【关键词】遗传算法,优化,离心压缩机,叶栅,神经网络
【论文摘要】离心压缩机中的静止叶栅（包括叶片扩压器，回流器等）作为气流能量转换的主要元件，其中亦不可避免的存在有效能量的损失。以单机为例，目前我国设计和生产的机器，其整机效率的期望值为83%左右，但研究表明叶轮的效率则可高达90%以上。由此可见，静止件中的能量损失导致整级效率下降7%之多。对压缩机来说，这是一个可观的能量损失比例。长期以来，人们在对中的主要部件－叶轮投注大量精力进行研究的同时，对其配套的静止叶栅的研究却极为有限。随着对节能型压缩机日益增高的性能需要，人们不得不把目光逐步投向静止叶栅的研究，以期挖掘其可能存在的节能潜力，希望由此提高机组的整体运行效率。如何设计出具有zui小能量损失的静止叶栅，是摆在研究者人们面前的一个越来越紧迫的任务。
近年来得到快速发展的遗传算法，是一类模拟达尔文自然进化论的仿生随机优化方法。遗传算法着眼于从一组（种群）潜在解（个体）中寻找问题的解。通过在这一组当前潜在解之间进行一定的遗传操作，如选择，杂交和变异，便有望产生更好的解。这一过程反复进行，直至找到一个可以被接受的解。遗传算法较之其它搜索技术具有许多*性。这些*性包括：1）鲁棒性。遗传算法在计算上简单，搜索有效，且无须对搜索空间附加限制性假定。2）固有并行性。遗传算法通过一组解，而非单个解进行搜索，因此具有固有的并行性。3）全局性。遗传算法在搜索过程中使用随机操作，可以探测更广的搜索空间，因而zui有希望获得全局*解。
本学位论文将遗传算法引入静止叶栅的优化设计，对遗传算法在这一领域内应用进行了深入而系统的发展和研究。论文的工作及所获得的结果广泛而有明确工程应用价值。主要工作有：
1．基于叶栅优化问题的复杂性考虑，对现有标准遗传算法进行了改进，以更有效求解这些问题。提出了三个改进型遗传算法，即对偶适应性遗传算法，方向进化遗传算法和概率二值搜索遗传算法。在对偶适应性遗传算法中，提出了一个待优化目标函数的对偶函数，将该对偶函数巧妙的结合进标准遗传算法，从而使遗传算法可以自适应地进行变异运算，提高算法获得全局*解的能力。在方向进化遗传算法中，提出一个新的遗传算子，方向进化算子。该算子以个体的祖父代和父代的进化趋势指导子代的个体变异，可以使新解以zui大概率在*区域产生。在概率二值搜索遗传算法中，提出对个体基因二值位在遗传进化中的表现进行统计记录，以此记录为指导产生若干新鲜解补入种群，以改良种群质量。三个新算法与标准遗传进行的数值实验和设计实例对比显示了新算法对遗传算法收敛性的改进是十分可观的（参见Fan, Xi, Wang, Inverse Problems in Engineering, 2000）。
2．论文系统提出静止叶栅遗传算法设计理论和设计模型（参见Fan, Journal of Power and Energy, Proc. Instn. Mech. Engrs, 1998）。在设计模型中，以改进型遗传算法为基础，探索了气动叶栅设计中遗传算子的选取及运算规律，提出了适合遗传算法操作的叶栅个体参数化技术和相应的基因编码方法。与此同时，在设计模型中，还尝试将遗传算法与人工神经网络进行结合，提出在遗传算法叶栅设计方法中加入一个前馈人工神经网络策略，用于完成对已知叶片形状的流动分析，从而减少算法中实际CFD分析程序计算个体适应值的时间，缩短遗传算法进化周期。另外，提出直接受用前馈人工神经网络在遗传算法的训练和演化下完成叶栅气动设计任务的方法。所提出的遗传算法设计模型均具有广泛的通用性，可以与任何层次的CFD流场分析程序结合。可以对气动叶栅进行任意命题下的自动设计，既可以对叶栅进行传统意义上的正命题设计和逆命题设计，也可以实现叶栅的混合命题设计。
3．传统的叶轮及其它气动元件均为单点设计，即按一个给定工况点设计。如此设计出的元件在设计工况点附近尚能较好工作，但当实际运行工况偏离设计工况时，元件的性能就会急剧恶化。论文将航空机翼中多点设计的思想引入叶栅的气动设计当中，欲通过以元件的两个或更多个希望的运行工况点作为给定设计点，设计出在各个设计点之间均能较好工作的折中（trade-off）*化叶栅。论文提出气动叶栅多点设计问题的数学描述。对叶栅多点设计问题，提出三个有效获取问题Pareto解集的遗传算法方法求解策略，即全局适应值竞赛策略，双枝竞赛策略和Pareto占优竞赛策略。所提出的遗传算法多点设计方法得到扩压叶栅设计实例的实验验证（参见Fan, Xi, Wang, Journal of Power and Energy, Proc. Instn. Mech. Engrs, 2000, Fan, Xi, Wang, Chinese Journal of Mechanical Engineering, 2000）。
4．遗传算法在叶栅形状优化上的成功应用激励作者尝试用该方法进行叶栅流场的数值分析。论文研究和探讨了生物进行系统与守恒定律支配的非生物物理系统的相似性。基于这些相似性，提出了一个求解流场问题的初步的“遗传算法类”CFD方法。该方法以流场的解作为遗传进化个体，以候选解满足守流体守恒性（如质量守恒，能量守恒等）的误差作为其适应性的度量，通过遗传算法对流场进行求解。初步探讨了守恒性误差的求解方法所得结果令人鼓舞，它初步显示，遗传算法具有进行叶栅流场分析的巨大潜力。以此为起种类（参见Fan, Lu, Xu, Engineering Computation, 2000）。
关键词：遗传算法，优化，，叶栅，神经网络
Study of Evolutionary-Computation-Based Methods Applied to
Design of Stationary Circular Cascades in Centrifugal Compressors
