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A multiobjective design optimization system of exhaust manifold shapes with tapered pipes for a car engine has been developed by using divided range multiobjective genetic algorithm (DRMOGA) to obtain more engine power as well as to produce less pollutant. Although the present design problem is known to be highly non-linear, the exhaust manifold has been successfully designed to improve both objectives. A comparison of the results obtained by DRMOGA and MOGA was performed and DRMOGA was demonstrated to find better solutions than MOGA.

Abstract: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.

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This study investigates the flow structures behind an atmospheric entry capsule at Mach number 0.4 through an improved detached eddy simulation and a modal analysis. The simulated flowfields reveal relatively low-frequency peaks of St ≈ 0.016 and St = 0.17–0.2 in the aerodynamic coefficient variation, where St is the nondimensional frequency. Then, the dominant fluid structures that cause the frequency peaks are identified through dynamic mode decomposition and the compressive-sensing-based mode selection method. Many of the dominant fluid phenomena have a frequency of St ≈ 0.2. In this frequency range, the fluid phenomena are mainly characterized with a large-scale vortex shedding separated from the capsule’s shoulder part and with a helical fluid structure in the wake. Moreover, the variation in the lift coefficient of the capsule is mainly attributed to the large-scale vortex shedding phenomenon. Furthermore, a fluid phenomenon at a frequency of St = O(0.01) is found, which describes the pulsation, or periodic growth or shrinkage, of the recirculation bubble, accompanied by pressure fluctuation behind the capsule that exerts a large drag fluctuation of the capsule. Additionally, this phenomenon seems related to the dynamic instability phenomena of the capsule, as indicated by its time scale, which is close to that of the capsule’s attitude motion.

In this paper, a multi-objective design optimization for a three-element airfoil consisted of a slat, a main wing, and a flap was carried out. The objective functions were defined as the maximization of lift coefficient at landing (C l8) and near stall (C l20)conditions simultaneously. Genetic Algorithm (GA) was used as an optimizer. Although it has advantage of global exploration, its computational cost is expensive. To reduce the computational cost, the kriging model which was constructed based on several sample designs was introduced. The solution space was explored based on the maximization of Expected Improvement (EI) value corresponding to objective functions on the kriging model to consider the predicted value by kriging model and its uncertainty. The improvement of the model and the exploration of the optimum can be advanced at the same time by maximizing EI value. In this study, 90 sample points are evaluated using the Reynolds averaged Navier-Stokes simulation (RANS) for the construction of the kriging model. Through the present exploration process, several designs were obtained with better performance than the baseline setting in each objective function. Functional Analysis of Variance (ANOVA) which is one of the data mining techniques showing the effect of each design variable on the objectives is applied. Main-effects of the design variables are calculated to recognize which design variable has the effect on the objective functions. This result suggests that the gap and the deflection of the flap have a remarkable effect on each objective function and the gap of the slat has an effect on C l20 .

A multi-objective design exploration for a three-element airfoil consisted of a slat, a main wing, and a flap is carried out. The lift curve improvement is important to design high-lift system, thus design has to be performed under various angle of attacks. The objective functions considered here are to maximize the lift coefficient at landing and near stall conditions simultaneously. Genetic Algorithm (GA) is used as an optimizer. Although it has advantage of global exploration, its computational cost is expensive. To reduce the computational cost, the Kriging surrogate model which is constructed based on several sample designs is introduced. The solution space is explored based on the maximization of Expected Improvement (EI) value corresponding to objective functions on the Kriging models. The improvement of the model and the exploration of the optimum can be advanced at the same time by maximizing EI value. In this study, a total of 90 sample points are evaluated using the Reynolds averaged Navier-Stokes simulation (RANS) for the construction of the Kriging model. Through the present exploration process, several designs were obtained with better performance than the baseline setting in each objective function. To obtain the information of the design space, functional Analysis of Variance (ANOVA) which is one of the data mining techniques showing the effect of each design variable on the objectives is applied. Main-effects of the design variables are calculated to recognize the effect of design variables on the objective functions. This result suggests that the gap and the deflection of the flap have a remarkable effect on each objective function and the gap of the slat has an effect on near stall condition.