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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 lowfidelity 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.

Many candidate concepts of reusable space transportation vehicles have been proposed around the world. Our aim in this study is to apply an optimization method for conceptual designs of two-stage-to-orbit (TSTO) space planes with airbreathing engines on the first-stage boosters and to obtain necessary vehicle sizes and their optimal flight trajectories. First, we integrate analysis methods into the optimization problem, the solution of which yield the minimized total dry mass of the first-stage booster and the second-stage orbiter. This information allows us to determine the optimal vehicle configuration and flight trajectory for a highly feasible TSTO space plane. The optimal solutions show that TSTO space planes with boosters powered by rocket engines added to the airbreathing engines are lighter in total dry mass than vehicles with boosters propelled by only airbreathing engines. However, it is necessary to lighten and miniaturize vehicle components to achieve greater feasibility. In addition, the trajectory optimizations enable the booster to glide back to a launch site using little propellant, despite the long downrange path from the staging point of the ascent trajectory. This study confirms that the analysis and optimization method proposed are effective.

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