ABSTRACT
In centrifugal compressors, stationary cascades, generally including bladed diffusers and returning channel, are the key parts for gaseous energy transformation. It is inevitable that the energy loss occurs in these parts. For example, the expected aerodynamic efficiency of the single stage compressors that are currently produced in China is about 83%. But studies have demonstrated that the impellers’ efficiency can reach up to more than 90%. This implies that the energy loss in the stationary parts reduces the machines’ total efficiency more than 7%. This is a considerable proportion of the energy loss to compressors. However, for a long time period, researchers have made most part of their efforts on studying how to improve the most important parts, the impellers, of the compressors, while studies to the stationary parts are very limited. Since the requirements of the improvement on the performances of the energy-saving compressors are always continued, the researchers have no choice but to turn their sight to the stationary parts, expecting to find new energy-saving possibilities so as to increase the total machines’ efficiency further. Consequently, how to design the high efficient stationary parts that can have a minimum energy loss is an urgent task faced by the researchers of centrifugal compressors.
Genetic algorithms （GAs）, rapidly developed in recent years, are regarded as stochastic search techniques that mimic natural selection and Darwin’s main principle: survival of the fittest. GAs aim to fine the best solutions to a problem by generating a collection （“population”） of potential solutions （“individual”）. Better solutions are hopefully generated through certain genetic operations such as selection, crossover and mutation from the current set of potential solutions. The process is repeated until an acceptable solution is found. GAs Have many advantages over other search techniques. These include: 1） Robustness, GAs are computationally simple and powerful in the search for improvement and have no limitation on the search space. 2） Intrinsic parallelism, GAs carry out search through populations of points, not single point, which makes them intrinsically parallel. 3） Global property, GAs use random operation in their evolution processes that allow a wider exploration of the search space, and hence it is likely that the expected GA solution may by global optimum.
