【作者】 隋洪涛；

【导师】 黄明恪；

【作者基本信息】 南京航空航天大学 ， 流体力学， 2002， 博士

【摘要】 本文的主要目的是：结合流场解算器，将基因遗传算法应用于气动外形优化设计中，致力于发展一种可以不依赖于梯度信息的新型的气动外形优化设计方法。 基因遗传算法作为一种优化设计方法具有通用性强、稳定性好以及全局收敛等特性。但在气动优化设计时，由于适应度评估需多次调用流场解算器会导致传统基因遗传算法的计算工作量过大，因此需从优化器和解算器两个方面研究解决此问题。首先，本文在系统研究基因遗传算法的基础上，提出改进型实数编码方式使算法无编码精度限制而且能保持基因材料多样性；构造最佳保存的确定式复制算子、自适应均匀与非均匀变异算子和平均交叉算子，算子之间相互协调，使算法能减少复制误差、避免近亲繁殖，充分挖掘有限群体的潜力从而达到快速搜索的目的；根据具体问题提出自适应适应度定标技术以及构造了合适的适应度函数，最终发展了一种小种群演化方法。该方法不仅能够快速搜索，而且具有全局搜索和局部调优的能力，从而使算法适于求解高精度、大计算量优化设计问题。其次，本文研制了基于有限体积法的可以计算亚、跨、超音速绕流的通用的时间推进 Euler方程解算器和可以快速计算超音速绕流的空间推进Euler方程解算器。两种解算器都引入了适当的耗散项以抑制解的振荡，都对边界条件作了恰当的处理以满足物理事实，并且都取得了令人满意的效果。另外，在时间推进Euler方程解算器的求解中还采用了当地时间步长、隐式残值光顺和焓阻尼等技术以加速收敛。 参数的基因表达是基因遗传算法应用于工程问题中关键的一步，基因表达并不改变问题本身的性质，所改变的是问题的透彻度，这将直接影响基因遗传算法的搜索效率。本文在比较分析了点点式和几种参数曲线(Bezier 曲线和B样条曲线)的基因表达方式的基础上，指出基于参数曲线的基因表达方式不仅适合气动外形的特点，而且还可以将搜索空间缩小到由有限的参数曲线控制点构成的子空间，有助于算法的快速搜索；而点点式表达方式适于对气动外形作局部微量修改的情况。 将基因遗传算法应用于翼型优化设计时，对流场解算器作了进一步的改进，即将显式推进格式改为近似因式分解隐式推进格式，大大提高了收敛速度。本文在成功进行翼型重构反设计基础上，进行了有效的跨、超音速升阻比极大和阻力极小等翼型优化设计。然后将高效三维解算器与基因遗传算法相结合成功地实现了三维气动外形优化设计计算。在进行旋成体零升波阻力极小化设计时，根据流场特点将周向计算区域缩小为只有四层网格的扇形区，提到计算速度数倍，优化所得的旋成体优于卡门旋成体，而且其波阻力是随着来流马赫数的变化而变化的。在进行超音速座舱盖与机身组合体优化设计时采用计算速度较快的空间推进Euler方程解算器，优化得出机头的下垂量和座舱盖风挡形状是影响波阻力的主要因素，有较大的改进余地，而座舱盖最高点后的形状不是影响波阻力的主要因素等结论。 基因遗传算法及气动外形最优化设计 多目标优化设计问题一直受到工程界的高度重视，求解多目标优化问题的基本目的是求出Pareto解集。本文基于Pareto最优解的数学定义，通过构造新型的联赛式和子群并列选择复制等算子而构造了一种适于求解多目标优化设计问题的合作式Pareto基因遗传算法。通过等级法来正确识别每一代中近Pareto波阵面的解，从而消除选择误差达到快速收敛的目的。求解Pareto波阵面时，解的分布性至关重要，本文从两个角度来提高解的分布性：一是采用小生境技术解决了基因材料多样性损失问题；二是采用常规实数编码配合平均交叉算子解决了端点效应问题。然后本文将发展的方法应用于多目标翼型优化设计中，获得了理想的Pareto波阵面。最后定义了k阶有效解，基于此定义可以从搜索到的ParetO最优解集合中选出更优的解供决策者使用。 进化NASH平衡与基因遗传算法的基础都是生物进化论和遗传学，都是一种群体行为，两者有很多相同之处。基因遗传算法最成功之处在于揭示了生物进化和遗传的发展过程，而进化NASH平衡最大的成功之处是揭示了这个发展过程的最终结果。因此两者相互结合是很自然的。本文基于J．L．Lions分布式优化控制方法将NASH平衡与基因遗传算法相结合构造了分布式并行且非合作式NASH基因遗传算法以搜索各个互为矛盾的目标之间的NASH平衡点，这是一种新型的分布式并行多目标优化设计方法。本文探索性地将其应用于双目标翼型优化设计中，证明本方法是可行的。更多还原

