Uncertainty quantification has proven to be an indispensable study for enhancing reliability and robustness of engineering systems in the early design phase. Single and multi-fidelity surrogate modelling methods have been used to replace the expensive high fidelity analyses which must be repeated many times for uncertainty quantification. However, since the number of analyses required to build an accurate surrogate model increases exponentially with the number of random input variables, most surrogate modelling methods suffer from the curse of dimensionality. As an alternative approach, the Low-Rank Approximation method can be applied to high-dimensional uncertainty quantification studies with a low computational cost, where the number of coefficients for building the surrogate model increases only linearly with the number of random input variables. In this study, the Low-Rank Approximation method is implemented for multi-fidelity applications with additive and multiplicative correction approaches to make the high-dimensional uncertainty quantification analysis more efficient and accurate. The developed uncertainty quantification methodology is tested on supersonic aircraft design problems and its predictions are compared with the results of single- and multi-fidelity Polynomial Chaos Expansion and Monte Carlo methods. For the same computational cost, the Low-Rank Approximation method outperformed both in surrogate modeling and uncertainty quantification cases for all the benchmarks and real-world engineering problems addressed in the present study.

Surrogate (metamodel) based optimization has numerous potential applications in the field of naval architecture. It is aimed here to establish a methodology for the aft form optimization for minimum viscous resistance, thus the present study is focused on the aft form where the viscous effects become dominant. It is necessary to solve this problem within acceptable time span from practical naval architectural point of view which requires metamodeling techniques currently under investigation. Accordingly, the present paper investigates the metamodeling ability of the Kriging interpolation and attempts to explore its capabilities and limitations in the aft form optimization from viscous resistance point of view. As metamodeling techniques become more widely used, their constraints are more apparent. Especially in highly nonlinear design spaces, the effect of dimensionality should be taken into consideration. Taking all those factors into account, the present paper is to examine the capabilities of Kriging and to establish the learning performance in terms of RMS error, correlation coefficient and required number of training points according to selected optimization algorithm for multidimensional ship design problem. The results show that, at least 5% reduction in viscous pressure drag can be attained by the present optimization methodology.

Lifting hydrofoils are gaining importance, since they drastically reduce the wetted surface area of a ship hull, thus decreasing resistance. To attain efficient hydrofoils, the geometries can be obtained from an automated optimization process, based on simulations. However, hydrofoil high-fidelity simulations are computationally demanding, since fine meshes are needed to accurately capture the pressure field and the boundary layer on the hydrofoil. Moreover, the immersed depth varies dynamically, which makes the simulation of hydrodynamic forces challenging. Simulation-based optimization can therefore be very expensive.Automated surrogate models, trained by a limited number of simulations, can reduce the required computational demand for the optimization process. Furthermore, if an efficient low-fidelity hydrofoil performance prediction tool is available, using surrogate models in a multi-fidelity framework [2] can provide a further reduction in the total required simulation cost, by combining the accuracy of a few high-fidelity simulations with the adequate exploration capability of a greater number of low-fidelity computations.In this study, we propose a hydrofoil optimization procedure based on two simulation methods, a dedicated hydrofoil potential flow solver [1] for low-fidelity and RANS for both medium-and highfidelity. The RANS solver uses adaptive grid refinement [2] to attain maximum accuracy with the lowest computational budget. Moreover, two distinctive improvements are provided within the surrogate modeling process. The first one aims to increase the accuracy of the uncertainty estimation when very few sample points are available and the second one provides better noise-canceling for the data in the sample points, with an estimation of the uncertainty due to the noise filtering.In this study, the proposed automated multi-fidelity surrogate model procedure will be tested for a parameterized geometric model of a realistic hydrofoil. The influence of the surrogate modeling technique and the effect of different combinations of fidelity levels on the efficiency of the optimization and the performance of the hydrofoil will be investigated.

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