  The presence of uncertainties are inevitable in engineering design and
analysis, where failure in understanding their effects might lead to the
structural or functional failure of the systems. The role of global sensitivity
analysis in this aspect is to quantify and rank the effects of input random
variables and their combinations to the variance of the random output. In
problems where the use of expensive computer simulations are required,
metamodels are widely used to speed up the process of global sensitivity
analysis. In this paper, a multi-fidelity framework for global sensitivity
analysis using polynomial chaos expansion (PCE) is presented. The goal is to
accelerate the computation of Sobol sensitivity indices when the deterministic
simulation is expensive and simulations with multiple levels of fidelity are
available. This is especially useful in cases where a partial differential
equation solver computer code is utilized to solve engineering problems. The
multi-fidelity PCE is constructed by combining the low-fidelity and correction
PCE. Following this step, the Sobol indices are computed using this combined
PCE. The PCE coefficients for both low-fidelity and correction PCE are computed
with spectral projection technique and sparse grid integration. In order to
demonstrate the capability of the proposed method for sensitivity analysis,
several simulations are conducted. On the aerodynamic example, the
multi-fidelity approach is able to obtain an accurate value of Sobol indices
with 36.66% computational cost compared to the standard single-fidelity PCE for
a nearly similar accuracy.
