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An integrated method of multi-objective optimization
for complex mechanical structure
Abstrct:
Now someone has put forward an integrated approach for complex mechanical structures of multi-objective optimization, and integrated prototyping, finite element analysis and optimization. In order to explore it for the advantages of the traditional method, the robot in the mixed-mode aerial vehicles (HMAWV) have adopted this optimization, the purpose of doing so is to increase their area of ??work, lower costs in sufficient strength to the premise will be designed variable geometry, and geometric dimensions to the design parameters, NLPQL NSGA - II of the comprehensive application to obtain the best solution. The results showed that this integrated approach is more efficient than the exhaustive search algorithm. NSGA - II can be close to the global cutting-edge technology, and NLPQL and NSGA - II The relative error is negligible. Therefore, this integrated approach is effective, and shows its potential in the field of engineering applications.
1、Introduction
In order to increase market competitiveness, structural design, analysis and optimization of the same like concurrent engineering have been integrated into the concept development stage. Scientific literature to design a new product in a variety of technologies, including computer programming more and more popular, because, along with the advance of computer and software technology revolution, and the superiority of the programming reflects the efficiency and accuracy.Traditional computer programming is like this: First, engineers draw a sketch of the product; the use of computer-aided design (CAD) software to the geometric model Subsequently, most of the engineers to the CAD model is imported into finite element analysis tools to evaluate it Finally, structural performance, some commercial software from ANSYS, MSC / NASTRAN, ABAQUS, to complete the size and topology optimization. Have been many important advances in this direction, some researchers use the domestic research tools MSC / NASTRAN to achieve structural optimization al. Barkeret secondary development of the MSC / NASTRAN, and has been confirmed by two instances. Recently, Hansen, and Horst, according to the refined finite element model developed a multi-level optimization procedure, that is the first step with the development to find slightly optimize the topological parameters, the second step application of MSC / NASTRAN optimization of the thickness and longitudinal section of the model, but simplify the boundary conditions. Although many efforts in this way, but due to the traditional optimization algorithm of the detention, the solution is still trapped in a region, and ignore the many nonlinear factors that such a program is not accurate.This novel method is a synchronous finite element software integrated into the optimization procedure. It uses a random search algorithm as the optimization method, which not only can prevent the optimizer is trapped in the local area, and can achieve accurate global optimal solution. The Many optimize the tool has been carried out development in the the field of literature, CAOSS appear than an earlier, it is a module expansion finite element program. Bakhtiary et al. Proposed a new interface between CAOSS and MSC / NASTRAN, then Meskeet al this interface the leading FEMsolvers, MSC / NASTRAN, MSC / Fatigue, ABAQUS, MSC. Marc and MSC.Patran the way. Proprietary software DynOPS is a choice as other optimization tools, The Giger, and Ermanni use DynOPS finite element analysis software ANSYS is applied to the development of composite fiber reinforced plastic motorcycle rims. Hilmann introduced an optimization software, the SFE concept, this software is used in the automotive industry in Germany. ISIGHT is another optimization software, which includes a wide range of classical and non classical optimization methods, such as Design of Experiments (DOE), the approximate exchange technology, multi-criteria analysis methods and quality engineering. Qian and Yuan successfully UG, of ICEM-of CFD and FLUENT integration to ISIGHT, and the Design of Experiments (DOE) is used to design the underhood. Later, Cullimore et al. In order to optimize an observation space telescope, the MSC / NASTRAN and Fluent integrated into ISIGHT. Although many optimization tool has been extensively developed, but the multi-objective optimization of complex mechanical structures is still a challenge.In this study, a complete design methodology and the structure of multi-objective optimization is advanced. Finite element analysis using ANSYS software and optimization algorithms to be integrated into a commercial optimization the software ISIGHT-FD, and confirmed these integration process. As an application example, the multi-objective optimization of robot development, the purpose of doing so is to expand the scope of its application, under the premise of sufficient strength to reduce its quality by optimizing the geometric dimensions. Whether it is based on the rate of change of the classical algorithm or evolutionary algorithm are adopted to obtain the best solution.In the second part discusses the integration process with finite element model, simulation, and optimization algorithms. In the third section, the robot on the mixed-mode high-altitude operations car (HMAWV,) A case study was put out. Application contact element analog connections, to verify the results of the finite element analysis, the development of experimental stress analysis. And adoption of NLPQL and NSGA-II to the excellent of manipulation cases. Compare the results of the optimization algorithm. Furthermore, in order to verify that the best solution, the NSGA-II parameters define a different value. In the fourth section, conclusions and future scholars to study and discuss.
