課程總練習20121114 (1)

1、課程總練習一、試驗設計三、驗證試驗2.3交互作用Y值等高線圖分析二、數(shù)據(jù)挖掘技術(shù)2.2最優(yōu)化計算尋優(yōu)數(shù)論序貫法均勻設計法蒙特卡羅法網(wǎng)格法2.1逐步回歸分析建模線性模型混合模型高次模型二次模型均勻設計全面試驗法正交設計法單因素多次試驗法1、均勻設計試驗方案的構(gòu)造已知一試驗有四個因素，他們的試驗范圍及因素水平如下：X1:112；X2：1020；X3:200350 ；X4:20004000 表1、因素水平表NO.123456789101112X1123456789101112X2101214161820X3200250300350X4200022002400260028003000320034003

2、60038004000（1）給出12擬水平的因素水平表參考答案表1B、因素擬水平表NO.123456789101112X1123456789101112X2101012121414161618182020X3200200200250250250300300300350350350X4200022002400260028003000320034003600380040004000（2）給出12擬水平的試驗方案參考答案表1C、U12（124）試驗方案表NO.123456789101112X1123456789101112X2142014201218121810161016X330020035025

3、0200300250350300200350250X4380032002600200400034002800220040003600300024002、回歸分析建模請對表2的數(shù)據(jù)進行逐步回歸分析表2、U10（103）試驗方案及結(jié)果NO.12345678910X120202525303035354040X23.04.02.54.02.53.52.03.52.03.0X3850750900800700900800700850750Y98.497.899.297.398.397.798.298.098.497.7（1）、用一次模型，要求數(shù)據(jù)中心化處理，尋找出最好的回歸方程。 模型： Y= A0 +

4、A1X1 + A2X2 + A3X3 運行參數(shù)：N,M,B1,T2 4,10,3,1參考結(jié)果：I= 1 B=-3.866679E-02 F= 4.984817I= 2 B=-.6733327 F= 15.11584GG PAUSE AND PRESS ANY KEY FOR GO ON ? 1BO= 98.10001 F= 7.613494 R= .8276881 S= .3353738 FO= 1.69G9=1 SHOW THE EQUATION G9=? 1 J Y Y* Y-Y* A/% 1 98.4 98.48667 -8.666992E-02 -8.807918E-02 2 97.8

5、 97.81334 -1.333618E-02 -1.363618E-02 3 99.2 98.63001 .5699845 .5745811 4 97.3 97.62001 -.3200073 -.3288873 5 98.3 98.43668 -.136673 -.1390366 6 97.7 97.76334 -6.333923E-02 -6.483033E-02 7 98.2 98.58 -.3800049 -.3869704 8 98 97.57 .4300003 .4387758 9 98.4 98.38666 1.333618E-02 1.355303E-02 10 97.7 9

6、7.71333 -1.333618E-02 -1.365014E-02Y*= 98.10001+(-3.866679E-02)*(X1- 30)+(-.6733327)*(X2- 3)（2）、用一次模型加上交叉項，要求數(shù)據(jù)中心化處理，尋找出最好的回歸方程。模型： Y= A0 + A1X1 + A2X2 + A3X3 + A4X1*X2 + A5X1*X3 + A3 X2*X3運行參數(shù)：N,M,B1,T2 7,10,3,1參考結(jié)果：I= 1 B=-3.866679E-02 F= 50.02406I= 2 B=-.6733327 F= 151.6918I= 4 B= .105 F= 27.7445

7、4I= 5 B= 7.500037E-04 F= 10.8248I= 6 B=-7.500004E-03 F= 50.18734GG PAUSE AND PRESS ANY KEY FOR GO ON ?BO= 98.3625 F= 43.81083 R= .9909929 S= .1058679 FO= 1.69G9=1 SHOW THE EQUATION G9=? 1 J Y Y* Y-Y* A/% 1 98.4 98.37417 2.583313E-02 2.625318E-02 2 97.8 97.77583 2.416992E-02 2.471362E-02 3 99.2 99.15

8、501 4.499054E-02 4.535337E-02 4 97.3 97.35751 -5.750275E-02 -.0590984 5 98.3 98.32418 -2.416992E-02 -2.458792E-02 6 97.7 97.65083 4.916382E-02 5.032121E-02 7 98.2 98.3175 -.1175003 -.1196541 8 98 98.09499 -9.499359E-02 -9.693223E-02 9 98.4 98.34916 5.084229E-02 5.166899E-02 10 97.7 97.60083 9.916687

