轉(zhuǎn)向架構(gòu)架外文資料翻譯--基于確保疲勞強(qiáng)度和減輕重量的轉(zhuǎn)向架構(gòu)架設(shè)計(jì)

1、<p><b>　　中文3100字</b></p><p>　　基于確保疲勞強(qiáng)度和減輕重量的轉(zhuǎn)向架構(gòu)架設(shè)計(jì)</p><p>　　B.H.Park and K.Y.Lee</p><p>　　機(jī)械工程學(xué)院，延世大學(xué)，首爾，韓國(guó).</p><p>　　這份手稿是于2005年4月8日收到后接受修改,出版于2005年1

2、1月25日。</p><p>　　DOI: 10.1243/09544097F01405</p><p>　　摘要：在一個(gè)轉(zhuǎn)向架的設(shè)計(jì)發(fā)展過(guò)程中，轉(zhuǎn)向架構(gòu)架疲勞強(qiáng)度的影響是一個(gè)重要的設(shè)計(jì)準(zhǔn)則。此外,為了節(jié)約能源和材料需要減輕重量。在這項(xiàng)研究中，用有限元方法在各種加載條件下對(duì)轉(zhuǎn)向架構(gòu)架進(jìn)行疲勞分析是根據(jù)UIC的標(biāo)準(zhǔn)形成的，這種方法試圖通過(guò)人工神經(jīng)網(wǎng)絡(luò)和遺傳算法來(lái)減小轉(zhuǎn)向架構(gòu)架的重量。<

3、/p><p>　　關(guān)鍵詞：轉(zhuǎn)向架、強(qiáng)度、疲勞強(qiáng)度分析、神經(jīng)網(wǎng)絡(luò)、優(yōu)化。</p><p><b>　　1 簡(jiǎn)介：</b></p><p>　　轉(zhuǎn)向架是列車上一個(gè)非常重要的構(gòu)件，它承載著鐵道車輛在運(yùn)動(dòng)中的各種力。鐵道車輛的運(yùn)動(dòng)受到軌道的幾何形狀、輪軌相互作用、懸掛裝置和零部件的慣性力的影響。同時(shí)，一臺(tái)高速運(yùn)行列車的轉(zhuǎn)向架結(jié)構(gòu)的重量應(yīng)該盡可能輕。因此，轉(zhuǎn)

4、向架的強(qiáng)度應(yīng)該在國(guó)際標(biāo)準(zhǔn)如UIC[1]和JIS [2]的基礎(chǔ)上仔細(xì)地進(jìn)行計(jì)算分析，以獲得一個(gè)合理的設(shè)計(jì)方案。在過(guò)去的設(shè)計(jì)過(guò)程里，諸如一些試驗(yàn)，現(xiàn)場(chǎng)測(cè)試，并對(duì)原型改進(jìn)得到一個(gè)合理的設(shè)計(jì)等步驟需要許多時(shí)間和很高的成本。然而，在計(jì)算機(jī)輔助工程(CAE)產(chǎn)品設(shè)計(jì)中，應(yīng)用有限元分析方法(FE)可以減少所需的成本和時(shí)間。利用有限元分析方法研究轉(zhuǎn)向架構(gòu)架曾有幾次先例[3,4]。</p><p>　　此外，轉(zhuǎn)向架占車輛總重量的一

5、大部分。目前設(shè)計(jì)者在節(jié)省能源和材料的驅(qū)動(dòng)下對(duì)車輛的結(jié)構(gòu)進(jìn)行輕量化設(shè)計(jì)。在CAE產(chǎn)品設(shè)計(jì)步驟，降低重量的優(yōu)化方案以及最優(yōu)算法的應(yīng)用可使重量減輕并滿足約束條件的疲勞強(qiáng)度。</p><p>　　這是一個(gè)典型的疲勞約束下降低轉(zhuǎn)向架重量的結(jié)構(gòu)優(yōu)化問(wèn)題,但只是應(yīng)用現(xiàn)有數(shù)控優(yōu)化算法，問(wèn)題是無(wú)法解決的。在這一問(wèn)題上，疲勞約束作為一種分析不表達(dá)功能方面的設(shè)計(jì)變量。在這篇文章中，建立轉(zhuǎn)向架構(gòu)架的有限元模型是為了模擬疲勞試驗(yàn)。這項(xiàng)研究

