Combination of sensitivity-based and random sampling-based methodologies for efficient uncertainty quantification calculations with control variates method

A combined method of the sensitivity-based and random sampling-based methodologies is proposed for efficient uncertainty quantification calculations. The proposed method is based on the control variates (CV) method, in which a mean value of a target parameter can be estimated efficiently with a help of a mockup parameter whose mean value is well known. Standard deviations can be also efficiently estimated from two mean values of stochastic parameters; a target parameter itself and its square. In the present work, the CV method is applied to a toy problem, in which a linear approximation to a target parameter is regarded as a mockup parameter. This case corresponds to our proposed method to combine the sensitivity-based and random sampling-based methodologies. Numerical results reveal that the proposed method efficiently works. As a preliminary test of application of our proposed method to realistic problems, nuclear fuel burnup calculations are considered, and uncertainties of nuclides number densities after burnup are calculated. Uncertainties of number densities of cesium-134 and europium-151 are calculated by the proposed method, and it is demonstrated that we can carry out uncertainty quantification calculations more efficiently with our proposed method than with the normal random sampling method.