Hypersonic lifting body aerodynamic shape optimization based on the multiobjective evolutionary algorithm based on decomposition

Abstract

In this work, a volume and longitudinal stability-constrained multiobjective aerodynamic shape optimization is conducted. The aerodynamic shapes of lifting bodies are parameterized by using class function/shape function transformation parameterization method for maximum design flexibility. Hypersonic aerodynamic objectives and constraints are analyzed by solving the Reynolds-averaged Navier-Stokes equations in conjunction with a two-equation turbulence model. The Kriging technique is adopted to construct surrogate models aiming at reducing the computational cost. A two-stage method of infill sampling combined with multiobjective optimization is proposed to improve the performance of the surrogate models. Multiobjective evolutionary algorithm based on decomposition (MOEA/D) combined with penalty function method is employed to handle the multiobjective optimization problem with nonlinear constraints. The optimization results reveal that the two-stage method based on surrogates can reduce the computational cost significantly, and the accuracy of the surrogates around the Pareto front is sufficient. The two objectives are competing such that a set of Pareto optimal solutions are obtained, which are the best tradeoffs among the objectives. The unconstrained multiobjective optimization problem is also investigated with MOEA/D and nondominated sorting genetic algorithm II (NSGA-II) respectively to make a further comparison. The results show that the Pareto sets based on MOEA/D are more excellent and distribute more evenly than that obtained by NSGA-II. The computational efficiency of MOEA/D is about six times faster than that of NSGA-II. Lastly, aerodynamic characters of typical shape of Pareto front are analyzed under different flight conditions, and the results reveal favorable robustness of this shape.

Research of multi-point infill criteria based on multi-objective optimization front and its application on aerodynamic shape optimization

“…In the optimization process, the population size used in MOEA/D is 1000. As illustrated in Figure 10, the three optimized typical airfoils on the Pareto front are as follows: (1) CaseA, which has the minimum drag coefficient and the minimum section area, identified by solid circle; (2) CaseB, which has the compatible section area and drag coefficient, identified by solid pentagram, and (3) CaseC, which has the maximum section area and the maximum drag coefficient, identified by solid square. The samples with extreme objective characteristic are identified by lines with arrows, where Case1, Case2, and Case3, respectively, denote the airfoils with the minimum section area, the minimum drag coefficient, and the maximum drag coefficient and section area simultaneously.…”

“…The surrogate models introduced during expensive optimization design can efficiently deal with the conflict objectives, such as computational efficiency and accuracy, so they are widely used in expensive optimization design problems. [1][2][3][4][5][6] To construct the surrogate model, the first step is to choose a number of typical samples from design space, and then their responses to objective are computed by proper analysis tool with certain precision. After that, some mathematical approaches such as interpolation and fitting are employed to construct the surrogate model based on these responses of typical samples.…”

Obtaining minimum-drag shapes through surrogate-based global optimization: An application to the aerodynamic shape design of the landing gear master cylinder

“…[14][15][16] In addition, SVMs have been also applied for prediction in many areas, such as finances or energy. [17][18][19][20][21] With respect to SBO applied to aerodynamic shape design of aeronautical configurations, there have been several approaches [22][23][24][25][26][27][28] in the last years trying to employ different surrogates (for instance, Kriging, Proper Orthogonal Decomposition, ANNs, etc.) and geometry parameterization techniques (PARSEC, Class Shape Transformation method, etc.…”

Design and optimization of three-dimensional supersonic asymmetric truncated nozzle

“…Design of experiments has been widely adopted to generate the samples required to construct a surrogate model. 21 Kwon and Choi 22 and Ma et al 23 applied Latin hypercube sampling to optimize the transonic airfoil and aerodynamic shape of a hypersonic lifting body, respectively. Orthogonal array has the advantage of uniform dispersion and evident comparability, which is an efficient and economic experiment design tool for the establishment of the surrogate model.…”