6、中使用的轉(zhuǎn)向架是由焊接構(gòu)架、搖枕、自導(dǎo)向機(jī)制、一系懸掛、二系懸掛和盤形制動(dòng)裝置組成。轉(zhuǎn)向架構(gòu)架疲勞強(qiáng)度的評(píng)估則根據(jù)國(guó)際標(biāo)準(zhǔn)UIC615-4 進(jìn)行“動(dòng)力單位轉(zhuǎn)向架和運(yùn)行齒輪轉(zhuǎn)向架構(gòu)架結(jié)構(gòu)強(qiáng)度試驗(yàn)”。該優(yōu)化問(wèn)題是由一個(gè)降低轉(zhuǎn)向架重量的對(duì)象函數(shù)和約束條件下的疲勞設(shè)計(jì)標(biāo)準(zhǔn)構(gòu)成。近似疲勞的約束的人工神經(jīng)網(wǎng)絡(luò)(ANN)函數(shù)和微觀遺傳算法(µGA)被用來(lái)解決這一優(yōu)化問(wèn)題。</p><p>　　2轉(zhuǎn)向架構(gòu)架的應(yīng)力分析&

7、lt;/p><p>　　2.1轉(zhuǎn)向架構(gòu)架的有限元模型</p><p>　　在這項(xiàng)研究中，分析對(duì)象是搖枕轉(zhuǎn)向架（圖1(a)）。對(duì)轉(zhuǎn)向架構(gòu)架有限元模型數(shù)值分析的目的是進(jìn)行除搖枕外轉(zhuǎn)向架疲勞強(qiáng)度的評(píng)估，拖車轉(zhuǎn)向架構(gòu)架是由28250個(gè)節(jié)點(diǎn)、23870個(gè)矩形殼單元、2710個(gè)六角形固體單元緊密連接而成。考慮到拖車轉(zhuǎn)向架構(gòu)架一系懸掛的邊界條件，彈簧邊界元件就可以建立，并且這些元件的剛度與一系懸掛完全相同。

8、拖車轉(zhuǎn)向架構(gòu)架有12根彈簧為基本懸掛單元。軟件程序使用Altair Hyper Mesh和ABAQU。</p><p>　　這個(gè)轉(zhuǎn)向架構(gòu)架材料是SWS490A，定義在文獻(xiàn)[2]，該材料的性能見(jiàn)表1。</p><p>　　2.2負(fù)載條件下評(píng)價(jià)轉(zhuǎn)向架構(gòu)架疲勞強(qiáng)度的影響</p><p>　　疲勞分析是基于暫行標(biāo)準(zhǔn)。</p><p>　　在職載荷主要

9、是為了確保使用時(shí)在已考慮到的主要力綜合作用過(guò)程中沒(méi)有任何發(fā)生疲勞裂紋的風(fēng)險(xiǎn)。載荷產(chǎn)生的情況，包含轉(zhuǎn)向架構(gòu)架的各種不同負(fù)載、直線軌道、曲線通過(guò)、軋制和跳躍的影響、和跟蹤扭曲。表2和3顯示各個(gè)負(fù)載的負(fù)載情況和應(yīng)用領(lǐng)域。</p><p>　　表1 轉(zhuǎn)向架構(gòu)架材料特性（MPa）</p><p><b>　　表2 主應(yīng)力情況</b></p><p>　　

10、在表2中， 是空車質(zhì)量， 是轉(zhuǎn)向架數(shù)量， 是單個(gè)轉(zhuǎn)向架質(zhì)量， 是乘客的平均質(zhì)量，g (m/)為重力加速度。根據(jù)表2和標(biāo)準(zhǔn)UIC 615-4[ 1 ]，主要載荷的情況可由表3進(jìn)行規(guī)定。疲勞強(qiáng)度分析時(shí)使用的變量如 的施加情況列在圖.1(a)中。</p><p>　　在每個(gè)節(jié)點(diǎn)， 每種載荷下的應(yīng)力由表3確定?？梢詮慕Y(jié)果看出，表5中定義的最大應(yīng)力和最小應(yīng)力的大小由圖2中步驟確定， 根據(jù) ，平均應(yīng)力 和 應(yīng)力幅值

