基于一种高效全局寻优算法的气动布局极多参数高精度优化设计
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摘要
气动布局设计对飞机的综合性能起着至关重要的作用。现代飞机设计对气动布局的设计要求可以归结为：气动性能更高，设计周期更短，设计耗费更低。气动布局优化设计技术是提高飞机气动性能及设计效率的有效手段，但是目前的气动布局优化技术在气动设计中发挥的作用还远未达到人们的期待。气动布局优化要获得良好的效果，需要具备三个基本要素：首先，参数化方式要能够充分表现所有可能的外形，即有效设计空间要大，以便包含最优的外形。这就要能处理足够多的设计参数，因为设计参数越多，所能表现的外形也越多、越精确。其次，寻优方法要能够充分搜索这个庞大的设计空间，得到全局最优或接近全局最优的布局。最后，目标函数解算器要有足够高的精准度，能够分辨优化过程中，气动特性的微小改变，同时，目标函数的变化要能够确实反映物理量的变化。一种优化设计方法，如果同时具备这三个要素(Global search, High accuracy, Manydesign parameters,简称GHM条件），就有可能找到真正的全局最优外形。经过数十年的发展，气动布局优化设计技术在三个要素上有了长足的进步，但是距离实现极多参数、高精度、全局寻优的终极目标还有较大的差距。目前大部分的优化设计技术都只具备其中的一个特征，少数优化设计技术具备其中的两个特征，同时具备这三个特征的优化设计技术在国内外都还没有出现，这也是目前的优化设计技术所取得的效果与预想还有很大差距的主要原因。
现代飞机设计对满足极多参数、高精度、全局寻优（GHM)的气动布局优化设计技术有着巨大的需求。本文的研究以满足这个需求为目标，通过解决GHM优化设计技术中的困难：比如多参数全局寻优难题，发展具备GHM优化能力的软件平台，为气动布局设计提供了一种新的工具。
本文首先总结了目前主流气动布局优化设计技术的特点，指出这些技术与GHM优化还有很大的差距。而基于伴随算子的气动布局优化设计技术多参数和高精度两个要素，未实现全局寻优。理论分析表明参数越多，目标函数成为多极值函数的可能性越高。随后，通过研究翼型、机翼和全机的气动特性-设计参数曲线和曲面，证实了这一点。在基于伴随算子的气动布局优化设计技术中，目前都在使用基于敏感导数的局部寻优算法，因而对于多极值的气动布局优化很难取得好的效果，这也是目前基于伴随算子的气动布局优化设计技术优化效果远不如预期，且未得到大规模的工业应用的主要原因。本文的研究以基于伴随算子的气动布局优化设计技术为基础，通过发展多参数全局寻优技术，并将其用在基于伴随算子的气动布局优化设计技术中，从而形成满足GHM条件的优化设计技术。
多参数全局寻优难于实现的关键在于全局寻优算法的计算量随着设计参数的增加急剧增长，迅速超出硬件系统计算能力。为了解决这个问题，本文提出了两个设想：1目标函数与设计参数之间的关系虽然很复杂，但还是有一些规律可循，而这些规律可能是多参数全局寻优算法的钥匙。2寻优过程就是目标函数信息的发现和利用过程。目前在基于伴随算子的气动布局优化技术中，敏感导数数信息并未得到充分的利用。而更好的利用这些信息，就可能得到更好的优化结果。基于这个设想，本文对目标函数-设计参数关系进行了进一步的研究和分析，发现了这样的规律：目标函数是少部分设计参数的多极值函数，是大部分设计参数单极值函数。据此提出了基于参数分类的多参数全局寻优算法（ParameterClassification Based Mixed Optimization, PCO),这种算法利用敏感导数信息将设计参数分成多极值设计参数和单极值设计参数，然后分别对这两种设计参数使用全局和局部寻优算法，这样就有可能在可接受的计算量内，获得全局最优解。随后，使用模型函数对该算法进行了优化验证，结果表明这种算法可以大幅提高优化效率和效果。
本文以雷诺平均NS方程作为主控方程，使用有限体积法，osher格式，多块结构网格发展了流场解算器和与该解算器耦合的伴随算子解算器，采用并行计算技术以提高速度。计算了RAE2822，M6等翼型和机翼的流场，并将计算结果与试验结果进行了对比，二者吻合良好。将伴随算子解算器计算得到的敏感导数与差分法计算得到的敏感导数进行了对比，二者也吻合较好。说明解算器具有较高的求解精度，能够满足GHM优化的要求。
最后，将流场解算、伴随算子解算、参数化、动网格、寻优等功能模块组合起来，就行成了具有GHM寻优能力的优化设计软件ADJ0PT。采用该平台对翼型、机翼和全机进行了优化验证，并与传统的伴随算子优化技术进行了对比。结果表明ADJ0PT确实具有一定的全局寻优能力，对大飞机的布局的优化，其减阻效果比传统的伴随算子优化技术提高了7倍以上。
Aerodynamic configuration design is vital to the overall performance of an aircraft,and the modern aircraft design requires higher aerodynamic performance, shorterdesign cycle and lower design costs for aerodynamic configuration design. Aneffective approach to improve aerodynamic performance and design efficiency isaerodynamic configuration optimization, but such technique has not-yet played its fullpotential function as expected. Satisfactory aerodynamic configuration optimizationdepends on the following three essential requirements: a) the optimization methodsenable full search of the huge design space, to obtain the global optimal or nearlyglobal optimal configuration; b) the cost function solver is accurate enough todistinguish the slight change of aerodynamic features in the optimization process, withthe change of the cost function veritably reflecting the change of the physical quantity;and c) the parameterization can fully represent all the possible shapes, i.e. a largeeffective design space to include the optimal shape, requiring the sufficient designparameters, as more parameters can represent more shapes and more accurate shapes(GHM requirements). An optimization design method meeting all the threerequirements is possible to find the true global best shape. Aerodynamic configurationoptimization design has advanced substantially in respect of the three requirementsafter decades of development; however, it is still a long way to reach the ultimatetargets of a great many parameters, high accuracy and global search. Currently mostoptimization techniques can only meet one of the above three requirements, only a fewcan meet two requirements, and the optimization technique that meets all the threerequirements is not seen in China or the world now, which is the main reason why theeffect of the optimization techniques is far below expectation.