This dissertation aims at introduction of genetic algorithms into the design of the stationary
cascades of centrifugal compressors. Some good developments and systematic studies are first carried out in application of genetic algorithms to this area. The researches and the relating results obtained in the dissertation are broad and practical in engineering appellations. The major works include:
1.Based on the consideration of complexities from the optimization problems of the aerodynamic cascades, the exiting standard genetic algorithm is improved in order to use it to solve the cascade optimization problems more efficiently. Three modified genetic algorithms, namely, dual fitness genetic algorithm, direction evolutionary genetic algorithm and probability binary search genetic algorithm, are proposed. In the dual fitness genetic algorithm, a dual function of the objective function optimized is presented. The dual function is then embedded into the standard genetic in order to make the mutation operation being performed adaptively with different probabilities and so as to make the algorithm having higher globally searching ability. In the direction evolutionary genetic algorithm, a new genetic operator, direction evolutionary operator, is proposed, this operator directs mutation operations of a child individual according to the evolution tendency of its grand parent and parent individuals. With the mutation operation, the individual can be yielded in an optimum region with a high probability. In the probability binary search genetic algorithm, the behaviour of the binary components at each allele locations of a chromosome are statistically recorded and are used to produce a set of fresh solutions that are added into a population, so that to improve the quality of the population. The numerical simulation and practical design examples show that the three novel genetic algorithms have much better convergence abilities than the standard genetic algorithm （see Fan, Xi, Wang, Inverse Problems in Engineering, 2000,）.
2.The genetic-algorithm-based design principles and models are first systematically established （see Fan, Journal of Power and Energy, Proc. Instn. Mech. Engrs, 1998）. In the genetic-based design models, based on the improved genetic algorithms, the tuning and operation patterns of the genetic operators in a design of the aerodynamic cascades are explored. Some parameterizations and their corresponding coding methods for aerodynamic cascades regarding to the operations of genetic algorithms are presented. In the meanwhile, in the proposed design models, incorporating genetic algorithms and artificial neural networks is attempted to solve cascade design problems. In this case, a genetic-algorithm-based design method is embedded with a feed forward artificial neural network that is used to compute the flow characters of give blade profiles. As the result, the fitness computational time can be reduced, and further the algorithm’s evolving epoch can be shortened. Moreover, the feed forward artificial neural networks are first used directly to complete a cascade aerodynamic design task, with the genetic algorithms being used to train and evolve the network. All the genetic-based design models established possess wide generalities. They can incorporate with any degree CFD solvers. They can implement automatic designs of an aerodynamic cascade in any required designs, i.e., a conventional direct design or inverse design, and a hybrid design.
3.Conventionally, the impellers and the other aerodynamic parts of centrifugal compressors are in single point design, i.e., are designed according to a given operation point. The elements so designed can rather well work under the operation conditions near the design point. But while the operating conditions are far off the design point they may work badly. The dissertation first introduces the ideas of “multi-point designs” form aeronautical airfoil design into the aerodynamic designs of the cascades of centrifugal compressors. In other words, through taking two or more operating points as the design points, it is expected that an optimal cascade design can be obtained that makes a good “trade off” between the design points. The mathematical formulations of the multipoint design problem for an aerodynamic cascade are first stated. Three Pareto genetic algorithm strategies, i.e., global fitness tournament, two-branch tournament, and Pareto dominate tournament, are then proposed for effectively obtain the Pareto set of the multipoint design problems of cascades. The genetic-algorithm-based multipoint design methods proposed are successfully examined with an experiment of a practical diffuser cascade design （see Fan, Xi, Wang, Journal of Power and Energy, Proc. Instn. Mech. Engrs, 2000, Fan, Xi, Wang, Chinese Journal of Mechanical Engineering, 2000）.
4.The successful uses of genetic algorithms in the cascade shape optimizations motivate the author to attempt an application of genetic algorithms to the flowfeild analysis of cascades. In the dissertation, some analogues between evolution of living organism systems in nature and inanimate physical systems governed by laws of conservation are studied and probed. From these analogues a new CFD method, genetic-algorithm-based numerical analysis method, is developed. The method, taking candidate solutions of a flowfield as the individuals to be evolved, and some errors of the solutions in satisfying certain conservation laws （e.g., mass conservation, energy conservation, etc.） within control spaces as the measures of their fitnesses, solves the flowfield through genetic algorithms. The calculation of the conservation errors and the formation of the individuals’ fitness function are preliminarily studied. The new methodology is illustrated with analyzing the flow field of a simple 2-dimensional circular diffuser cascade. The computational results obtained are encouraging. It preliminarily shows that genetic algorithms have a big potentiality to cascade flow field analysis. From the view of this point, it is hopefully that, through our diligent work, a new kind of CFD methods essentially different with the existing methods can very possibly be developed.
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