2、Parallel methods of integration procedures
Structural optimization of the key is to have the ability to automatically generate a variety of design of the virtual prototype model. Concurrent design and optimization, for the realization of the four basic steps to verify that the parametric model. ANSYS provides a parameterized language-modeling approach of ANSYS Design Language (APDL), can be used to automate the same task or even to establish the parameters of the mathematical modeling. Therefore, the automatic grid files and computing may be defined APDL file and the depth of carburized layer on inverse problem can also receive the analysis results. In addition, the use of finite element analysis software ANSYS, the processing mode to run the graphical user interface (GUI) will not appear and the preparation of the corresponding computer program, just run in the background command. APDL file including the design variables, and the output file, including the constraints and objectives, to optimize the control file can only integrate the two documents, the parallel optimization based on finite element analysis.Figure 1 illustrates a synchronous design and optimization process, as shown in the process is a cyclical process. ISIGHTFD control unit, which controls the performance of finite element analysis and optimization. In this simulation, finite element analysis and optimization to manual execution. Therefore, this process can improve the optimization efficiency, expand the design space of the variables.
Fig.1. Process flow of integrated optimization
2.2 Simulation process
The text of the compiler can generate the APDL documents, and APDL file can define any completed command in a graphical user interface (GUI) mode or batch mode. There is a level of classification, geometric quantities is the top level, then the surface, then line keypoint minimum. Therefore, the two modeling methods can be applied to the APDL file, whether it is from top to bottom or from bottom to top. In the present study, the method adopted from the bottom to the top of the basis for the definition, because of coordination, and their location can be parameterized. When we defined a geometric element that may arise special element type. H-refinement and p-refinement is refined by two grid structure analysis. H-refinement mesh improve the accuracy of an increasing number of elements, and p-refinement meshing accuracy improve to increase the degree of the elements of the shape function, but the p-refinement cost of more computation time. regular application of h-refinement has a higher solution precision. Verify the quality of elements, many of the provisions need to check they are the aspect ratio deviates from 90 °, in parallel to the edge of degree of deviation, maximum degree angle and customized values ??can be defined users. If there is no warning and error, it shows that all these terms are satisfied, and calculations can begin. When the solution has been completed, the results can be from the depth of carburized layer inverse problem solving, reading and written into an output file, the file will provide constraints and objective function optimization.
2.3 Optimization algorithm
For multi-objective optimization, the best way does not exist here, some only a number of ways. Only consider one factor in this program must be superior than other options, but taking into account other factors, this program than other programs, some of the These programs are famous as the best Pareto program.?????In the literature, many algorithms have been developed for the best Pareto program.In general, they can be divided into two, a listing search, including the greedy algorithm, hill-climbing algorithm, branch and bound algorithm, depth-first search algorithm to search for answers in some areas of the given design, they can solve problems in practical applications. But it can not be used in multiple-scale or complex non-linear problems, to spend a huge computational cost. The other is a random search algorithms, including random walk, tabu search, simulated annealing algorithm, Monte Carlo algorithm, evolutionary algorithm, the algorithm is supposed to solve the problem, irregular need to define the evaluation function for direct search to solve the problem. Compared to enumerate the search, random search better solutions to complex problems.The genetic algorithm (GA) is one of the most prominent random search methods, and it has been widely used. It comes from the principles of natural genetics and natural selection. The basic principle of genetics is to borrow to build artificial demand for the minimum amount of information on health algorithm. Deb introduced the basic theory and operating principle of the genetic algorithm (GA).In recent years, in order to find the best Pareto program, developed a new version of the various genetic algorithm, Knowles and Corne of PAES, Horn, et al. For multi-objective optimization is proposed NPGA the Zitzler proposed of SPEA, and practice. On the other hand, improved unmarked concept of the members of the species population, and was named on NSGA. Before the packet, all unmarked member is marshaled to a pressure in the healthy group, and each individual members of this group have the same reproductive potential. In order to maintain the diversity of the population, grouping members of the health value to be shared. Subsequently, the arrangement of another set of unmarked individual choreography, has been down, until all groups. Results, the first member of the health value, and have greater reproductive capacity than the rest of the population. Coello et al. Pareto packet over and over again repeated, so he felt that the the NSGA efficiency is not high. Clearly, a more efficient way to get the same result is very possible.As an advanced version of the NSGA, in order to improve computational efficiency, Deb 'et al. Introduced the NSGA-II, NSGA-II, each program must be determined that it named the program, the NSGA-II evaluation of special programs in the population around the density, in fact, this density is the average distance between two points. NSGA-II does not require external memory and other MOEAs. In addition, because it is an innovative organization, so some researchers have successfully applied to engineering problems. In this study, the robot on the mixed-mode aerial vehicles (HMAWV) is also used to optimize the structure size.
