In this study, efficient global optimization (EGO) with a multi-fidelity hybrid surrogate model for multi-objective optimization is proposed to solve multi-objective real-world design problems. In the proposed approach, a design exploration is carried out assisted by surrogate models, which are constructed by adding a local deviation estimated by the kriging method and a global model approximated by a radial basis function. An expected hypervolume improvement is then computed on the basis of the model uncertainty to determine additional samples that could improve the model accuracy. In the investigation, the proposed approach is applied to two-objective and three-objective optimization test functions. Then, it is applied to aerodynamic airfoil design optimization with two objective functions, namely minimization of aerodynamic drag and maximization of airfoil thickness at the trailing edge. Finally, the proposed method is applied to aerodynamic airfoil design optimization with three objective functions, namely minimization of aerodynamic drag at cruising speed, maximization of airfoil thickness at the trialing edge and maximization of lift at low speed assuming a landing attitude. XFOILis used to investigate the low-fidelity aerodynamic force, and a Reynolds-averaged Navier–Stokes simulation is applied for high-fidelity aerodynamics in conjunction with a high-cost approach. For comparison, multi-objective optimization is carried out using a kriging model only with a high-fidelity solver (single fidelity). The design results indicate that the non-dominated solutions of the proposed method achieve greater data diversity than the optimal solutions of the kriging method. Moreover, the proposed method gives a smaller error than the kriging method.

A multidisciplinary design methodology for a launch vehicle (LV) with a hybrid rocket was proposed in order to obtain qualitative design knowledge. In this study, a propulsion system performance and aerodynamic performance were empirically evaluated using a theoretical approach, and flight evaluation was performed by solving equations of motion to evaluate the motion along the horizontal/vertical directions and rotation around the body axis. To demonstrate the applicability of the proposed method, two types of multiobjective design problems were solved using multiobjective evolutionary algorithms, and the results were visualized using the parallel coordinate plot, which is a data mining technique. The first design problem has two objective functions: the maximization of the highest altitude and the minimization of the total mass. In this case, the effect of the constraint related to the body length and diameter ratio was evaluated. The second design problem also had two objective functions and two constraints for a realistic LV design: the maximization of the downrange and the minimization of the total mass. The target altitude was different for these problems although the objective functions were identical. As a result, the trade-off information was successfully acquired for each design problem. It was also found that the body length and diameter ratio were key factors in deciding the maximum altitude. Furthermore, during the downrange maximization, the characteristic geometries observed in the obtained nondominated solutions revealed the design required to fulfill the constraint related to the target altitude.

Powerful computer-aided design tools are presently vital for engineering product development. Efficient global optimization (EGO) is one of the most popular methods for design of a high computational cost problem. The original EGO is proposed for only one additional sample point. In this work, parallel computing is applied to the original EGO process via a multi-additional sampling technique. The weak point of the multi-additional sampling is it has slower convergence rate when compared with the original EGO. This paper applies the multi-fidelity technique to the multi-additional EGO process to see the effect of the number of multi-additional sampling points and the converge rate. A co-kriging method and a hybrid RBF/Kriging surrogate model are selected for the surrogate model in the EGO process to show the advantage of the multi-additional EGO process compared with the single-fidelity Kriging surrogate model. In the experiment, single-additional sampling points and two to four number of multi-additional sampling per iteration are tested with symmetry and asymmetry mathematical test functions. The results show the hybrid RBF/Kriging surrogate model can obtain the similar optimal points when using the multi-additional sampling EGO.

We redesigned the Mars Airplane Balloon Experiment Two (MABE-2) based on MABE-1 to improve the vehicle’s stability and controllability. Following the redesign, the MABE-2 vehicle had a larger horizontal tail volume than that of MABE-1 for improved stability performance. In addition, to further improve the stability and control characteristics, a rectangular planform was employed for the horizontal tail wing; in contrast, MABE-1 had a tapered planform. The vertical tail position of MABE-2 was moved to the end of the horizontal tail wing, because the vertical tail of MABE-1, which was positioned at the mid span of the horizontal tail wing, showed aerodynamic interaction with the horizontal tail wing. In this paper, we discussed the aerodynamic performance of a control surface based on computational fluid dynamics with variation in the deflection angle between the control surface and the horizontal tail (elevator), and we examined the effects of this redesign on longitudinal control characteristics. Numerical investigations confirmed the linear variation in the pitching moment and the aerodynamic force with the changing elevator deflection angle in MABE-2. Surface pressure observations indicated that MABE-2 shows a smooth variation in the pressure distribution with changing elevator deflection angle, while MABE-1 does not. These results demonstrate that the aerodynamic control characteristics of MABE-2 were improved in comparison to those of MABE-1.