Research On Uncertainty And High-dimensional Problems In Aerodynamic Shape Optimization Design

Aerodynamic shape optimization(ASO)design which combines CFD and optimization technology is a powerful and reliable technology in the aerodynamic design of aircrafts.With more than 40 years’ development,the gradient-based optimization methods and the surrogatebased optimization methods have been successfully applied to ASO.However,the aerodynamic design problems are becoming more and more complicated with the rapid development of aeronautical science and technology.There still exist some new complex problems needed to be solved.The thesis focuses on the uncertain and high-dimensional problems in ASO:1.Various uncertain factors are arisen in practical design and application of aircrafts.The traditional deterministic optimization has not considered the influence of uncertainties,so its optimal design may be very sensitive to uncertainties,which can result in a poor off-design performance and even failure to meet the design requirement.To consider the uncertainties in ASO,it is needed to quantitatively describe the uncertainty factors,efficiently evaluate the influence of inputs’ uncertainty on aerodynamic performance.It also needed to design efficiently the uncertainty-based ASO optimization framework.2.The number of design parameters are greatly increased with more and more complex engineering problems in aircraft design,which makes ASO high dimensional,expensive,multimodal and nonlinear.As to the optimization methods,the direct gradient-based optimization method is prone to fall into a local optimum.The surrogate-based optimization methods cannot obtain best results because it is difficult to guarantee the accuracy of high dimensional surrogate model.Moreover,the computational cost will suffer from the curse of dimensionality.At present,some studies are limited to improve the fitting ability of surrogate model by adjusting model parameters and to develop the sampling methods to these high dimensional optimization problems.Though these measures can improve the optimization effect to a certain extent,they cannot radically reduce the difficulty of high-dimensional aerodynamic optimization.Therefore,it is necessary to develop new methods to solve high dimensional aerodynamic optimization problems.The contents of this thesis are as follows:(1)The influence of uncertainties on the aerodynamic characteristics is considered.Uncertainty analysis and global sensitivity analysis are introduced.Two kinds of non-intrusive polynomial chaos(NIPC)methods are introduced: NIPC method based on regression analysis and NIPC method based on Galerkin projection.Then,the uncertainty analysis of aerodynamic characteristics is considered.At present,the uncertainty analysis of aerodynamic characteristics considering the uncertainty of flight conditions has been attracted many researches.The uncertainty analysis considering geometric uncertainties is rarely involved.The uncertainty and global sensitivity analysis considering the geometric uncertainties are carried out by using the NIPC methed based on regression analysis.The NIPC method based on Galerkin projection becomes inefficient as the number of random variables adopted to describe uncertainties increases.This deficiency becomes significant in stochastic aerodynamic analysis considering the geometric uncertainty because the description of geometric uncertainty generally needs many parameters.To solve the deficiency,a Sparse grid-based polynomial chaos(SGPC)expansion is used to uncertainty and sensitivity analysis for stochastic aerodynamic analysis considering geometric and operational uncertainties.From the results of uncertainty analysis,due to the presence of nonlinear flow characteristics such as shock wave and boundary layer interference in transonic flow,the most influential areas of uncertainty on transonic aerodynamic characteristics are mainly concentrated in the boundary layer area after shock wave and shock wave.Through the global sensitivity analysis,we can find out the contribution of each uncertain variable.The global sensitivity analysis can provide quantitative guidance for further reduction of variable space in the subsequent design work.In addition,it can be observed that which deformation modes have the greatest influence on the aerodynamic characteristics,which provides a useful reference for the control of manufacturing error.(2)To consider the uncertainty in the aircraft design and weaken the influence of the uncertainty on the optimal design results,the uncertain-based ASO is carried out in the paper.An adaptive stochastic optimization framework is developed for the uncertain-based robust ASO,which can efficiently optimize the aerodynamic robustness design.The results of optimal design show that the developed adaptive optimization method can efficiently obtain better optimization results.Compared with the aerodynamic characteristics of initial airfoils,robust optimization design can achieve well resistance reduction while reducing the sensitivity of drag characteristics to uncertainties.Compared with the design results of deterministic optimization,the drag characteristics of the airfoil are less fluctuant,but the resistance is slightly increased,which indicate that the aerodynamic performance is reduced properly while improving the robustness.Robust optimization can well balance performance,robustness and maintain aerodynamic performance robustness on the basis of improving aerodynamic performance,which is more suitable for engineering practice.(3)The design parameters are greatly increased with the complexity of the aerodynamic design,which will lead to reduce the optimization effect of the current ASO methods.Therefore,the thesis focuses on developing the new methods to tackle the high-dimensional problems encountered in the current ASO.The main two studies are as follows: 1.Based on the idea of mapping,a new aerodynamic shape parameterization method based on POD is developed.The POD analysis is used to transform the basis functions of CST method into the orthogonal basis functions.Through this space coordinate transformation,a set of reduced dimensional POD basis functions are used to describe the geometric variation of aerodynamic shape.The optimization results of ASO indicated that better optimization results can be obtained with fewer design parameters by the novel airfoil parameterization method.2.Based on the idea of decomposition,a new optimization method based on high-dimensional model representation(HDMR)and "teaching" and "learning" based optimization(TLBO)algorithm is developed.The results of the high dimensional aerodynamic optimization design verified the superiority of the developed method.