11、 由下式定義：</p><p>　　表3主應(yīng)力載荷（KN）</p><p>　　根據(jù)每一節(jié)點(diǎn)上的，可以得到如圖.3所示的古德曼圖。應(yīng)力幅值需滿足下式要求：</p><p>　　圖2 最大和最小應(yīng)力的確定</p><p>　　圖3 修改后的古德曼圖</p><p>　　許用應(yīng)力 從古德曼圖中獲得，n是設(shè)計(jì)因數(shù)。表4

12、中的初始設(shè)計(jì)的分析結(jié)果如圖3中所示。如圖3所示，疲勞強(qiáng)度大多滿足古德曼應(yīng)力圖的要求。在焊接和磨削處，</p><p>　　一些節(jié)點(diǎn)違反古德曼圖。最高值的n是1.04。</p><p>　　3轉(zhuǎn)向架構(gòu)架的優(yōu)化設(shè)計(jì)中</p><p>　　3.1 人工神經(jīng)網(wǎng)絡(luò)的設(shè)計(jì)因數(shù)n</p><p>　　疲勞強(qiáng)度約束為一個(gè)三層逼近誤差反向傳播神經(jīng)BPN網(wǎng)絡(luò)。神

13、經(jīng)網(wǎng)絡(luò)塑造了人腦執(zhí)行某一特定任務(wù)或處理信息的方式[6]。人工神經(jīng)網(wǎng)絡(luò)的高度非線性逼近函數(shù)得到了很好的利用。反向傳播是一種多用途的學(xué)習(xí)算法。</p><p>　　考慮轉(zhuǎn)向架構(gòu)架的疲勞強(qiáng)度，設(shè)計(jì)因子n被選擇作為輸出參數(shù)，然而其上蓋板、下蓋板和里面的側(cè)架垂直蓋板是被選擇作為輸入?yún)?shù)網(wǎng)絡(luò)。</p><p>　　表4和圖4顯示各個(gè)設(shè)計(jì)變量的初始值，上、下限值和最初的重量。</p>&l

14、t;p>　　首先，疲勞分析數(shù)據(jù)應(yīng)該在逼近人工神經(jīng)網(wǎng)絡(luò)時(shí)獲得。這三個(gè)水平的設(shè)計(jì)變量的全因子設(shè)計(jì)被用來(lái)產(chǎn)生訓(xùn)練數(shù)據(jù)集。每一個(gè)變量如表4所示有初始值和上下限值。三項(xiàng)測(cè)試驗(yàn)證了近似模型的可靠性。</p><p>　　用于BPN的特定的節(jié)點(diǎn)通過(guò)27次最嚴(yán)格的試驗(yàn)選擇。這些結(jié)點(diǎn)呈現(xiàn)在圖5中。</p><p>　　在這項(xiàng)研究中，圖6所示的神經(jīng)網(wǎng)絡(luò)模型被應(yīng)用于在每個(gè)節(jié)點(diǎn)上逼近設(shè)計(jì)因子。</p&

15、gt;<p>　　表5標(biāo)記了選定節(jié)點(diǎn)設(shè)計(jì)因子近似結(jié)果。測(cè)試數(shù)據(jù)及疲勞分析數(shù)據(jù)之間的最高百分比誤差為5.34%，結(jié)果表明，該模型的測(cè)試成功完成。</p><p><b>　　表4設(shè)計(jì)變量和限值</b></p><p><b>　　3.2遺傳算法優(yōu)化</b></p><p>　　遺傳算法(GAs)是一種基于自然選

16、擇力學(xué)和自然遺傳學(xué)的搜索算法。遺傳算法會(huì)結(jié)合收斂性解決方案得到全局最優(yōu)或近似解，已經(jīng)被成功運(yùn)用到各種各樣的一些功能優(yōu)化問(wèn)題。數(shù)量增加時(shí)，算法找到一個(gè)更好的解決辦法。然而，一個(gè)更大的數(shù)量規(guī)模需要更多的計(jì)算時(shí)間才能找到最合適的解決方案。因此，戈德堡[7,8]提出了串行遺傳算法(SGA)，它通過(guò)與常規(guī)遺傳算法相比一個(gè)更小的規(guī)模。在SGA的基礎(chǔ)上，Krishnakumar[9]在1989年提出了µGA。</p><