【Abstract】 The goal of this dissertation is to apply the Genetic Algorithms to aerodynamic optimization problems based on the CFD-Solver and to develop a new gradient free optimization method for aerodynamic problems.Genetic Algorithms, as a good optimization method, have features of robustness and global convergence. However, the traditional Genetic Algorithms will expend too much time to estimate the fitness values when applied to the aerodynamic optimizations. The way to remedy this problem in this dissertation is by improving the efficiency of the optimizer and the solver. Firstly, a small population evolutionary algorithm is developed by using the following techniques: A) A new kind of real coding without limitation of accuracy is studied systemically in order to keep the diversity of the genes. B) Three operators, elitist determined reproduction, adaptive mutation and average crossover are newly constructed. These operators can avoid inbreeding between individuals of the population, decrease the reproduction error and tap the potentialities of the limited size of population. C) The adaptive fitness scaling is developed and the suitable fitness function is designed for the specific optimization problem. Secondly, two kinds of CFD-Solvers, as fitness evaluators in GAs search, have been developed using the finite volume methods in the dissertation. One is developed by time-marching method based on the unsteady Euler equations for subsonic, transonic and supersonic flow simulations in two/three dimensions. The measures for acceleration in convergence are used by means of local tune stepping, enthalpy damping and implicit smoothing. The other is developed by space-marching method based on the steady Euler equations, which has been proved to have fast convergence for supersonic flows over 3-D bodies.As all known, the representation of the parameters to be optimized is an important factor when the Genetic Algorithms are used for solving engineering problems. The representation itself doesn’t change the nature of the problem, but effects the searching efficiency of the algorithm. It is verified though our research that the representation using Spline curves can reduce the searching scope and hence accelerate the convergence of the Gas, for it only needs a few of control points to describe an aerodynamic shape. While the point by point representation is suitable for minor modification of aerodynamic shapes.The implicit scheme of the Euler solver, as evaluator, is used in the GAs for airfoil optimizations. The airfoils are optimized based on the minimization of the drag and the maximization of the ratio of the lift to drag after the success of the reconstruction design of the airfoils. Then, the GAs are extended to the three dimensional aerodynamic optimizations. The 3-D unsteady Euler solver is accelerated by reducing the computational domain to four mesh layers in circumference when the GAs are used to the dragminimization of the revolution body at zero angle. We found that the optimized revolution body has the lower drag as compared with the well-known Karman-body that the drag is constant according to the linearized theory while the drag of the optimized body varies with the Mach number of the far field. The steady Euler solver is applied to the optimization of the canopy-fuselage. The optimized results show that the droop of the fuselage and the geometry of the windshield are the main elements to effect the drag at the supersonic conditions.Multi-objective optimization problem is always interested to the engineering field. Theoretically, the solution of this problem is the set of Pareto solution. A Pareto Genetic Algorithm (Pareto-GAs) is developed through constructing a set of operators and strategies based on the definition of the Pareto solution. It is remind that the Pareto-GAs is a cooperative multi-objective optimization method. In the searching process, the Pareto-GAs is speeded up by presenting a ranking method which can identify accurately the individuals who are closer to the Pareto front. As for更多还原