Kriging Surrogate Modelling of Multiplication Factor With Random Effect

Abstract Large computational expenses hinder the use of Monte Carlo simulations in reactor design optimization. Surrogate modelling could therefore be used to reduce such computational expense by constructing computationally inexhaustive models for certain reactor responses of interests. However, the random effect inherited in Monte Carlo neutronics simulation results are generally not considered during constructing such surrogates, which is expected to result in large surrogate prediction biases. In this work, a stochastic Kriging surrogate modelling technique is used to reproduce Monte Carlo estimated multiplication factor while explicitly taking their random effects into account. It is shown that involving random effect in Kriging surrogate modelling process could significantly improve the accuracy of surrogate predicted multiplication factors. Specifically, it could mitigate the fluctuation appeared in Kriging surrogate predicting biases, and narrow the surrogate predictions centered around the mean values of referenced Monte Carlo simulated multiplication factor. It is analyzed that stochastic random effect resulted non-smoothing variation of multiplication factor with varying design inputs is responsible for such observation. As Kriging method follows Gaussian process assumption, where the commonly adopted Radial Basis Kernel (RBK) is not able to model the non-smoothing distance related correlation appeared in responses with random effect. Including an additional extrinsic covariance in the Kriging modelling process could therefore mitigate such non-smoothing behavior and stabilize surrogate model’s prediction performance.