3.A case study: manipulators of HMAWV
HMAW a top mechanical products in the field of construction machinery, is widely used in power industry, municipal engineering, and fire department. Its scope of work can reach a height of about 19 ??m. Because the operator must ensure the safety of facilities, the structural design must be absolutely reliable. In this study, an integrated design, strength analysis and structural optimization.
Fig.2. Hybrid mode aerial working
Fig.3. Extended status of HMAWV
Shown in Figure 2, HMAWV 19 parts: 1 - hydraulic foot, 2 - chassis, 3 - turret, 4 - the main hydraulic cylinders, arm 5 -, 6 - Auxiliary arm, 7 -pull rods, 8 - before support, 9 - the second arm, 10 - the second arm of the auxiliary, 11 - support, 12 - contraction of the hydraulic cylinder, 13 - the first parallel to the hydraulic cylinder, 14 - the first contraction of the arm, 15 -contraction of the hydraulic cylinder, 16 - the second contraction of arm, 17 - contraction arm, 18 - second parallel hydraulic cylinder, 19 - Operating Room. The table can be divided into two parts according to the movement: First, include 1-10 of the folded part, including 11-17 the extension of. Therefore, the mixed model table with integrated folding and extension of both worlds. When it works, hydraulic system to control the movement of each component, the main hydraulic cylinder to control the movement of the folded part. The parallel between this and the first arm and auxiliary arm movement is similar to the second arm and the second auxiliary arm to follow the same law of motion. Energy by dragging the rod to pass from the first arm to the second arm. When the contraction of the second contraction of the hydraulic cylinder control arm, the main contraction of the hydraulic cylinder control the extension of the movement. Chain to control the third contraction of the arm 13 to -18 partial control of the balance of the operating room, Figure 3 shows the conditions of the working vehicle.
