外文翻譯(提高板材的成形回彈預(yù)測(cè)精度的數(shù)據(jù)挖掘方法的應(yīng)用)

1、<p><b>　　外文資料</b></p><p>　　Application of Data Mining Method to Improve the Accuracy of Springback Prediction in Sheet Metal Forming</p><p>　　Xu Jing—ring(許京荊)， ZHANG Zhi—wei(張志

2、偉)， Wu，Yi—min(吳益敏)</p><p>　　School of Electrornechanical Engineering and Automation，Shanghai University，Shanghai 200072，P．R．China</p><p>　　Abstract: A new method was worked out to improve the pr

3、ecision of springback prediction in sheet metal forming by combining the finite element method(FEM)with the data mining(DM)technique．First the genetic algorithm (GA) was adopted for recognizing the materia1 parameters．Th

4、en according to the even design idea，the suitable calculation scheme was confirmed，and FEM was used for calculating the springback．The computation results were compared with experiment data，the difference between them wa

5、s tak</p><p>　　Key words :springback prediction，pattern recognition，genetic algorithm，F(xiàn)EM ，even design idea，H0MR，data mining．</p><p>　　1 Introduction</p><p>　　The springback in shee

6、t metal forming can be described as the change of sheet metal shape compared with the shape of the tools after forming process. Sheet metals with high strength--to--modulus ratio such as high strength steels and aluminum

7、 alloys are particularly prone to springback， and these materials are becoming more important in automotive industry to reduce the car weight and increase fuel efficiency．The final component shape does not conform to the

8、 tool geometry due to the springback o</p><p>　　Currently，the finite element method(FEM )has been used to calculate the springback of sheet metals in forming process[2-7],． but the results of calculation are

9、 not correct，and the calculation results of U—shape component show that the average error is 62％. It cannot be directly used for die design．</p><p>　　There are a lot of nonlinear factors，such as large deform

10、ation, friction, impact and materia1 characters, which will influence the sheet metal forming and springback. Because the data mining technique is a good method to treat the complex factors and data,． in order to predict

11、 the springback correctly in sheet metal forming , a new method is developed for springback prediction in the present paper．The FEM is used to calculate the springback．The computation results are compared with experiment

12、al </p><p>　　2 FEM Calculation Model</p><p>　　Sheet metal forming process is a typical topic related to impact and contact treatment, which refers to non-linear problems, such as large displacem

13、ent，large rotation , friction and contact[11] .． From the mechanics viewpoint the forming process is a dynamic and interactive action of multi-body contact system ，and for the forming process，the response of the system t

14、he time has to be examined．The response can be determined by the following governing equation.</p><p>　?。?1) Sheet metal forming process can be described by the dynamic equation：

15、 （1）</p><p>　　where is the Cauchy stress， is the body force density， is the acceleration，and ρ is the current density.</p><p>　　(2)The solution of dynamic equation should sat

16、isfy the following traction boundary conditions：</p><p><b>　?。?）</b></p><p>　　Where ，=1，2，3，is the unit outward normal to current boundary，and，= 1，2，3，is the surface force.</p>

17、<p>　　(3)The displacement boundary condition can be expressed as follows：</p><p><b>　　（3）</b></p><p>　　where ，=1，2，3，are the given displacement functions，and are the initial c

18、oordinates of particle at moment ．</p><p>　　(4)The contact discontinuity condition along the sliding contact surface area is</p><p><b>　　（4）</b></p><p>　　According to t

19、he above equation and boundary conditions，a formula can be obtained by the principle of virtual work，given as</p><p><b>　　(5)</b></p><p>　　where means virtual work． is virtual displa

20、cement， is the boundary of surface force．</p><p>　　After discretization， the following equation can be solved by the FEM ：</p><p><b>　?。?）</b></p><p>　　where is the glo

21、bal mass matrix，is the vector of global nodal acceleration,is the vector of global forces(including nodal forces，surface loads and body loads)，and F is the vector of equivalent nodal forces composed by element stress， me