Large need to the optimization techniques that meet the GHM requirements existsin the modern aircraft designing. The objects of the essay is to meet the need bysolving the difficulties exists in the development of GHM optimization technique，such as global search difficulty with many parameters，and develop a new optimizationsoftware platform to provide a new and advance tool to modern aircraft design.
The characters of the main aerodynamic optimization techniques are analyzed inthe paper and the shortcomings of them are given. The Adjoint based optimizationtechnique successfully meets the two requirements of three： many parameters and highaccuracy? but the global search requirement is still not fulfilled. The technical analysisshows that the cost function are more probably to have more than one minimum as thenumber of the parameter increasing, and this is validated by the following study ofcurves and surfaces of aerodynamic characteristic-parameters of wing section，wing and aircraft. Now, most of the Adjoint based aerodynamic optimization technique wasperformed with the local optimization algorithm based on the sensitivity derivative,thus the optimization cannot get good results. This is the main reason why the effect ofthe Adjoint based optimization techniques is far below expectation and not widely usedin engineering. The global search technique with a large number of parameters will bedeveloped in the essay, and the new search algorithm will be used in the Adjoint basedoptimization technique to compose a new optimization technique that meets GHMrequirements.
The main difficulty of the global search with a large number of parameters is thehuge increase of the calculation load of common global search algorithm which maysoon exceeds the ability of today and future hardware. Two guess is proposed in thepaper to solve the problem:1) through the relations between cost functions andparameters are complex, some regulations exists and this may be the key of the globalsearch algorithm with a large number of parameters.2) the optimization is just theprocedures to find and use the messages in the cost function and parameters. Thesensitivity derivative messages are not well used in Adjoint based optimization today，so we can improve the optimization technique by promote better usages of thesensitivity derivatives.
Then the relations between the parameters and cost functions are studied again anda regulation is found: the cost function is single-extremum to the most of theparameters but multi-extremum to the other parameters. Thus the author successfullydeveloped a new optimization algorithm based on parameter classification(ParameterClassification Based Mixed Optimization，PCO). The design parameters are divided tosingle-extremum parameters and multi-extremum parameters, and then global searchalgorithm is used for multi-extremum parameters while local search algorithm is usedfor single-extremum parameters, thus the global optimization results can be found inacceptable computational load with more than100parameters. The new searchalgorithm is certificated with model functions, the results show that the newoptimization algorithm can improve the optimization efficiency and result greatly.