9、E-02 .1015014Y*= 98.3625+(-3.866679E-02)*(X1- 30)+(-.6733327)*(X2- 3)+( .105)*(X1- 30)*(X2- 3)+( 7.500037E-04)*(X1- 30)*(X3- 800)+(-7.500004E-03)*(X2- 3)*(X3- 800)（3）、用二次模型，要求數(shù)據(jù)中心化處理，尋找出最好的回歸方程。模型： Y= A0 + A1X1 + A2X2 + A3X3 + A4X12 + A5X22 + A6X32運行參數(shù)：N,M,B1,T2 7,10,3,2參考結(jié)果：I= 1 B=-3.866679E-02 F=

10、9.471841I= 2 B=-.6733327 F= 28.7222I= 4 B= 3.545463E-03 F= 2.502815I= 6 B= 6.454537E-05 F= 8.294935GG PAUSE AND PRESS ANY KEY FOR GO ON ?BO= 97.60001 F= 9.308587 R= .9389425 S= .2432969 FO= 1.69G9=1 SHOW THE EQUATION G9=? 1 J Y Y* Y-Y* A/% 1 98.4 98.50258 -.1025772 -.1042451 2 97.8 97.82924 -2.92434

11、7E-02 -.0299013 3 99.2 98.86411 .3358917 .3386006 4 97.3 97.20865 9.135437E-02 9.388938E-02 5 98.3 98.58213 -.2821274 -.2870065 6 97.7 97.90879 -.2087936 -.213709 7 98.2 98.16864 3.135681E-02 3.193158E-02 8 98 97.80409 .1959076 .1999057 9 98.4 98.40258 -2.571106E-03 -2.612913E-03 10 97.7 97.72924 -2

12、.924347E-02 -2.993191E-02Y*= 97.60001+(-3.866679E-02)*(X1- 30)+(-.6733327)*(X2- 3)+( 3.545463E-03)*(X1- 30) 2+( 6.454537E-05)*(X3- 800) 2（4）、用二次模型加上交叉項，要求數(shù)據(jù)中心化處理，尋找出最好的回歸方程。模型： Y= A0 + A1X1 + A2X2 + A3X3 + A4X12 + A5X22 + A6X32+ A7X1*X2 + A8X1*X3 + A9X2*X3運行參數(shù)：N,M,B,T2 10,10,3,2參考結(jié)果：I= 1 B=-3.685734

13、E-02 F= 124.0948I= 2 B=-.6552383 F= 392.1966I= 3 B= 4.523612E-04 F= 2.392688I= 5 B=-.2241233 F= 15.17404I= 6 B= 3.975873E-05 F= 51.82186I= 9 B=-5.796138E-03 F= 117.4773GG PAUSE AND PRESS ANY KEY FOR GO ON ?BO= 97.95531 F= 115.4989 R= .9978425 S= 5.993314E-02 FO= 1.69G9=1 SHOW THE EQUATION G9=?J Y Y*

14、 Y-Y* A/% 1 98.4 98.4459 -4.589844E-02 -4.664475E-02 2 97.8 97.81109 -1.109314E-02 -1.134268E-02 3 99.2 99.14382 5.617523E-02 5.662826E-02 4 97.3 97.26024 3.976441E-02 4.086784E-02 5 98.3 98.28944 1.055908E-02 1.074169E-02 6 97.7 97.72467 -2.467346E-02 -2.525431E-02 7 98.2 98.20213 -2.136231E-03 -2.

15、175388E-03 8 98 98.02953 -2.953339E-02 -3.013611E-02 9 98.4 98.42968 -2.967072E-02 -3.015317E-02 10 97.7 97.66351 .0364914 3.735046E-02Y*= 97.95531+(-3.685734E-02)*(X1- 30)+(-.6552383)*(X2- 3)+( 4.523612E-04)*(X3- 800)+(-.2241233)*(X2- 3) 2+( 3.975873E-05)*(X3- 800) 2+(-5.796138E-03)*(X2- 3)*(X3- 80

16、0)（5）、用二次模型加上交叉項，要求數(shù)據(jù)中心化處理，并且剔除不顯著項從而尋找出最好的回歸方程。模型： Y= A0 + A1X1 + A2X2 + A3X3 + A4X12 + A5X22 + A6X32+ A7X1*X2 + A8X1*X3 + A9X2*X3運行參數(shù)：N,M,B,T2 10,10,3,2參考結(jié)果：I、I= 1 B=-3.866679E-02 F= 37.94709I= 2 B=-.6733327 F= 115.0699I= 6 B= 5.172763E-05 F= 30.88384I= 9 B=-5.209428E-03 F= 25.05857GG PAUSE AND PR