22、ans the vector of velocity．</p><p>　　3 Mathematical Model of Springback Prediction in Sheet</p><p>　　Metal Forming</p><p>　　3.1 The parameters selection for FEM calculation</p>

23、;<p>　　Metal stamping process includes forming and springback．The stresses statuses of the two steps are different．So the simulation techniques for the two steps are also different in the application of FEM .．<

24、/p><p>　　First．the dynamic explicit method is used for calculating the forming，and then the previous calculation results are input to calculate the springback with the static implicit method adopted．According t

25、o this procedure the computation efficiency is improved．But the final calculation results are different from the experimental results due to different inputting parameters in the FEM calculation．In order to study the eff

26、ect of inputting parameters on the FEM results, the appropriate parameters shou</p><p>　　3.2 Determining the source data</p><p>　　(1) Determination of material model coefficients and FEM calcula

27、tion</p><p>　　Based on the stamping experiment in Fig.1, a quarter of experiment device is taken for the FEM calculation as shown in Fig.2.</p><p>　　The stamping experiment was carried out on th

28、e Zwick testing machine．The angle，and were measured(see Fig．3)，，，The FEM code ANSYS／LS．DYNA 5．71 is used for simulating forming and springback procedure． </p><p>　　Fig.2 Finite element model</p><

29、p>　　Fig．3 Measured angle and in experiment</p><p>　　The material character constants and invariable geometrical parameters for calculation are listed in Table 1．</p><p>　　Table 1 Materia1 ch

30、aracter constants and invariable geometrical parameters</p><p>　　Two different methods are applied to the springback simulation of FEM ．At the forming stage the explicit dynamic method is adopted, and the FE

31、M model is meshed by the four-node shell element．The shell formula is provided with the reduced integration point and Hourglassing control．It is called the Belytschko-Leriathan algorithm. The material model character bel

32、ongs to the elastoplastic behavior with isotropic hardening and has a power law constitutive relation-ship，which includes the Cowper-Symon</p><p>　　where is the yield stress， is the strain rate， is the strai

33、n，，P are the Cowper-Symonds strain rate coefficients， is the strength coefficient，and is the hardening index．</p><p>　　The symmetric displacement constrains are applied. The punch，die and blank holder are d

34、efined as rigid bodies， the blank hold force and the punch velocity are loaded, and the contact between components is defined as surface-to-surface contact. The solving procedure is not terminated until the stroke is ach

35、ieved．</p><p>　　At the free springback stage the static implicit analysis is applied to solving the geometry nonlinear behavior of the blank after the rigid bodies are removed．The stress and displacement res

36、ults after forming are transferred to initial springback mode1．The material model character becomes elastic one and the rigid displacement is forbidden by adding constrains in the stamping direction．</p><p>

37、　　After the axial tensile test of sheet metal, based on the stress-strain curves the material model coefficients in Eq.(7) are identified by our genetic algorithm code, given in Table [2].</p><p>　　(2)Genera

38、ting source data</p><p>　　Many factors can influence the FEM calculation results．In this paper，except above input consent coefficients and invariable parameters，the five variable parameters， ，，，and ，are exam

39、ined and their varying ranges are shown in Table 3．</p><p>　　Here，the even design idea is adopted to arrange the FEM scheme[17] According to the even design table (the arranged 30 tests at most allowing 13

40、variable parameters)and its attached utility table, with the varying range of the five parameters，，，，and ，30 sets of data sample are taken as the scheme of FEM for calculated angles and in Table 4．</p><p>　　

41、．2Table 4 30 sets of data sample and their FEM calculation results</p><p>　　3.3 Mathematical model of springback Prediction by HOMR method </p><p>　　Pattern recognition indicates that samples in

42、 multi-dimensional space are projected into a 2D domain and separated from different classes by using appropriate methods such as the principal component analysis method(PCA)，the linear map method(LMAP)，the partial least