一個針對復雜機械結構的多目標優(yōu)化集成方法（譯文）
徐冰，陳南，車華軍
東南大學機械工程學院，中國南京211189
摘要：
現(xiàn)在已經(jīng)有人提出了一個針對復雜機械結構的多目標優(yōu)化集成方法，這種方法集成了原型建模，有限元分析和優(yōu)化。為了探索它相對于傳統(tǒng)方法的優(yōu)勢，在混合模式高空作業(yè)車（HMAWV）上的機械手已經(jīng)采用了這種優(yōu)化，這樣做的目的是增加其工作領域，在足夠的強度前提下降低成本，將設計變量的幾何尺寸，并且?guī)缀纬叽缒軌騾?shù)設計，NLPQL和NSGA – II被綜合應用去獲得最佳解決方案。結果顯示這種集成方法比窮舉搜索算法更有效率。NSGA -Ⅱ可以接近全球前沿技術，而NLPQL和NSGA - II兩者的相對誤差是微不足道的。因此，這種集成方法是有效的，并在工程應用領域顯示了其潛力。
1． 引言
為了提高產(chǎn)品的市場競爭力,結構設計、分析以及優(yōu)化就像同步工程一樣已經(jīng)被整合進入概念發(fā)展階段的過程?？茖W文獻里有設計一個新產(chǎn)品各種各樣的技術,其中計算機編程越來越流行，因為，伴隨著計算機能力和軟件技術革命的前進，編程的優(yōu)越性已經(jīng)在效率和精度上體現(xiàn)了出來。
傳統(tǒng)的計算機編程是這樣的：首先，工程師繪制產(chǎn)品的草圖；其次，使用計算機輔助設計(CAD) 軟件建立幾何模型，隨后，大部分工程師將這個CAD模型導入到有限元分析工具中去評價它的結構性能，最后，由ANSYS ，MSC /NASTRAN，ABAQUS等一些商用軟件來完成尺寸和和拓撲優(yōu)化。在這個方向已經(jīng)有許多重要的進步，一些研究人員利用國產(chǎn)研究工具MSC / NASTRAN去實現(xiàn)結構優(yōu)化，Barkeret al 介紹了關于MSC /NASTRAN的二次開發(fā)，并且已經(jīng)被兩個實例證實了。最近，Hansen 和 Horst 根據(jù)精細的有限元模型開發(fā)了一個多級優(yōu)化程序，也就是說第一步用發(fā)展找略優(yōu)化拓撲參數(shù)，第二步應用MSC / NASTRAN優(yōu)化模型的厚度和縱切面，不過簡化了邊界條件。雖然以這種方式做出了許多努力，但是由于傳統(tǒng)優(yōu)化算法的禁錮，解決方案仍然被困在現(xiàn)在的某個區(qū)域，并且忽視了許多非線性因素以致于這種方案還不精確。
這種新奇的方法是一種同步的將有限元軟件集成到優(yōu)化程序的方法。它采用隨機搜索算法做為優(yōu)化方法,這不僅可以防止優(yōu)化器被困住在當?shù)氐膮^(qū)域，并且可以達到全球精確的最優(yōu)方案。許多優(yōu)化工具已經(jīng)在文學領域進行開發(fā)，CAOSS出現(xiàn)得比較早,它是一個模塊擴展有限元程序。Bakhtiary et al 提出了CAOSS和MSC / NASTRAN之間的新接口，接著Meske
et al介紹了這個接口通往FEMsolvers，MSC/NASTRAN, MSC/Fatigue, ABAQUS, MSC.Marc 以及MSC.Patran的方式。私有軟件DynOPS是作為優(yōu)化工具的另外一個選擇，Giger 和 Ermanni 利用DynOPS把有限元分析軟件ANSYS應用到開發(fā)復合纖維增強塑料摩托車鋼圈中。Hilmann介紹了一個優(yōu)化軟件SFE concept，這個軟件被廣泛用于德國的汽車行業(yè)。ISIGHT是另一個優(yōu)化軟件，它包括廣泛的經(jīng)典和非經(jīng)典的優(yōu)化方法,如實驗設計(DOE)，近似交換技術，多標準分析和質量工程方法。Qian 和 Yuan 成功將UG, ICEM-CFD,和FLUENT集成到ISIGHT，并且實驗設計(DOE)被用于設計underhood。后來，Cullimore et al.為了優(yōu)化一個觀測太空望遠鏡而將MSC / NASTRAN和 Fluent 集成到ISIGHT。盡管許多優(yōu)化工具已經(jīng)被廣泛開發(fā)，但是對復雜機械結構的多目標優(yōu)化仍然是個挑戰(zhàn)。