17、p>　　圖4轉(zhuǎn)向架構(gòu)架的設(shè)計(jì)變量X</p><p><b>　　圖5節(jié)點(diǎn)約束條件</b></p><p>　　在這項(xiàng)研究中，五個(gè)個(gè)體規(guī)模的µGA得到使用。µGA流程圖如圖7。</p><p>　　該優(yōu)化問(wèn)題是定義如下</p><p>　　F( X ) (kg) 是蓋板的重量，N是設(shè)計(jì)變量的個(gè)數(shù)，

18、 A () 是第i個(gè)的蓋板的面積，(mm)是第i個(gè)蓋板的厚度。SWS490A的密度7.85×10 kg/</p><p>　　圖6 3-3-1神經(jīng)網(wǎng)絡(luò)模型</p><p>　　表5各項(xiàng)測(cè)試中人工神經(jīng)網(wǎng)絡(luò)設(shè)計(jì)因子和疲勞分析的誤差</p><p><b>　　圖8遺傳算法結(jié)果</b></p><p>　　圖8顯示

19、目標(biāo)函數(shù)F(X)的優(yōu)化過(guò)程使用µGA。三種不同仿真研究在小于誤差0.5%的范圍進(jìn)行了。最優(yōu)值的最好結(jié)果是0.504噸(表6)。轉(zhuǎn)向架構(gòu)架的重量比最初的設(shè)計(jì)降低了4.7%。約束條件變成節(jié)點(diǎn)4862處的1.000了(見(jiàn)表7)。優(yōu)化結(jié)果的值和設(shè)計(jì)變量最優(yōu)值的分析結(jié)果之間最大誤差為2.93%。</p><p><b>　　表6 優(yōu)化結(jié)果</b></p><p>　

20、　表7設(shè)計(jì)因子預(yù)測(cè)值與比較值</p><p>　　表7表明神經(jīng)網(wǎng)絡(luò)模型的近似最優(yōu)值滿足修改后的古德曼圖，但在實(shí)際計(jì)算最佳厚度, 古德曼圖節(jié)點(diǎn)4862是不符合的。這是由于預(yù)測(cè)和分析模型之間的誤差。</p><p><b>　　4 總結(jié)</b></p><p>　　在這項(xiàng)研究中，轉(zhuǎn)向架構(gòu)架的疲勞強(qiáng)度是在轉(zhuǎn)向架發(fā)展步驟中根據(jù)標(biāo)準(zhǔn)UIC估計(jì)的。在這個(gè)過(guò)

21、程中成功采用了商品化研制。然后，轉(zhuǎn)向架構(gòu)架降低重量的問(wèn)題解決了。</p><p>　　疲勞強(qiáng)度并不滿足修改后的古德曼圖表的設(shè)計(jì)條件。然而，進(jìn)行了降低轉(zhuǎn)向架構(gòu)架重量?jī)?yōu)化后的，重量比最初的設(shè)計(jì)降低了4.7%。在這個(gè)過(guò)程中，使用了BPN網(wǎng)絡(luò)和GA的方法。</p><p>　　近似模型滿足設(shè)計(jì)約束，但預(yù)測(cè)和分析模型之間的誤差導(dǎo)致優(yōu)化設(shè)計(jì)的分析結(jié)果違反了設(shè)計(jì)約束。</p><p&

22、gt;<b>　　參考文獻(xiàn)</b></p><p>　　1 International Union of Railways. Motive power units,bogies and running gear, bogie frame structure strengthtests . UIC 615 – 4, 1994.</p><p>　　2 Japanese

23、Industrial Standard.Truck frames for railway rolling stock – general rules for design. JIS E 4207, 1992.</p><p>　　3 Dietz, S., Netter, H., and Sachau, D.Fatigue life prediction of a railway bogie under dynam