43、 square method(PLS)and the Fisher vector method，etc[18]． . .But for complicated data a single method cannot separate the samples from different classes completely．In this paper，the hierarchical optimal map recognition me

44、thod(H0MR)is ad</p><p>　　(1)Evaluation of the source data</p><p>　　The improvement of springback can be described as the increase in the bottom angle and decrease in the flange angle ．Here，is ad

45、opted and means the globally measured angle as shown in Fig.3，and means the global calculation angle, and represents the difference between FEA calculations and experiments．It is assumed that the error is less than 10％ ，

46、that is， is defined as target function，and the samples satisfying are good sample defined as Class 1，the others are poor sample defined in Class 2.Using </p><p>　　Now we evaluate the data in the Table 5．Fix

47、the hyper-polyhedron criterion division rate = 100％ and the division rate =87.5％ after exchanging the class．Hyper-polyhedron criterion division rate is larger than 80％ and it is proved that the data structure is good for

48、 using to establish mathematical model. </p><p>　　(2)Establishment of mathematical model</p><p>　　During the FEM simulating procedure，we hope to get the best match of variables，，，,， for good tar

49、get．So we append 10 random samples using as prediction but not for establishing mathematical model．</p><p>　　Now we utilize the obtained data including 30 samples as training collectivity of the pattern reco

50、gnition and use HOMR method to get the map in Fig.4．</p><p>　　Fig.4 HOMR map</p><p>　　Fig．4 shows that the PCA map becomes the best map result by using the HOMR method ,the abscissa P(1)is the f

51、irst principal component，and the ordinate P(2)is the second principal component．The samples of Class 1 are separated absolutely，in the box the samples of Class 1 and Class 0 satisfy the condition of，and the boundary line

52、s of box mean the boundary equations of good samples area by H0MR method．This model is expressed by a set of listed inequalities in Eq.(8)and it is showed that the calculat</p><p><b>　?。?）</b><

53、;/p><p>　　Figure 4 also shows that there are 4 random samples in good sample area，as shown in Table 6．That implies that if the values of parameters variables，，，， ，，are chosen by Table 6，the simulation error is

54、less than 10％ ．For verifying the correctness of the mathematical model，4 random samples in good sample area are chosen to calculate by the FEM ．Finally the good results.are obtained in Table 6．</p><p>　　Tabl

55、e 6 Random samples in good sample area and sample verification</p><p>　　4 Conclusions</p><p>　　(1)The material parameter recognition can be improved by using GA， and it provides more accurate si

56、mulation of forming and springback calculation． </p><p>　　(2)According to even design idea，using appropriate inputting parameters can improve the efficiency of forming and springback calculation．</p>

57、<p>　　(3)Using the H0MR method，the mathematical model of springback simulation error can be reduced effectively，and the calculation accuracy can be controlled effectively．</p><p>　　(4)A new method is ap

58、plied to improve the FEM calculation accuracy for springback prediction and the calculating error can be less than 10％.</p><p><b>　　中文翻譯</b></p><p>　　提高板材的成形回彈預(yù)測(cè)精度的數(shù)據(jù)挖掘方法的應(yīng)用</p>

59、;<p>　　許京荊，張志偉，吳益敏</p><p>　　上海大學(xué)，機(jī)械工程及自動(dòng)化學(xué)院，上海200072</p><p>　　摘要：結(jié)合有限元方法（FEM）與數(shù)據(jù)挖掘（DM）技術(shù)，制定了一種可以提高板材成型回彈預(yù)測(cè)的精度新的方法。首先，為了確認(rèn)的材料參數(shù)，遺傳算法（GA）已經(jīng)獲得通過。然后根據(jù)設(shè)計(jì)理念，確認(rèn)適合的計(jì)算方案，采用有限元方法（FEM）計(jì)算回彈。計(jì)算結(jié)果與實(shí)驗(yàn)數(shù)據(jù)

