Bi-fidelity adaptive sparse reconstruction of polynomial chaos using Bayesiancompressive sensing

Abstract In recent years, non-intrusive polynomial chaos expansion (NIPCE) has been known as a practical method for uncertainty quantification (UQ) of stochastic problems. However, this method suffers from the curse of dimensionality, such that the computational cost of constructing the expansion rises dramatically with an increase in the dimension of the stochastic space. Due to this issue, the application of classical NIPCE in real-world industrial problems with a large number of uncertainty sources is unaffordable. To manage the computational cost of UQ in high-dimensional stochastic problems, this paper introduces a novel efficient method for multi-fidelity sparse reconstruction of NIPCE. The developed framework is established by incorporating a multi-task adaptive Bayesian compressive sensing (MTABCS) method into the regression-based NIPCE. Firstly, a set of inexpensive deterministic computations is used to compress the chaos expansion by recovering the bases strongly affecting the response. Subsequently, the sparsely constructed expansion is refined according to a limited number of high-fidelity computations. Two challenging CFD test cases, namely, the transonic RAE2822 airfoil and the NASA rotor 37, are considered to assess the performance of the developed method in realistic large-sized engineering problems. The investigations indicated that, in addition to a considerable reduction in computational cost, the present method is able to accurately reproduce the results of the classic NIPCE. It is observed that the MTABCS approach reduces the computation workload of UQ analysis in the test cases by one order of magnitude compared to the standard chaos expansion method.