24、ic loads though</p><p>　　simulation. Veh. Sys. Dyn., 1998, 29, 385 – 402.</p><p>　　4 Oyan, C.Structural strength analysis of the bogie frame in Taipei rapid transit systems. Proc. Instn Mech. En

25、grs,</p><p>　　Part F: J. Rail and Rapid Transit, 1998, 212 (F3), 253 – 262.</p><p>　　5 European Rail Research Institute.Programme of tests to be carried out on wagons with steel underframe andbo

26、dy (suitable for being fitted with the automatic buffing and draw coupler) and on their cast steel frame bogies.</p><p>　　ERRI B12/RP 17, 7th edition, 1993.</p><p>　　6 Hagan, M. T.Neural network

27、 design, 1996 (PWS Publish Company, Boston, MA).</p><p>　　7 Goldberg, D. E.Sizing populations for serial and parallel genetic algorithms. Proceeding of the 3rd International Conference on Genetic algorithms,

28、 Arlington, VA, 1989,pp. 70 – 79 (Morgan Kaufmann).</p><p>　　8 Goldberg, D. E. Genetic algorithms in search, optimization and machine learning , 1989 (Addison-Wesley,</p><p>　　Boston, MA).</p

29、><p>　　9 Krishnakumar, K. Micro-genetic algorithm for stationary and non-stationary function optimization. SPIE,</p><p>　　Intell. Control Adapt. Syst. , 1989, 1196, 282 – 296.</p><p>　

30、　Bogie frame design in consideration of fatigue strength and weight reduction</p><p>　　B H Parkand K Y Lee</p><p>　　School of Mechanical Engineering,Yonsei University,Seoul,Republic of Korea<

31、/p><p>　　The manuscript was received on 8 April 2005 and was accepted after revision for publication on 25 November 2005.</p><p>　　DOI: 10.1243/09544097F01405</p><p>　　Abstract: In the

32、 development of a bogie, the fatigue strength of a bogie frame is an important design criterion. In addition, weight reduction is required in order to save energy and material .In this study, the fatigue analysis of a bo

33、gie frame by using the finite-element method is performed for various loading conditions according to the UIC standards and it is attempted to minimize the weight of the bogie frame by artificial neural network and genet

34、ic algorithm.</p><p>　　Keywords: bogie, strength, fatigue analysis, neural network, optimization.</p><p>　　1 INTRODUCTION</p><p>　　A bogie in a train is a very important structural

35、component loaded by various forces in the rail way vehicle motion. The motion of a railway vehicle is affect by the geometry of the track, the interaction between wheels and rails, the suspension, and the inertias of com

36、ponent part s. In the meantime, the weight of a bogie structure should be as light as possible at higher running speed. Therefore, the strength of the bogie should be carefully calculated and analysed by the internationa

37、l standard</p><p>　　In addition, the bogie has a large proportion of the total weight of a vehicle. Savings of energy and material are currently design drivers towards lightweight vehicle constructions. In C

38、AE product</p><p>　　design step, optimization for weight reduction and application of the optimal algorithm can make the light weight and the constraint conditions for the fatigue strength satisfy.</p>

39、<p>　　It is a typical structural optimization problem to minimize the weight of the bogie under the fatigue constraint, but the problem cannot be solved by simply applying the existing numerical optimization algor

40、ithms. In the problem, the fatigue constraint is</p><p>　　not expressed as an analytical function in terms of the design variables.</p><p>　　In this article, the FE model of the bogie frame is c

41、onstructed to simulate the fatigue test. The bogie that is used in this study is composed of welded frame, bolster, self-steering mechanism, primary suspension, secondary suspension, and disc brake system. The fatigue st

42、rength of the bogie frame is estimated by the international standard UIC615-4 ‘Motive Power Units Bogies and Running Gear Bogie Frame Structure Strength Test’. The optimization problem is composed of an object function f

43、or the </p><p>　　2 STRESS ANALYSIS OF THE BOGIE FRAME</p><p>　　2.1 FE model of the bogie frame</p><p>　　In this study, the analysed bogie frame is a bolster type bogie (Fig. 1(a)).