60、相比較，它們之間的差異作為數(shù)據(jù)源和馬克的被叫做分層優(yōu)化圖識(shí)別方法（HOMR）新的模式識(shí)別方法在有限元方法中被應(yīng)用于計(jì)算規(guī)例總結(jié)。最后，回彈仿真數(shù)學(xué)模型成立了。在模型的基礎(chǔ)上，與實(shí)驗(yàn)結(jié)果相比，回彈的計(jì)算誤差可以控制在10％以內(nèi)。</p><p>　　關(guān)鍵詞：回彈預(yù)測(cè)，模式識(shí)別，遺傳算法，有限元，設(shè)計(jì)思路，分層優(yōu)化圖識(shí)別方法，數(shù)據(jù)挖掘。</p><p><b>　　1引言</b

61、></p><p>　　與成型工序后的工具形狀相比，板材成形回彈可以描述為金屬板材形狀的變化。具有高強(qiáng)度模量比的金屬板材，如高強(qiáng)度鋼和鋁合金，尤其容易回彈，而且這些材料對(duì)重量輕，高燃油率的汽車業(yè)變得越來越重要。由于零件回彈，最后一個(gè)部分的形狀不符合刀具幾何，所以模具設(shè)計(jì)變得非常困難。為了補(bǔ)償回彈，目前的汽車模具開發(fā)和建設(shè)過程需要試模。模具設(shè)計(jì)和建設(shè)是在新的車式發(fā)展過程中最耗時(shí)的步驟之一。因此，如何找到一種有

62、效而可靠的回彈預(yù)測(cè)方法具有重要意義。</p><p>　　目前，有限元法（FEM）已被用于計(jì)算金屬板材形成過程中回彈中，金屬板材回彈。但計(jì)算結(jié)果不正確，以及U形構(gòu)件的計(jì)算結(jié)果表明，平均誤差為62％ 。它不能直接用于模具設(shè)計(jì)。</p><p>　　很多非線性因素，如大變形，摩擦，撞擊，材料特性，都會(huì)影響到板材成型和回彈。由于數(shù)據(jù)挖掘技術(shù)是檢測(cè)復(fù)雜因素和數(shù)據(jù)的一個(gè)好方法，為了準(zhǔn)確預(yù)測(cè)金屬板材成

63、形回彈，本文將描述預(yù)測(cè)回彈的新方法。將計(jì)算結(jié)果與實(shí)驗(yàn)數(shù)據(jù)進(jìn)行比較，兩者之間的區(qū)別作為源數(shù)據(jù)，一個(gè)新的數(shù)據(jù)挖掘模式識(shí)別被應(yīng)用于有限元的總結(jié)計(jì)算中。根據(jù)分層優(yōu)化圖識(shí)別方法（HOMR）建立超多面體模型，建立了回彈仿真的數(shù)學(xué)模型。在數(shù)學(xué)模型的基礎(chǔ)上，可以預(yù)見的回彈，與實(shí)驗(yàn)結(jié)果，其誤差可控制在10％內(nèi)。</p><p><b>　　2有限元計(jì)算模型</b></p><p>　　

64、金屬板材成形過程是一個(gè)與影響和表面質(zhì)量相關(guān)典型的問題，是非線??性問題，如大位移，大轉(zhuǎn)動(dòng)，摩擦和接觸。根據(jù)力學(xué)的觀點(diǎn)，形成過程是一個(gè)多體接觸系統(tǒng)的動(dòng)態(tài)和交互式的運(yùn)動(dòng)，關(guān)于成型過程，系統(tǒng)的動(dòng)態(tài)與時(shí)間尚有待確定。系統(tǒng)的動(dòng)態(tài)可以根據(jù)以下方程來確定</p><p>　　（1）金屬板材成形過程可以用動(dòng)態(tài)方程描述：</p><p><b>　?。?）</b></p>

65、<p><b>　　式中—柯西應(yīng)力；</b></p><p><b>　　— 流體密度；</b></p><p><b>　　—加速度；</b></p><p><b>　　ρ—電流密度。</b></p><p>　?。?）動(dòng)態(tài)方程的解必須滿

