Uncertainty quantification in the calculation of k_{eff} using sensitity and stochastic sampling method

Hu Ze-Hua^{1,1}, Ye Tao^{1,2}, Liu Xiong-Guo^{1,2}, Wang Jia^{1,2}

1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China; 2. Software Center for High Performance Numerical Simulation, China Academy of Engineering Physics, Beijing 100088, China

Abstract The sensitivity and uncertainty analysis(S/U) method based on the first order perturbation theory is commonly employed to calculate the uncertainties in-nuclear reactor's integral parameters, such as the neutron effective multiplication factor(k_{eff}), due to uncertainties in nuclear data. However, this method is only theoretically suitable for the linear model because of its first order approximation. Moreover, S/U method is difficult to incorporate into a neutronics code, because the adjoint angular flux is needed to obtain the sensitivity coefficient of an integral parameter to nuclear data. Meanwhile, the sampling approach based on parametric random sampling of input parameters, an easy implemented method, evaluates the uncertainties in the integral parameters by performing a set of neutronics simulations inputted with a set of stochastic nuclear data sampled from a multinomial normal distribution with nuclear cross section mean values and covariance data. The sampling approach is considered as a more exact method, as linear approximation is not needed. With the increase of computational power, the sampling methods with consuming more time are now possible. The sampling approach is incorporated into SURE, a sensitivity and uncertainty analysis code developed in IAPCM, as a functional module. A careful verification of the new function is necessary before it is used to analyze complicated problems, such as multi-physical coupling calculations of nuclear reactor. Two simple fast criticality benchmark experiments, namely Godiva(HEU-MET-FAST-001) and Jezebel(PU-MET-FAST-001), are selected to verify the sampling module of SURE. The uncertainties in nuclear data are given by multigroup covariance matrices processed from ENDF/B-VⅡ. 1 data. The uncertainties in the computed value of k_{eff} resulting from uncertainties in the nuclear data are calculated with both S/U and sampling methods. The uncertainties due to reaction cross sections for each nuclide in two benchmarks given by two methods with the multigroup covariance matrices are in good agreement. Since the S/U module of SURE code is verified extensively, the correctness of the sampling function of the code is confirmed as well. The distribution of the k_{eff} from the sampling approach obeys the normal distribution pretty well, which indicates that k_{eff} varies linearly with the nuclear data under its uncertainty range, since the nuclear data used in calculations are assumed to be normal distribution in the sampling method. The results from the sampling method also support the S/U method with linear approximation as a suitable uncertainty quantification method for k_{eff} calculation.

Fund:Project supported by the Key Laboratory of Neutron Physics of China Academy of Engineering Physics（Grant No. 2013AA02), Sub-item of Special Project of the National Energy Bureau, China（Grant No. 2015ZX06002008), National Magnetic Confinement Fusion Energy Research Project, China（Grant No. 2015GB108002).

Hu Ze-Hua,Ye Tao,Liu Xiong-Guo et al.. Uncertainty quantification in the calculation of k_{eff} using sensitity and stochastic sampling method[J]. Acta Physica Sinica, 2017, 66(1):
.
doi:10.7498/aps.66.012801.

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