The flow solver and its coupled Adjoint solver were developed in the paper withOsher flux difference splitting scheme, the finite volume method multi-block structuredgrid，based on Reynolds averaged Navier-Stokes equations. The Mpi parallelcomputation technique is used in the program to improve the computation speed. Theflow field of Rae2822，M6and etc wing section and wing is calculated and comparedwith the test results? the comparing results show that the accuracy of the flow solver issatisfied. The sensitivity derivatives of a wing section is calculated with Adjoint solverand compared with the results calculated by traditional method，the results also metquite well.
The flow solver, adjoint solver, shape parameterization program、grid updatesoftware and PCO search program are composed to optimization software platformADJOPT. Wing section，wing and a large aircraft are optimized with this softwareplatform and the optimization results were compared with the results optimized withtraditional Adjoint based optimization technique. The results show that the ADJOPTreally have global search ability with many parameters. The drag reduction is morethan7times of the drag reduction of traditional Adjoint method.
现代飞机设计对满足极多参数、高精度、全局寻优（GHM)的气动布局优化设计技术有着巨大的需求。本文的研究以满足这个需求为目标，通过解决GHM优化设计技术中的困难：比如多参数全局寻优难题，发展具备GHM优化能力的软件平台，为气动布局设计提供了一种新的工具。
本文首先总结了目前主流气动布局优化设计技术的特点，指出这些技术与GHM优化还有很大的差距。而基于伴随算子的气动布局优化设计技术多参数和高精度两个要素，未实现全局寻优。理论分析表明参数越多，目标函数成为多极值函数的可能性越高。随后，通过研究翼型、机翼和全机的气动特性-设计参数曲线和曲面，证实了这一点。在基于伴随算子的气动布局优化设计技术中，目前都在使用基于敏感导数的局部寻优算法，因而对于多极值的气动布局优化很难取得好的效果，这也是目前基于伴随算子的气动布局优化设计技术优化效果远不如预期，且未得到大规模的工业应用的主要原因。本文的研究以基于伴随算子的气动布局优化设计技术为基础，通过发展多参数全局寻优技术，并将其用在基于伴随算子的气动布局优化设计技术中，从而形成满足GHM条件的优化设计技术。
多参数全局寻优难于实现的关键在于全局寻优算法的计算量随着设计参数的增加急剧增长，迅速超出硬件系统计算能力。为了解决这个问题，本文提出了两个设想：1目标函数与设计参数之间的关系虽然很复杂，但还是有一些规律可循，而这些规律可能是多参数全局寻优算法的钥匙。2寻优过程就是目标函数信息的发现和利用过程。目前在基于伴随算子的气动布局优化技术中，敏感导数数信息并未得到充分的利用。而更好的利用这些信息，就可能得到更好的优化结果。基于这个设想，本文对目标函数-设计参数关系进行了进一步的研究和分析，发现了这样的规律：目标函数是少部分设计参数的多极值函数，是大部分设计参数单极值函数。据此提出了基于参数分类的多参数全局寻优算法（ParameterClassification Based Mixed Optimization, PCO),这种算法利用敏感导数信息将设计参数分成多极值设计参数和单极值设计参数，然后分别对这两种设计参数使用全局和局部寻优算法，这样就有可能在可接受的计算量内，获得全局最优解。随后，使用模型函数对该算法进行了优化验证，结果表明这种算法可以大幅提高优化效率和效果。
本文以雷诺平均NS方程作为主控方程，使用有限体积法，osher格式，多块结构网格发展了流场解算器和与该解算器耦合的伴随算子解算器，采用并行计算技术以提高速度。计算了RAE2822，M6等翼型和机翼的流场，并将计算结果与试验结果进行了对比，二者吻合良好。将伴随算子解算器计算得到的敏感导数与差分法计算得到的敏感导数进行了对比，二者也吻合较好。说明解算器具有较高的求解精度，能够满足GHM优化的要求。
最后，将流场解算、伴随算子解算、参数化、动网格、寻优等功能模块组合起来，就行成了具有GHM寻优能力的优化设计软件ADJ0PT。采用该平台对翼型、机翼和全机进行了优化验证，并与传统的伴随算子优化技术进行了对比。结果表明ADJ0PT确实具有一定的全局寻优能力，对大飞机的布局的优化，其减阻效果比传统的伴随算子优化技术提高了7倍以上。
Aerodynamic configuration design is vital to the overall performance of an aircraft,and the modern aircraft design requires higher aerodynamic performance, shorterdesign cycle and lower design costs for aerodynamic configuration design. Aneffective approach to improve aerodynamic performance and design efficiency isaerodynamic configuration optimization, but such technique has not-yet played its fullpotential function as expected. Satisfactory aerodynamic configuration optimizationdepends on the following three essential requirements: a) the optimization methodsenable full search of the huge design space, to obtain the global optimal or nearlyglobal optimal configuration; b) the cost function solver is accurate enough todistinguish the slight change of aerodynamic features in the optimization process, withthe change of the cost function veritably reflecting the change of the physical quantity;and c) the parameterization can fully represent all the possible shapes, i.e. a largeeffective design space to include the optimal shape, requiring the sufficient designparameters, as more parameters can represent more shapes and more accurate shapes(GHM requirements). An optimization design method meeting all the threerequirements is possible to find the true global best shape. Aerodynamic configurationoptimization design has advanced substantially in respect of the three requirementsafter decades of development; however, it is still a long way to reach the ultimatetargets of a great many parameters, high accuracy and global search. Currently mostoptimization techniques can only meet one of the above three requirements, only a fewcan meet two requirements, and the optimization technique that meets all the threerequirements is not seen in China or the world now, which is the main reason why theeffect of the optimization techniques is far below expectation.