66、足以下條件：</p><p><b>　?。?）</b></p><p>　　式中—當(dāng)前邊界的法向單元體；</p><p><b>　　—表面應(yīng)力。</b></p><p>　?。?）位移邊界條件可表示如下：</p><p><b>　　（3）</b>

67、</p><p>　　式中（=1，2，3，）—位移函數(shù)；</p><p>　　—在t時(shí)刻的初始坐標(biāo)值。</p><p>　?。?）接觸間斷條件沿滑動(dòng)接觸面面積</p><p><b>　?。?）</b></p><p>　　根據(jù)上述方程和邊界條件，公式可以通過虛功原理，可得出：</p>

68、;<p><b>　　(5)</b></p><p><b>　　式中 —虛功；</b></p><p><b>　　—虛位移；</b></p><p><b>　　—邊界表面應(yīng)力。</b></p><p>　　離散化后，下面的公式可以解

69、決有限元分析：</p><p><b>　?。?）</b></p><p>　　式中—球面質(zhì)量；</p><p>　　—球面節(jié)點(diǎn)加速度矢量；</p><p>　　—球面力（包括節(jié)點(diǎn)力，表面負(fù)荷和身體負(fù)荷）向量；</p><p>　　F—由單元應(yīng)力組成的等效節(jié)點(diǎn)力向量；</p>

70、<p><b>　　— 速度矢量。</b></p><p>　　3在金屬板材成形的回彈預(yù)測(cè)數(shù)學(xué)模型</p><p>　　3.1的有限元計(jì)算參數(shù)的選擇</p><p>　　金屬?zèng)_壓過程包括成型和回彈包括。兩個(gè)步驟應(yīng)力狀態(tài)是不同的。因此，對(duì)于這兩個(gè)步驟的模擬技術(shù)在有限元的應(yīng)用上是不同的。</p><p>　　首先，

71、動(dòng)力顯式方法用于計(jì)算的形成，然后前面的計(jì)算結(jié)果輸入到與靜態(tài)隱式計(jì)算方法，采用回彈。根據(jù)這一程序，提高了計(jì)算效率。但由于在不同的有限元中輸入?yún)?shù)計(jì)算，最終的計(jì)算結(jié)果不同與實(shí)驗(yàn)結(jié)果。為了研究輸入?yún)?shù)的有限元計(jì)算結(jié)果的影響，應(yīng)選擇適當(dāng)?shù)膮?shù)。應(yīng)該對(duì)以下的五個(gè)參數(shù)，如虛擬沖壓速度，，，，，進(jìn)行檢查。</p><p><b>　　3.2確定源數(shù)據(jù)</b></p><p>　?。?/p>

72、1）確定材料和有限元計(jì)算模型系數(shù)</p><p>　　基于圖1的沖壓實(shí)驗(yàn),實(shí)驗(yàn)裝置的四分之一的有限元計(jì)算如圖2所示。</p><p><b>　　圖1.實(shí)驗(yàn)裝置</b></p><p>　　沖壓試驗(yàn)在茲維克的試驗(yàn)機(jī)進(jìn)行。角度和是待測(cè)角度見（圖3），其中，，。使用有限元軟件ANSYS / LS.DYNA 5.71來模擬成型和回彈過程。</p

73、><p><b>　　圖2 有限元模型</b></p><p>　　圖3實(shí)驗(yàn)中測(cè)量角度和</p><p>　　材料的特性常數(shù)和幾何參數(shù)如表1所示。</p><p>　　表1材料的特性常數(shù)和幾何參數(shù)</p><p>　　兩種不同的方法應(yīng)用到有限元回彈模擬。在形成階段，采用顯式動(dòng)態(tài)方法和有限元模型是由四節(jié)

