Research On Flight Vehicle Shape Optimization Design Algorithms And Multi-output Surrogate Model

The shape of an flight vehicle has a significant influence on the overall performance of the aircraft.As the performance requirements for the aircraft increase,the requirements for the aircraft shape design optimization methods also increase.Nowadays,there are still several problems that need to be improved for surrogate-based aircraft shape optimization design: 1)only when the parameters of the optimization algorithm are set properly according to the problem at hand,can satisfaction optimization result be obtained.But the characteristics of the engineering problem are difficult to obtain before the optimization,which makes it hard to set proper parameter for optimization algorithm.2)The sample infilling strategy are sensitive to the distribution of the samples,and it is hard to balance global search and local search.3)Traditional multi-objective optimization is searching for the whole Pareto front,but the designer is interested in only part of the front.4)There are many multiple output prediction problems in engineering,and there exist potential correlation among the outputs.If they are handled with the single-output surrogate,the computation will be expensive and the precision will be low.Focusing on these issues,this paper studies aircraft shape optimization design algorithms and multi-output surrogate model.Firstly,the supporting techs and algorithms are studied to lay the foundation for the optimization platform.Then the single objective optimization algorithm and sample infilling strategy,multi-objective optimization algorithm and algorithms considering the designer's preference,the multi-output least-squares support vector regression machines and its application to the aircraft shape design are studied.This paper proposes corresponding solution for all the former issues to promote the development of the application of surrogate based optimization(SBO)in the engineering optimization problem.The main contents of this paper are as follows:1.For single objective optimization algorithm and sample infilling strategy,this paper proposes an improved optimization algorithm which has better performance,and a new sample infilling algorithm which can use several different surrogate model.Firstly,the optimization principles of three commonly used algorithms are studied.Then test functions with different characteristics are used to test the performance of these algorithms.The results indicate that differential evolution(DE)algorithm has better performance,but parameter setting can influence its performance significantly.This paper proposes an improved DE algorithm,which has better performance and reduces the influence of parameter setting.For surrogate model,three commonly used models are studied in depth.Through the derivation their mathematical form,this paper finds a unified mathematical form for these surrogate model.After an intensive study through all the existing sample infilling strategies,the conditions for the function value,first derivative and second derivative that should be met when a design point is supposed as the global optimal are concluded.Together with the unified mathematical form for the surrogate model,this paper proposes a new one-step sample infilling strategy,which can use any surrogate model that has the unified form to provide the prediction.This is helpful to analyze the performance of variance surrogate model,in order to improve SBO efficiency.After the testing and analyzing of the new strategy,it is found that the new strategy is good at global exploration but not good enough at local exploitation.In order to further improve its performance,through combining one-step and two-step method a hybrid strategy is proposed.The function and aerodynamic optimization cases are used to validate the proposed method.2.For multi-objective optimization algorithm and designer's preference,this paper proposes a local coordinate system based crossover operator and applies it to MOEA/D-DE to improve the performance robust of the algorithm;this paper also proposes a multi-objective optimization algorithm considering the designer's preference.Three commonly used optimization algorithms are studied firstly,and 19 test functions with different characteristics are used to test their performance.The results show that MOEA/D-DE algorithm has better performance,but the crossover rate influence its performance greatly.In order to improve the performance robustness of MOEA/D-DE,a local coordinate system based crossover operator is proposed,which makes the algorithm obtaining satisfactory results without altering the crossover rate when facing optimization problems with different characteristics.This paper also proposes a multi-objective optimization approach considering the designer's preference based on MOEA/D-DE.The proposed approach utilizes reference point to represent the preference information,and the search is focused only on the part of Pareto front which makes the utilization of computational resource more reasonable,and the final result contain more valuable solutions for the designer.The results of airfoil and three dimensional shape optimization cases show that the optimization algorithm considering preference can obtain better Pareto solutions than traditional multi-objective optimization algorithm.3.For multi-output prediction problems,this paper studies the multi-output least-squares support vector regression machines(MLS-SVR)in depth,and proposes an efficient gradientbased model selection algorithm for MLS-SVR,based on which the application of MLS-SVR to optimization design field is explored.MLS-SVR can predict multiple outputs simultaneously considering the potential correlations among the outputs.This paper studies the mathematical form of MLS-SVR in depth at first,and proposes an efficient gradient-based model selection algorithm,which makes MLS-SVR's application to engineering problem possible.Based on the new model selection algorithm,an airfoil inverse design algorithm is proposed utilizing the multi-output prediction ability of MLS-SVR to approximate the target foil step by step.Three airfoil inverse design cases at different station are used to validate the efficiency of the proposed algorithm.In order to improve the efficiency of multi-objective optimization,this paper proposes a multi-objective optimization frame based on MLS-SVR,and the testing results show that the proposed approach can improve the efficiency of multi-objective optimization.4.The supporting techs of SBO for aircraft shape design are studied,which laid the foundation for constructing SBO platform to solve single/multiple optimization problems of aircraft shape optimization design.The supporting techs include objective evaluation,shape parameterization and grid deformation.The numerical solution of Reynolds-averaged Navier–Stokes equations is studied to evaluate the aerodynamic performance.Two dimensional method of moment and high frequency method physical optics are used to evaluate the radar cross section of two and three dimensional configuration.Shape parameterization methods are used to describe the shape using a set of parameters.The airfoil parameterization methods and free-form deformation are studied to parameterize two-dimensional curve and three-dimensional surface configurations of aircraft respectively.In order to achieve automation of optimization process,the grid of new shape for objective evaluation should be generated automatically.A grid deformation method based on volume spline interpolation and transfinite interpolation is studied to automatically generate the multi-block calculating grid for the new shape according to the original grid.