44、The numerical analysis by the FE method is performed to evaluate the fatigue strength of the bogie frame except the bolster.</p><p>　　The bogie is modelled using shell and solid elements and the FE model is

45、shown in Fig.1(b ).The trailer bogie frame is meshed to have 28, 251 nodes, 23,870 rectangular shell elements, and 2710 hexagonal solid elements.</p><p>　　Considering the boundary conditions of the trailer b

46、ogie frame for the primary suspension, the spring boundary elements are established and the stiffness of the elements is the same as the primary suspension. There are 12 spring elements for the primary suspension in the

47、trailer bogie frame. The software programs used are Altair Hyper Mesh and ABAQUS .</p><p>　　The material used in the bogie frame is SWS490A defined in reference [ 2 ] and the material properties are shown in

48、 Table 1.</p><p>　　2.2 Load conditions and the evaluation of fatigue strength of the bogie frame</p><p>　　The fatigue analysis is based on the UIC standard. The main in- service load case is des

49、igned to verify the absence of any risk of fatigue cracks occurring under the combined effect of the main forces encountered during service. The load case consists of different load scenarios for the bogie frame involvin

50、g experiencing straight track, curve negotiation, rolling and bouncing effects, and track twist. Tables 2 and 3 show each load and application area and load scenarios.</p><p>　　In Table 2, mv(kg) is the empt

51、y mass of vehicles, nb the number of bogie, mþ(kg) the bogie mass, C1(kg)the passenger mass per seat, and g (m/s) and the acceleration due to gravity. From Table 2 and UIC 615-4 [1], the load cases of main in-servic

52、e are defined in Table 3. Variables Fz1, Fz2, Fy, Ft1, Ft2 of the loads applied during the fatigue strength analysis are presented in Fig.1(a).</p><p>　　At each node, the stress resulted from each load case

53、of Table 3 is determined. From the result, the maximum values max and the minimum values min defined in reference [5] are determined by the steps shown in Fig.2. From max and min, the mean stress m and the stress amplitu

54、des a are defined as follows</p><p>　　From m and a at each node, the Goodman diagram shown in Fig.3 is obtained. Stress amplitudes have to satisfy the following equation</p><p>　　The permissible

55、 stress p is obtained from the Goodman diagram and n is the design factor. The analysis result of the initial design in Tab le 4 is presented in Fig.3. As shown in Fig.3, the fatigue</p><p>　　strength satisf

56、ies mostly the Goodman diagram. At welding and grinding locations, some nodes violate the Goodman diagram. The maximum value of n is 1.04.</p><p>　　3 OPTIMAL DESIGN OF THE BOGIE FRAME</p><p>　　3

57、.1 ANN for the design factor n</p><p>　　The constraint for the fatigue strength is approximated by a three -layered error back propagation neural BPN network. Neural networks are developed to model the way i

58、n which the human brain performs</p><p>　　a particular task or processes information [6]. The use of ANN to approximate the functions with a high degree of non-linearity is well established.</p><p

59、>　　Back propagation is a general-purpose learning algorithm. Considering the fatigue strength of the bogie frame, the design factor n is chosen as the output parameter, whereas the upper cover plate, the lower cover p

60、late, and the inner vertical cover plate of the side frame are chosen as the input parameters of the network. Table 4 and Fig.4 show each design variable and initial, upper , and lower values with the initial weight.<

61、/p><p>　　First, the fatigue analysis data have to be obtained when approximated by an ANN. The three-level full-factorial design for three design variables is used in order to generate training data sets. Each

62、variable has initial, lower, and upper values, as shown in Table 4. The reliability of approximate model is verified by the three test data sets.</p><p>　　The specific nodes to be used in BPN are selected at

63、 the locations with the severest values through the experiments of 27 times. These nodes are presented in Fig.5.</p><p>　　In this study, the neural network model of Fig.6 is applied to approximate the design

64、 factor at each node.</p><p>　　The approximate results for the design factor at the selected nodes are marked in Table 5. As the maximum percentage error between the test data and the fatigue analysis data i

65、s 5.34 percent, it is concluded that the training of the model is successfully accomplished.</p><p>　　3.2 Genetic algorithm for optimization</p><p>　　Genetic algorithms (GAs) are the search algo

