【關(guān)鍵詞】遺傳算法,優(yōu)化,離心壓縮機(jī),葉柵,神經(jīng)網(wǎng)絡(luò)
【論文摘要】離心壓縮機(jī)中的靜止葉柵（包括葉片擴(kuò)壓器，回流器等）作為氣流能量轉(zhuǎn)換的主要元件，其中亦不可避免的存在有效能量的損失。以單機(jī)為例，目前我國設(shè)計(jì)和生產(chǎn)的機(jī)器，其整機(jī)效率的期望值為83%左右，但研究表明葉輪的效率則可高達(dá)90%以上。由此可見，靜止件中的能量損失導(dǎo)致整級(jí)效率下降7%之多。對(duì)壓縮機(jī)來說，這是一個(gè)可觀的能量損失比例。長期以來，人們?cè)趯?duì)中的主要部件－葉輪投注大量精力進(jìn)行研究的同時(shí)，對(duì)其配套的靜止葉柵的研究卻極為有限。隨著對(duì)節(jié)能型壓縮機(jī)日益增高的性能需要，人們不得不把目光逐步投向靜止葉柵的研究，以期挖掘其可能存在的節(jié)能潛力，希望由此提高機(jī)組的整體運(yùn)行效率。如何設(shè)計(jì)出具有zui小能量損失的靜止葉柵，是擺在研究者人們面前的一個(gè)越來越緊迫的任務(wù)。
近年來得到快速發(fā)展的遺傳算法，是一類模擬達(dá)爾文自然進(jìn)化論的仿生隨機(jī)優(yōu)化方法。遺傳算法著眼于從一組（種群）潛在解（個(gè)體）中尋找問題的解。通過在這一組當(dāng)前潛在解之間進(jìn)行一定的遺傳操作，如選擇，雜交和變異，便有望產(chǎn)生更好的解。這一過程反復(fù)進(jìn)行，直至找到一個(gè)可以被接受的解。遺傳算法較之其它搜索技術(shù)具有許多*性。這些*性包括：1）魯棒性。遺傳算法在計(jì)算上簡單，搜索有效，且無須對(duì)搜索空間附加限制性假定。2）固有并行性。遺傳算法通過一組解，而非單個(gè)解進(jìn)行搜索，因此具有固有的并行性。3）全局性。遺傳算法在搜索過程中使用隨機(jī)操作，可以探測(cè)更廣的搜索空間，因而zui有希望獲得全局*解。
本學(xué)位論文將遺傳算法引入靜止葉柵的優(yōu)化設(shè)計(jì)，對(duì)遺傳算法在這一領(lǐng)域內(nèi)應(yīng)用進(jìn)行了深入而系統(tǒng)的發(fā)展和研究。論文的工作及所獲得的結(jié)果廣泛而有明確工程應(yīng)用價(jià)值。主要工作有：
1．基于葉柵優(yōu)化問題的復(fù)雜性考慮，對(duì)現(xiàn)有標(biāo)準(zhǔn)遺傳算法進(jìn)行了改進(jìn)，以更有效求解這些問題。提出了三個(gè)改進(jìn)型遺傳算法，即對(duì)偶適應(yīng)性遺傳算法，方向進(jìn)化遺傳算法和概率二值搜索遺傳算法。在對(duì)偶適應(yīng)性遺傳算法中，提出了一個(gè)待優(yōu)化目標(biāo)函數(shù)的對(duì)偶函數(shù)，將該對(duì)偶函數(shù)巧妙的結(jié)合進(jìn)標(biāo)準(zhǔn)遺傳算法，從而使遺傳算法可以自適應(yīng)地進(jìn)行變異運(yùn)算，提高算法獲得全局*解的能力。在方向進(jìn)化遺傳算法中，提出一個(gè)新的遺傳算子，方向進(jìn)化算子。該算子以個(gè)體的祖父代和父代的進(jìn)化趨勢(shì)指導(dǎo)子代的個(gè)體變異，可以使新解以zui大概率在*區(qū)域產(chǎn)生。在概率二值搜索遺傳算法中，提出對(duì)個(gè)體基因二值位在遺傳進(jìn)化中的表現(xiàn)進(jìn)行統(tǒng)計(jì)記錄，以此記錄為指導(dǎo)產(chǎn)生若干新鮮解補(bǔ)入種群，以改良種群質(zhì)量。三個(gè)新算法與標(biāo)準(zhǔn)遺傳進(jìn)行的數(shù)值實(shí)驗(yàn)和設(shè)計(jì)實(shí)例對(duì)比顯示了新算法對(duì)遺傳算法收斂性的改進(jìn)是十分可觀的（參見Fan, Xi, Wang, Inverse Problems in Engineering, 2000）。