74、點(diǎn)殼單元?jiǎng)澐志W(wǎng)格。外殼公式是由減少的結(jié)合點(diǎn)和沙漏控制提供的。這就是所謂的Belytschko - Leriathan算法。該材料模型的特點(diǎn)是屬于各向同性硬化彈塑性行為，有一個(gè)電源法律本構(gòu)關(guān)系艦，其中包括考珀-西蒙茲乘數(shù)考慮應(yīng)變率：</p><p><b>　　(7)</b></p><p><b>　　式中—屈服應(yīng)力，</b></p>

75、;<p><b>　　—應(yīng)變率，</b></p><p><b>　　—應(yīng)變，</b></p><p>　　，P—考珀-西蒙茲應(yīng)變率系數(shù)，</p><p><b>　　—強(qiáng)度系數(shù)，</b></p><p><b>　　—硬化指數(shù)。</b>&l

76、t;/p><p>　　應(yīng)用位移約束的對(duì)稱。沖頭，模具和壓邊圈是剛體，加載空行程力和壓頭速度，以及組件之間的接觸是表面接觸。直到得到結(jié)果，求解過程才會(huì)終止。</p><p>　　在自由回彈階段，靜態(tài)隱式分析的方法，被用于解決移除剛體后的空白幾何非線性行為。成型后的應(yīng)力和位移結(jié)果被傳輸?shù)匠跏蓟貜椖Ｐ汀Ｔ撟址兂蓮椥圆牧夏Ｐ椭?，而且位移的剛性約束，被禁止加入到?jīng)_壓方向上。</p>&

77、lt;p>　　板材進(jìn)行軸向拉伸試驗(yàn)后，根據(jù)方程(7)中的應(yīng)力應(yīng)變曲線的材料模型系數(shù)，被我們的遺傳算法代碼識(shí)別，見表[2].</p><p><b>　　表2材料模型系數(shù)表</b></p><p><b>　　生成源數(shù)據(jù)</b></p><p>　　許多因素會(huì)影響有限元計(jì)算結(jié)果。在本文中，除了上面的輸入系數(shù)和參數(shù)不變，

78、這五個(gè)變量參數(shù)，，，和 ，需要審查和他們的取值范圍如表3所示。</p><p>　　表3 ，，，和 取值范圍</p><p>　　在這里，設(shè)計(jì)思路采用有限元法的計(jì)劃安排。根據(jù)設(shè)計(jì)表（30個(gè)參數(shù)最多允許安排13個(gè)可變參數(shù)測(cè)試）和其附加表，在表4中列出了參數(shù) ，，，和 的變化范圍，以30組數(shù)據(jù)作為有限元的樣本計(jì)算出的角度和。</p><p>　　表4 30組數(shù)據(jù)樣本和有

79、限元計(jì)算結(jié)果</p><p>　　3.3采用分層優(yōu)化圖識(shí)別方法預(yù)測(cè)回彈的數(shù)學(xué)模型</p><p>　　模式識(shí)別表明，在多維空間的樣本被投影到一個(gè)二維域和使用，如主成分分析法（PCA）的，線性圖方法（LMAP）中，最小二乘法（PLS的適當(dāng)方法，從不同類別分開）和費(fèi)舍爾向量法等。但對(duì)于復(fù)雜的數(shù)據(jù)，一個(gè)方法不能分離完全不同類的樣品。在本文中，分層優(yōu)化圖識(shí)別方法（H0MR）被用于構(gòu)建數(shù)學(xué)模型。首先

80、，根據(jù)給定的條件數(shù)據(jù)樣本分為好的和壞的樣本。該分層優(yōu)化圖識(shí)別方法，結(jié)合了主成分分析，線性圖方法，偏最小二乘法，費(fèi)舍爾的方法來獲得不同種類的樣品，樣品的圖放在二維域中，然后把選擇最好的識(shí)別圖作為第一個(gè)圖。以第一個(gè)映射樣本作為新的數(shù)據(jù)，形成第二個(gè)圖，經(jīng)過多次預(yù)測(cè)后，獲得最終的圖。將包括良好的樣品的所有圖的交集創(chuàng)建超多面體，用其邊界方程來構(gòu)造數(shù)學(xué)模型。</p><p><b>　?。?）數(shù)據(jù)源的評(píng)估</