在這項研究中,一個完整的設計方法和多目標結構優(yōu)化是先進的。用ANSYS軟件和優(yōu)化算法進行有限元分析被集成到一個商業(yè)優(yōu)化軟件ISIGHT-FD，并且詳細的證實了這些集成過程。作為一個應用的例子，多目標優(yōu)化的機械手得到了開發(fā)，這樣做的目的是擴大其使用范圍,同時在足夠強度的前提下通過優(yōu)化幾何尺寸減輕其質量。無論是基于變化率的古典算法還是現(xiàn)在的進化算法都被采納來取得最佳方案。
在第二部分中, 探討了包含有限元模型的集成程序，仿真過程,和優(yōu)化算法。在第三部分中，混合模式高空作業(yè)車（HMAWV）上的機械手作為一個研究實例被提了出來。應用接觸單元模擬連接，來驗證有限元分析的結果，開發(fā)試驗應力分析。并且采納NLPQL和NSGA-II去優(yōu)操縱宗器。比較兩種算法的優(yōu)化結果。而且，為了驗證對最佳方案的影響，對NSGA-II的參數(shù)定義不同值。在第四部分中，做結論并且讓將來的學者去研究討論。
2． 并行方法的集成程序
結構優(yōu)化的關鍵是有沒有能力自動生成各種設計的虛擬樣機模型。為實現(xiàn)并行設計和優(yōu)化，四個基本步驟必須驗證參數(shù)化模型。 ANSYS提供了一種參數(shù)化的有l(wèi)anguage-ANSYS建模方法設計語言(APDL)，可以用來自動化相同的任務甚至建立數(shù)學模型等方面的參數(shù)。因此,自動網(wǎng)格文件和計算有可能定義APDL文件,并且滲碳層深度逆問題求解也可以得到分析結果。此外,運用有限元分析軟件ANSYS,對運行處理模式,即圖形用戶接口(GUI)將不會出現(xiàn)并編制相應的計算程序，只是在后臺運行命令。APDL文件包括設計變量,和輸出文件包括約束和目標,優(yōu)化控制文件僅能整合這兩個文件,實現(xiàn)并行基于有限元分析的優(yōu)化。
圖一闡述了同步設計和優(yōu)化過程，如圖所示的過程是一個循環(huán)的過程。ISIGHTFD是控制單元,它控制著有限元分析和優(yōu)化的性能。在這個模擬過程中，有限元分析和優(yōu)化能夠在沒有人工操作的情況下執(zhí)行。因此,這一過程可以提高其優(yōu)化效率,擴大變量的設計空間。
圖一 集成優(yōu)化過程流程圖
2.1 有限元分析模型
文本的編譯器能夠生成APDL文件,而且APDL文件可以在圖形用戶界面(GUI)模式或批處理模式中定義任何完成的命令。那里是一個層級的分類,即幾何量是頂部的等級,然后表面,然后線,keypoint最低。因此兩種建模方法可以應用于APDL文件,無論是從上到下還是從下到上。在本研究中,方法采用從下到頂部被定義的基礎,因為要協(xié)調,并且他們的位置可參數(shù)化的很容易。當我們在界定了可能產(chǎn)生的幾何元素特殊的元素類型。H-refinement和p-refinement是兩種網(wǎng)格結構分析提煉的方法。H-refinement嚙合精度提高越來越多的元素,而p-refinement嚙合精度的提高增加程度的形函數(shù)的元素,但p-refinement成本更多的計算時間。h-refinement定期應用方法具有較高的求解精度。驗證了該質量的元素,許多條款需要檢查,他們是長寬比偏離90°,在平行相對邊緣的偏離度,最大值在度角而且定制的值可以被定義用戶。如果沒有警告和錯誤出現(xiàn),它表明所有這些條款都滿意,和計算可以開始了。當解決方案已經(jīng)完成,結果即可從滲碳層深度逆問題求解,閱讀和寫進一個輸出文件,該文件將提供約束和目標函數(shù)優(yōu)化。
2.2 仿真過程
仿真在計算機工作站上運行，并且要占用許多計算資源。仿真過程是:首先,給設計變量分配初始值，然后用ANSYS在批量模型中執(zhí)行有限元分析；
其次,設計變量提取APDL文件,而約束和目標函數(shù)提取的輸出文件到ANSYS,并且保存ISIGHT-FD中;第三,證明該算法的收斂性,如果持平這個程序將被終止,而不是融合。優(yōu)化算法用于修改價值觀的設計變量和有限元分析和優(yōu)化是重復的,直到持平問題。優(yōu)化接近最優(yōu)解，這一系列的問題的解決方案為單目標優(yōu)化問題，且是一個單一的最優(yōu)的解決方案。