66、rithms based on the mechanics of natural selection and natural genetics. GA would make the combination convergence solutions that are globally optimal or</p><p>　　nearly so, and it has been successfully appl

67、ied to a variety of some functional optimization problems. As the population size increases, the algorithms find a better solution. However, a bigger population size requires more computational time to find the optimum s

68、olution. For this reason, Goldberg [7, 8] proposed serial GA (SGA), which used a small population size when compared with conventional GAs.On the basis of SGAs, Krishnakumar [9] proposed mGAs in 1989.</p><p>

69、;　　In this study, the mGA with a population size of five individuals is used. The flow chart of mGA used in this study is illustrated in Fig.7.</p><p>　　The optimization problem is defined as follows </p&

70、gt;<p>　　where F(X)(kg) is the weight of the plates, N the number of design variables, A() the area of the ith plate, and Xi(mm) the thickness of the ith plate. The density ρ of SWS490A is 7.85×10 kg/</p&g

71、t;<p>　　Figure 8 shows the optimization process of the object function F(X) using mGA. Three different simulations were performed with errors , 0.5 percent . The optimum value of the best result is 0.504 ton (Tabl

72、e6). The weight of the bogie frame was reduced by 4.7 percent than the initial design. The constraint condition n becomes 1.000 at node 4862 (Table 7). Between the values of the optimising results and the values of the a

73、nalysed results by the optimal values of design variables, the maximum erro</p><p>　　Table 7 shows that the optimal value of the approximated ANN model satisfies the modified Goodman diagram, but in the actu

74、al calculation with optimal thickness, the Goodman diagram is violated at node 4862. This is due to the error between the prediction and analysis models.</p><p>　　4 CONCLUSIONS</p><p>　　In this

75、study, the fatigue strength of the bogie frame was estimated by the UIC in the developing step of the bogie. In this process, the post-process was developed. Then, the weight reduction problem of the bogie frame was solv

76、ed .</p><p>　　The fatigue strength was not satisfied by the design conditions of the modified Goodman diagram. However, after the optimization to reduce the weight of the bogie frame was performed, the weigh

77、t was reduced by 4.7 percent than the initial design . In the process , the BPN network and the GA were used.</p><p>　　The approximated model satisfies the design constraint, but the analysis result of the o

78、ptimal design violates the design constraint because of the error between prediction and analysis models.</p><p>　　REFERENCES</p><p>　　1. International Union of Railways. Motive power units, bog

79、ies and running gear, bogie frame structure strength tests. UIC 615-4, 1994.</p><p>　　2. Japanese Industrial Standard. Truck frames for railway rolling stock general rules for design. JIS E4207, 1992.</p&

80、gt;<p>　　3. Dietz, S., Netter, H., and Sachau, D. Fatigue life prediction of a railway bogie under dynamic loads though simulation. Veh. Sys. Dyn., 1998, 29, 385-402.</p><p>　　4. Oyan, C. Structural s

81、trength analysis of the bogie frame in Taipei rapid transit systems. Proc. Instn Mech. Engrs,</p><p>　　Part F: J. Rail and Rapid Transit, 1998, 212 (F3), 253-262.</p><p>　　5. European Rail Resea

82、rch Institute. Programme of tests to be carried out on wagons with steel under frame and body (suitable for being fitted with the automatic buffing and draw coupler) and on their cast steel frame bogies.</p><p

83、>　　ERRI B12/RP 17, 7th edition, 1993.</p><p>　　6. Hagan, M. T. Neural network design, 1996 (PWS Publish Company, Boston, MA).</p><p>　　7. Goldberg, D. E. Sizing populations for serial and par

84、allel genetic algorithms. Proceeding of the 3rd International Conference on Genetic algorithms, Arlington, VA, 1989, pp. 70 – 79 (Morgan Kaufmann).</p><p>　　8. Goldberg, D. E. Genetic algorithms in search, o

85、ptimization and machine learning , 1989 (Addison-Wesley, Boston, MA).</p><p>　　9. Krishnakumar, K. Micro-genetic algorithm for stationary and non-stationary function optimization. SPIE, Intell. Control Adapt