2．論文系統(tǒng)提出靜止葉柵遺傳算法設(shè)計(jì)理論和設(shè)計(jì)模型（參見Fan, Journal of Power and Energy, Proc. Instn. Mech. Engrs, 1998）。在設(shè)計(jì)模型中，以改進(jìn)型遺傳算法為基礎(chǔ)，探索了氣動(dòng)葉柵設(shè)計(jì)中遺傳算子的選取及運(yùn)算規(guī)律，提出了適合遺傳算法操作的葉柵個(gè)體參數(shù)化技術(shù)和相應(yīng)的基因編碼方法。與此同時(shí)，在設(shè)計(jì)模型中，還嘗試將遺傳算法與人工神經(jīng)網(wǎng)絡(luò)進(jìn)行結(jié)合，提出在遺傳算法葉柵設(shè)計(jì)方法中加入一個(gè)前饋人工神經(jīng)網(wǎng)絡(luò)策略，用于完成對(duì)已知葉片形狀的流動(dòng)分析，從而減少算法中實(shí)際CFD分析程序計(jì)算個(gè)體適應(yīng)值的時(shí)間，縮短遺傳算法進(jìn)化周期。另外，提出直接受用前饋人工神經(jīng)網(wǎng)絡(luò)在遺傳算法的訓(xùn)練和演化下完成葉柵氣動(dòng)設(shè)計(jì)任務(wù)的方法。所提出的遺傳算法設(shè)計(jì)模型均具有廣泛的通用性，可以與任何層次的CFD流場(chǎng)分析程序結(jié)合?？梢詫?duì)氣動(dòng)葉柵進(jìn)行任意命題下的自動(dòng)設(shè)計(jì)，既可以對(duì)葉柵進(jìn)行傳統(tǒng)意義上的正命題設(shè)計(jì)和逆命題設(shè)計(jì)，也可以實(shí)現(xiàn)葉柵的混合命題設(shè)計(jì)。
3．傳統(tǒng)的葉輪及其它氣動(dòng)元件均為單點(diǎn)設(shè)計(jì)，即按一個(gè)給定工況點(diǎn)設(shè)計(jì)。如此設(shè)計(jì)出的元件在設(shè)計(jì)工況點(diǎn)附近尚能較好工作，但當(dāng)實(shí)際運(yùn)行工況偏離設(shè)計(jì)工況時(shí)，元件的性能就會(huì)急劇惡化。論文將航空機(jī)翼中多點(diǎn)設(shè)計(jì)的思想引入葉柵的氣動(dòng)設(shè)計(jì)當(dāng)中，欲通過以元件的兩個(gè)或更多個(gè)希望的運(yùn)行工況點(diǎn)作為給定設(shè)計(jì)點(diǎn)，設(shè)計(jì)出在各個(gè)設(shè)計(jì)點(diǎn)之間均能較好工作的折中（trade-off）*化葉柵。論文提出氣動(dòng)葉柵多點(diǎn)設(shè)計(jì)問題的數(shù)學(xué)描述。對(duì)葉柵多點(diǎn)設(shè)計(jì)問題，提出三個(gè)有效獲取問題Pareto解集的遺傳算法方法求解策略，即全局適應(yīng)值競(jìng)賽策略，雙枝競(jìng)賽策略和Pareto占優(yōu)競(jìng)賽策略。所提出的遺傳算法多點(diǎn)設(shè)計(jì)方法得到擴(kuò)壓葉柵設(shè)計(jì)實(shí)例的實(shí)驗(yàn)驗(yàn)證（參見Fan, Xi, Wang, Journal of Power and Energy, Proc. Instn. Mech. Engrs, 2000, Fan, Xi, Wang, Chinese Journal of Mechanical Engineering, 2000）。
4．遺傳算法在葉柵形狀優(yōu)化上的成功應(yīng)用激勵(lì)作者嘗試用該方法進(jìn)行葉柵流場(chǎng)的數(shù)值分析。論文研究和探討了生物進(jìn)行系統(tǒng)與守恒定律支配的非生物物理系統(tǒng)的相似性?；谶@些相似性，提出了一個(gè)求解流場(chǎng)問題的初步的“遺傳算法類”CFD方法。該方法以流場(chǎng)的解作為遺傳進(jìn)化個(gè)體，以候選解滿足守流體守恒性（如質(zhì)量守恒，能量守恒等）的誤差作為其適應(yīng)性的度量，通過遺傳算法對(duì)流場(chǎng)進(jìn)行求解。初步探討了守恒性誤差的求解方法所得結(jié)果令人鼓舞，它初步顯示，遺傳算法具有進(jìn)行葉柵流場(chǎng)分析的巨大潛力。以此為起種類（參見Fan, Lu, Xu, Engineering Computation, 2000）。
關(guān)鍵詞：遺傳算法，優(yōu)化，，葉柵，神經(jīng)網(wǎng)絡(luò)
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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