2.3 優(yōu)化算法
對于多目標優(yōu)化，最好的方法是不存在，這里有的僅僅是一系列方法。當只考慮一個因素時，這個方案比其他方案都要優(yōu)越，但是考慮到另一個因素時這個方案就比其他方案要差一些了。這些方案作為最佳Pareto方案而著名。
在文獻中可以知道許多算法被開發(fā)出來用于獲得最佳Pareto方案。
一般來說,他們可以分為兩種,一種是列舉搜索,包括貪心算法,爬山算法,分枝定界算法,深度優(yōu)先搜索等,這些算法在給定的設計一些領域中搜索答案,他們可以解決實際應用中出現(xiàn)的問題。但卻無法被應用在多個尺度或復雜的非線性問題,因為要花費巨大的計算成本。另一種是隨機搜索算法,包括隨機漫步,禁忌搜索、模擬退火算法、蒙特卡羅算法,進化算法等,這些算法原本要解決的問題,評價功能不規(guī)則的需要定義直接搜索而解決問題。相比以列舉搜索,隨機搜索能較好地解決復雜問題。
遺傳算法(GA)是其中一個最突出的隨機檢索方法，并且目前它已得到了廣泛的應用。它來源于自然遺傳學的原則和自然選擇。一些遺傳學的基本原理被借用來人工構建需求最小量問題信息的健康算法。Deb介紹了基因算法（GA）的基本理論和工作原理。
近年來，為了尋找最佳Pareto方案，有人開發(fā)了各種基因算法的新版本，Knowles和 Corne 提出了PAES, Horn et al.針對多目標優(yōu)化提出了NPGA, Zitzler提出了SPEA，并且用于實踐。另一方面，改進人口成員種類的無標記概念，并命名為NSGA。在分組之前，所有無標記成員被編排到一個壓健康小組中，并且這個小組中每一個單獨的成員具有同樣的生殖潛能。為了維護人口的多樣性，編組成員的健康值被共享。隨后，編排另一組無標記個體， 一直編排下去直到所有人都分好組。結果，第一層成員的健康值最大，并且比其他人口有更大的生殖能力。Coello et al.認為Pareto分組必須一遍又一遍的重復進行，所以他覺得NSGA效率并不高。顯然，用一種效率更高的方式獲得相同的結果是非常有可能的。
作為一個高級的NSGA版本，為了提高計算效率，Deb et al.推出了NSGA-II，在NSGA-II中，每一個方案必須測定它命名的方案有多少，NSGA-II評估在人口中特殊方案周圍的密度，事實上，這個密度是兩點間的平均距離。NSGA-II不需要和其他MOEAs一樣的外部存儲器。此外，因為它是一個創(chuàng)新的機構，所以它的效率比以前的版本高，而且由于它的性能非常好以至于在最近它非常受歡迎。
NSGA-II被一些研究人員成功應用到工程問題上。在這次研究中，混合模式高空作業(yè)車（HMAWV）上的機械手也采用了它來優(yōu)化結構尺寸。
3. 實例研究：混合模式高空作業(yè)車（HMAWV）上的機械手
HMAW是一種在工程機械領域的頂級機械產(chǎn)品，目前廣泛應用于電力行業(yè)、市政工程、消防部門等。它的工作范圍內可以達到大約19米高度。因為操作員工作在沒有其他保護設施的操作室里面，必須要保證機械裝置的安全，所以結構設計必須是絕對可靠的。在這次研究中，介紹了一種集成了設計、強度分析以及結構優(yōu)化的方法。
圖2：混合模式高空作業(yè)車
圖3：HMAWVD的延伸狀態(tài)
如圖2所示，HMAWV由19個部件組成，其中：1-液壓支腳，2-底盤，3-回轉臺，4-主液壓缸，5-第一手臂，6-輔助第一手臂，7-拉棒，8-前支撐，9-第二手臂，10-輔助第二手臂，11-后支撐，12-主收縮液壓缸，13-第一平行液壓缸，14-第一收縮手臂，15-收縮液壓缸，16-第二收縮手臂，17-第三收縮手臂，18-第二平行液壓缸，19-操作室。這些工作臺可以根據(jù)運動情況分成兩部分：一是包括1-10的折疊部分，二是包括11-17的延伸部分。因此，混合模型工作臺集成了折疊和延伸的兩種優(yōu)點。當它工作時，液壓系統(tǒng)控制每一個部件的運動，主液壓缸控制折疊部分的運動。這和第一手臂與輔助第一手臂之間的平行運動比較相似，第二手臂和輔助第二手臂也遵循同樣的運動規(guī)律。能量通過拖棒從第一手臂傳遞到第二手臂。當收縮液壓缸控制第二收縮手臂的時候，主收縮液壓缸控制延伸部分的運動。利用鏈條控制第三收縮手臂，13-18部分控制操作室的平衡，圖3展示了該作業(yè)車的一個工況。