81、b></p><p>　　回彈的改善可以描述為增加底角和減少在法蘭角。文中，如圖3所示，它意味著全球性計(jì)算的角度，代表之間的有限元分析計(jì)算和實(shí)驗(yàn)。假設(shè)誤差小于10％，即，為目標(biāo)函數(shù)，和滿意的樣品是好的樣品，定義為1級(jí)樣品，其余的都是次品，定為2級(jí)樣品。將，，，和 作為特征變量，為目標(biāo)值，將以上的數(shù)據(jù)源整理和歸類，可得表5中所列出的新數(shù)據(jù)。</p><p>　　現(xiàn)在，我們將表5中的數(shù)據(jù)

82、進(jìn)行評(píng)估。修補(bǔ)交換分類后的多面體標(biāo)準(zhǔn)分裂速度= 100％，和分裂速度=87.5％。多面體的標(biāo)準(zhǔn)分裂速度大于80％，證明了數(shù)據(jù)結(jié)構(gòu)可以用于建立良好的數(shù)學(xué)模型。</p><p><b>　　表5數(shù)據(jù)的分類</b></p><p><b>　　建立數(shù)學(xué)模型</b></p><p>　　在有限元模擬過程中，我們希望能得到最佳匹配的

83、變量，，，，，作為目標(biāo)。所以我們追加10個(gè)隨機(jī)樣本作為預(yù)測(cè)使用，但不建立數(shù)學(xué)模型。</p><p>　　現(xiàn)在，我們利用包括30個(gè)樣本在內(nèi)的實(shí)測(cè)數(shù)據(jù)作為試驗(yàn)的模式識(shí)別集體，和使用分層優(yōu)化圖識(shí)別方法獲得如圖4所示的圖。</p><p>　　圖4表明，通過使用分層優(yōu)化圖識(shí)別方法，主成分分析法的圖就是最佳效果圖，橫坐標(biāo)P（1）是第一個(gè)主要組成部分，縱坐標(biāo)P（2）是第二主成分。第1類樣品完全分開，表

84、中的 1級(jí)和 0級(jí)樣品滿足的條件，框內(nèi)的邊界線，就是用分層優(yōu)化圖識(shí)別方法得到的好樣本區(qū)域的邊界方程。方程式（8）中的一系列不等式體現(xiàn)了該模型，它是表明，在滿足不等式計(jì)算誤差小于10％。</p><p><b>　　圖4 分層優(yōu)化圖</b></p><p><b>　　（8）</b></p><p>　　圖4還表明，好樣區(qū)中

85、有4個(gè)隨機(jī)樣本，如表6所示。這意味著，如果參數(shù)變量，,， ，的值，從表6中來選擇，其模擬誤差小于10％。為驗(yàn)證數(shù)學(xué)模型的正確性，4好樣區(qū)隨機(jī)選取樣本，通過有限元計(jì)算。最后，表6中的樣本滿足的要求。</p><p>　　表6良好樣品示范區(qū)隨機(jī)樣本的和樣品核查</p><p><b>　　4結(jié)論</b></p><p>　?。?）材料參數(shù)的識(shí)別可以

86、通過使用遺傳算法加以改進(jìn)，并提供更準(zhǔn)確的成形和回彈模擬計(jì)算。</p><p>　　(2）根據(jù)設(shè)計(jì)思路，采用適當(dāng)?shù)妮斎雲(yún)?shù)，可以提高成形和回彈計(jì)算效率。</p><p>　?。?）通過利用分層優(yōu)化圖識(shí)別方法，能有效降低數(shù)學(xué)模型的回彈模擬誤差，和有效控制計(jì)算精度。</p><p>　　（4）被應(yīng)用于改善回彈預(yù)測(cè)的有限元計(jì)算精度的新方法，其計(jì)算誤差小于10％。</p