Efficient Surrogate-Based Optimization Method And Its Application In Aerodynamic Design

Aerodynamic design optimization technology based on CFD plays an important role in the design of high performance aircraft. On one hand, in order to ensure the performance of the designed shape as more consistent with which under real flight conditions as possible, highfidelity numerical flow simulation methods are required to be directly coupled in the aerodynamic design, hence the computational expense will be dramatically increased. On the other hand, in order to improve the aerodynamic performance of the aircraft as much as possible, the optimization algorithms are required to have high quality. Therefore, to develop aerodynamic design optimization method with high efficiency and high quality has broad application prospects. This research is dedicated to develop an efficient and effective surrogated-based aerodynamic design method and explore its application in aerodynamic design problems.In this thesis, the research works are carried out in the following aspects:(1) Several adaptive infill sampling criteria for kriging model(including the gradientenhanced Kriging model) based optimization method are studied and a parallel infill strategy is proposed to improve the efficiency. For traditional surrogate-based optimization method, there is no infill step or the expected improvement(EI) infill criterion is used, in which the latter is usually called EGO method. However, in this research, 5 kinds of infill criteria are studied, including: minimum of the predicted objective function(MP), maximum of expected improvement(EI), minimum of the lower confidence bounding(LCB), maximum of the probability of improvement(PI), and maximum of the RMSE(RMSE). Then, all of the criteria are extended to the constrained form, that is, the constrained infill criteria: CMP, CEI, CLCB, CPI, and CRMSE are developed. Based on the aforementioned criteria, an efficient parallel infill strategy is proposed. For this strategy, multiple new sample points are obtained in each updating cycle under different infill criterion so that they can be validated in parallel.(2) The aforementioned infill criteria which are originally for single-objective optimization are extended to multi-objective optimization, hence the multi-objective infill criteria for unconstrained optimization of MMP、MEI、MLCB、MPI、MRMSE and for constrained optimization of CMMP、CMEI、CMLCB、CMPI、CMRMSE are developed in this research. As a result, efficient adaptive sampling method for multi-objective optimization are developed.(3) An efficient kriging-based optimization method either for single-objective or multi-objective optimization is developed. Moreover, an efficient single- and multi-objective optimization method using gradient-enhanced kriging(GEK) is also developed. The benchmark analytical test cases show that, for single-objective optimization problems, both two surrogatebased optimizers get better results than the genetic algorithm(GA) and have a much higher efficiency than the GA, while for multi-objective optimization problems, the two surrogatebased optimizers can get a result as good as the multi-objective genetic algorithm NSGA-II with a much high efficiency. The test cases also shows the kriging-based multi-objective optimization method is feasible to high-dimensional problems. Besides, the effectiveness of the constraint handling method is also verified.(4) Combining the design of experiments, surrogate models, traditional optimizers and the infill criteria, an efficient surrogate-based parallel optimization codes are developed. This codes can be applied to any user-defined single-objective or multi-objective optimization problems, unconstrained or strongly constrained problems. To construct an initial surrogate model, the Latin hypercube sampling, uniform design and Monte Carlo sampling are available for choice of design of experiments(DoE). Multiple surrogate models are available for choice, including the second-order polynomial response surface, Kriging with 4 kinds of correlation functions, and gradient-enhance Kriging with variety kinds of correlation functions. For the adaptive sampling, the aforementioned infill criteria can be used individually or simultaneously, both for single- and multi-objective problems. For the optimization process on the surrogate models, which is the so- called “sub optimization” in this thesis, the pattern search algorithm, quasi-Newton method, sequential quadratic programming, and genetic algorithms are available, they can be used individually or simultaneously. In order to get a better optimum on the surrogate model, a hybrid optimization strategy is used in this research.(5) An efficient kriging-based inverse airfoil design method and an airfoil multi-objective design optimization method are developed. Combining the Adjoint solver, an efficient GEKbased multi-objective airfoil design optimization method is also developed. The test cases validated the effectiveness of the airfoil inverse design method, the efficiency of the Krigingbased multi-objective optimization method, and the superiority of the GEK-based multiobjective optimization method over the Kriging-based. To further validate the developed airfoil design optimization methods, they are then successfully applied to real engineering airfoil design, including wind-turbine airfoil, rotor airfoil, and flying wing airfoil.(6) An efficient kriging-based single- and multi-objective wing design optimization method is developed and successfully applied to real engineering wing design: multi-objective design optimization of a flying wing with 58 design variables. Firstly, the wing design optimization method is exhaustively tested:(a) a transonic wing is optimized in a comprehensive way: only the planform shape is optimized, only the section shape is optimized, and the planform shape and section shape optimized simultaneously;(b) 4 section shapes of a transport wing is optimized. These test cases are carried out using the EGO method and the proposed parallel infill strategy respectively, and the results also showed the superiority of the parallel infill strategy. Then, the wing design optimization method is successfully applied to a real engineering multi-objective flying wing design, which both considering the take-off performance and the cruise performance.(7) The developed kriging-based optimization method is also applied to single- and multiobjective optimization of multi-element airfoils. The results showed its feasibility to the design optimization of high-lift devices.(8) Combining the efficient surrogate-based optimizer and multidisciplinary feasible(MDF) method, an efficient kriging-based multidisciplinary design optimization method is developed. Benchmark test cases show that this method is more efficient and effective than a kriging-based concurrent subspace optimization(CSSO) method. Then, by coupling an efficient aeroelastic numerical simulation method, this method is successfully applied to a multidisciplinary design of a transport wing, which improved both the aerodynamic and structural performance.