Stochastic field representation using bi-fidelity combination of proper orthogonal decomposition and Kriging

Abstract

In the current paper efficient uncertainty quantification (UQ) of high dimensional stochastic fields is performed via a bi-fidelity surrogate model. The method is based on combination of proper orthogonal decomposition (POD) and Kriging method. In the developed method, the trend function of the Kriging model is estimated via a low cost POD, whilst the stochastic Gaussian contribution is tuned using a limited number of high-fidelity computations. The proposed method is applied to three test cases, including a highly nonlinear test function, thermally driven flow in a cavity with stochastic wall temperatures and turbulent heat transfer in a ribbed channel with stochastic heat flux boundary condition. Implementing both POD and POD–Kriging methods leads to significant reduction of computational cost in comparison to the classical full polynomial chaos expansion (PCE) with least cost saving of more than 60%. Furthermore, in all cases combined POD–Kriging method performs either superior or at least similar to the POD method. More specifically, in surrogate models with lower number of low- and high-fidelity samples greater gains in accuracy are obtained. Consequently, for a specific level of accuracy, POD–Kriging method requires lower computational cost.