Neutron field reconstruction with consideration of the spatial correlation of the cross-section value error
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ron Field Reconstruction with Consideration of the Spatial Correlation of the CrossSection Value Error A. A. Semyonov, A. A. Druzhaev*, and N. V. Schukin National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia *email: [email protected] Received July 4, 2012
Abstract—A method for reconstructing the neutron field in a reactor with consideration of the spatial corre lation of the crosssection value error was analyzed. It was shown that this method is more accurate than the classical approach to reconstruction. An efficient way of using this technique was proposed. The efficiency for the RBMK critical test facility was estimated. Keywords: neutron field reconstruction, crosssection value errors, correlations, RBMK critical test facility. DOI: 10.1134/S1063778814130109
INTRODUCTION Realtime monitoring is now obligatory for all types of power reactors. Monitored are the safety related parameters such as the fuel temperature, the integrity of fuelelement claddings, and the proper functionality of incore sensors. The values of these parameters are estimated on the basis of the incore sensor signals. Since the list of controlled parameters does not match the list of measured parameters, one is forced to invoke the mathematical procedure of reconstructing the values of unknown variables. This procedure normally uses a priori knowledge of both the object structure (the mathematical model of the object) and the probable deviations of the mathe matical model from reality (the model of noise or errors). The results of parameter estimation depend significantly on both the model of the object and the noise model. Two basic approaches to reconstruction are used in reactor calculations. (1) Parameter fitting method: L( p1, φ) = q(p 2 );⎫ (1) ⎬ M φ = m, ⎭ where L is the transfer operator, M is the sensor posi tioning operator, ϕ is the neutron flux vector, q is the neutron source vector, m is the sensor readings vector, and p1 and p2 are the vectors of fitted parameters of the mathematical model. (2) Linearization method: L φ = q(p 2 );⎫ (2) ⎬ M φ = m. ⎭ The parameter fitting procedure involves identify ing the p1 and p2 mathematical model parameters that are known with a large uncertainty and finding their
values that minimize the deviation of the calculation results from the measurement results. The linearization method is a particular case of the parameter fitting method where the fitted parameters are volume neutron sources and deviations of the sen sor readings. The linearization with respect to the unknown neutron flux is used to solve the problem. This method has become widely used owing to the availability of efficient computational procedures for the determination of these parameters. Both approaches significantly restrict the descrip tion of uncertainties of the mathematical model. The first approach does not allow one to take into account the random parameter fluctuations such as the fluctu ations of water density in a turbulent flow of coolant through the core: there ar
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