promising, especially considering the new generation of neutronic solvers that are being developed in the frame of the DESCARTES project.

[1]  A. Piacentini,et al.  A new representation of data‐assimilation methods: The PALM flow‐charting approach , 2001 .

[2]  Jacques Verron,et al.  A singular evolutive extended Kalman filter for data assimilation in oceanography , 1998 .

[3]  Jérôme Vialard,et al.  Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks , 2003 .

[4]  N. B. Ingleby,et al.  The Met. Office global three‐dimensional variational data assimilation scheme , 2000 .

[5]  Samuel Buis,et al.  PALM: a computational framework for assembling high-performance computing applications , 2006 .

[6]  Olivier Talagrand,et al.  Assimilation of Observations, an Introduction (gtSpecial IssueltData Assimilation in Meteology and Oceanography: Theory and Practice) , 1997 .

[7]  P. Courtier,et al.  The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). I: Formulation , 1998 .

[8]  Samuel Buis,et al.  PALM: a computational framework for assembling high‐performance computing applications , 2006, Concurr. Comput. Pract. Exp..

[9]  John Derber,et al.  The National Meteorological Center's spectral-statistical interpolation analysis system , 1992 .

[10]  S. Cohn,et al.  Ooce Note Series on Global Modeling and Data Assimilation Construction of Correlation Functions in Two and Three Dimensions and Convolution Covariance Functions , 2022 .

[11]  Anthony Hollingsworth,et al.  The statistical structure of short-range forecast errors as determined from radiosonde data , 1986 .

[12]  I. Rutherford.  Data Assimilation by Statistical Interpolation of Forecast Error Fields , 1972 .

[13]  Claude Lemaréchal,et al.  Some numerical experiments with variable-storage quasi-Newton algorithms , 1989, Math. Program..

[14]  Andrew F. Bennett,et al.  Inverse Methods in Physical Oceanography: Frontmatter , 1992 .

[15]  R. Daley.  Atmospheric Data Analysis , 1991 .

[16]  A. Bennett.  Inverse Methods in Physical Oceanography , 1992 .

[17]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[18]  A. Simmons,et al.  The ECMWF operational implementation of four‐dimensional variational assimilation. I: Experimental results with simplified physics , 2007 .

[19]  Geir Evensen,et al.  Advanced Data Assimilation for Strongly Nonlinear Dynamics , 1997 .

[20]  Stéphane Laroche,et al.  Implementation of a 3D variational data assimilation system at the Canadian Meteorological Centre. Part I: The global analysis , 1999 .

[21]  O. Talagrand.  Objective Validation and Evaluation of Data Assimilation , 2003 .