Large need to the optimization techniques that meet the GHM requirements existsin the modern aircraft designing. The objects of the essay is to meet the need bysolving the difficulties exists in the development of GHM optimization technique，such as global search difficulty with many parameters，and develop a new optimizationsoftware platform to provide a new and advance tool to modern aircraft design.
The characters of the main aerodynamic optimization techniques are analyzed inthe paper and the shortcomings of them are given. The Adjoint based optimizationtechnique successfully meets the two requirements of three： many parameters and highaccuracy? but the global search requirement is still not fulfilled. The technical analysisshows that the cost function are more probably to have more than one minimum as thenumber of the parameter increasing, and this is validated by the following study ofcurves and surfaces of aerodynamic characteristic-parameters of wing section，wing and aircraft. Now, most of the Adjoint based aerodynamic optimization technique wasperformed with the local optimization algorithm based on the sensitivity derivative,thus the optimization cannot get good results. This is the main reason why the effect ofthe Adjoint based optimization techniques is far below expectation and not widely usedin engineering. The global search technique with a large number of parameters will bedeveloped in the essay, and the new search algorithm will be used in the Adjoint basedoptimization technique to compose a new optimization technique that meets GHMrequirements.
The main difficulty of the global search with a large number of parameters is thehuge increase of the calculation load of common global search algorithm which maysoon exceeds the ability of today and future hardware. Two guess is proposed in thepaper to solve the problem:1) through the relations between cost functions andparameters are complex, some regulations exists and this may be the key of the globalsearch algorithm with a large number of parameters.2) the optimization is just theprocedures to find and use the messages in the cost function and parameters. Thesensitivity derivative messages are not well used in Adjoint based optimization today，so we can improve the optimization technique by promote better usages of thesensitivity derivatives.
Then the relations between the parameters and cost functions are studied again anda regulation is found: the cost function is single-extremum to the most of theparameters but multi-extremum to the other parameters. Thus the author successfullydeveloped a new optimization algorithm based on parameter classification(ParameterClassification Based Mixed Optimization，PCO). The design parameters are divided tosingle-extremum parameters and multi-extremum parameters, and then global searchalgorithm is used for multi-extremum parameters while local search algorithm is usedfor single-extremum parameters, thus the global optimization results can be found inacceptable computational load with more than100parameters. The new searchalgorithm is certificated with model functions, the results show that the newoptimization algorithm can improve the optimization efficiency and result greatly.
The flow solver and its coupled Adjoint solver were developed in the paper withOsher flux difference splitting scheme, the finite volume method multi-block structuredgrid，based on Reynolds averaged Navier-Stokes equations. The Mpi parallelcomputation technique is used in the program to improve the computation speed. Theflow field of Rae2822，M6and etc wing section and wing is calculated and comparedwith the test results? the comparing results show that the accuracy of the flow solver issatisfied. The sensitivity derivatives of a wing section is calculated with Adjoint solverand compared with the results calculated by traditional method，the results also metquite well.
The flow solver, adjoint solver, shape parameterization program、grid updatesoftware and PCO search program are composed to optimization software platformADJOPT. Wing section，wing and a large aircraft are optimized with this softwareplatform and the optimization results were compared with the results optimized withtraditional Adjoint based optimization technique. The results show that the ADJOPTreally have global search ability with many parameters. The drag reduction is morethan7times of the drag reduction of traditional Adjoint method.
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