17、ESS ANY KEY FOR GO ON ?BO= 97.78928 F= 41.05093 R= .9851141 S= .1215527 FO= 1.69G9=1 SHOW THE EQUATION G9=? 1 J Y Y* Y-Y* A/% 1 98.4 98.30526 9.474182E-02 9.628234E-02 2 97.8 97.8924 -.0923996 -9.447811E-02 3 99.2 99.09703 .1029663 .1037967 4 97.3 97.30928 -9.277344E-03 -9.534782E-03 5 98.3 98.38274

18、 -8.274078E-02 -.0841717 6 97.7 97.70941 -9.407044E-03 -9.628499E-03 7 98.2 98.26927 -.0692749 -7.054471E-02 8 98 98.03702 -3.701782E-02 -3.777329E-02 9 98.4 98.46573 -6.572723E-02 -6.679597E-02 10 97.7 97.53192 .1680756 .1720323Y*= 97.78928+(-3.866679E-02)*(X1- 30)+(-.6733327)*(X2- 3)+( 5.172763E-0

19、5)*(X3- 800) 2+(-5.209428E-03)*(X2- 3)*(X3- 800)II、對方程各項進行F檢驗f1= 1, f2= M-2=10-2=8F4=25.06>F1,8(0.01)= 11.3 方程各項通過=0.01的F檢驗。III、對整個方程（或者總方程）進行F檢驗f1=N*-1= 4, f2=M-N*=10-5=5，F(xiàn)4,5(0.01)= 11.4， F= 41.05093 >F4,5(0.01)= 11.4，總的方程通過=0.01的F檢驗。3、最優(yōu)化計算（1）用蒙特卡羅法對下列的方程進行單指標優(yōu)化計算求出最大值及其對應的參數(shù)，并列出原程序Y = 34.9

20、272 + 1.1785×10-3*(X2-120)2 + 9.5338×10-2*(X1-6.2)*(X2-120) + 5.0045×10-3*(X2-120)*(X3-30)X1：5.07.4；X2：40200；X3：2040，實驗中Y的最大值為38.09參考結(jié)果與程序：ZM=? 38N=? 4000X1= 6.7514 X2= 167.8 X3= 21.47 Y= 38.0922X1= 7.281201 X2= 152.6 X3= 30.635 Y= 39.64366X1= 6.0218 X2= 48.84 X3= 35.365 Y= 40.1932X1=

21、 6.7178 X2= 189.4 X3= 25.245 Y= 42.37781X1= 5.2496 X2= 67.8 X3= 25.35 Y= 44.08297X1= 5.7224 X2= 40.68 X3= 23.98 Y= 48.34332X1= 7.373 X2= 183.24 X3= 38.255 Y= 49.32518X1= 5.0174 X2= 51.96 X3= 24.635 Y= 49.8811X1= 7.310601 X2= 198.08 X3= 30.57 Y= 50.60194X1= 5.4938 X2= 42.04 X3= 20.105 Y= 51.19925X1=

22、6.9032 X2= 199.68 X3= 38.655 Y= 51.20252X1= 7.358 X2= 198.04 X3= 38.285 Y= 53.956X1= 5.0768 X2= 42.2 X3= 20.005 Y= 54.28314X1= 5.0792 X2= 41.84 X3= 20.07 Y= 54.36256X1= 7.3238 X2= 199.72 X3= 39.59 Y= 54.78419X1= 7.3988 X2= 199.44 X3= 39.17 Y= 55.08927S1= 6.000001E-04 S2= .04 S3= .005Ok S1= 6.00

23、0001E-04 S2= .04 S3= .005參考程序：10 INPUT"ZM=" ZM 20 INPUT"N="N 30 G=20*N35 S1=(7.4-5)/N:S2=(200-40)/N :S3=(40-20)/N40 FOR I =1 TO G50 A1=INT(N*RND(1) 60 A2=INT(N*RND(1) 70 A3=INT(N*RND(1) 90 X1= 5 + A1*S1 100 X2= 40 + A2*S2 110 X3= 20 + A3*S3 120 Y1= 34.9272 + 0.0011785*(X2-120)2 +

24、 0.095338*(X1-6.2)*(X2-120)130 Y2=0.0050045*(X2-120)*(X3-30)140 Y=Y1+Y2150 IF Y< ZM THEN 190160 IF Y>ZM THEN ZM =Y170 PRINT TAB(1)"X1="X1;TAB(16)"X2="X2;TAB(31)"X3="X3;180 PRINT TAB(46)"Y="ZM190 NEXT I200 PRINT "S1="S1;"S2="S2;"S

25、3="S3210 END（2）用網(wǎng)格法對下列的方程進行單指標優(yōu)化求出最逼近理論值的最優(yōu)參數(shù)，并列出原程序Y = 39.5715-0.7771*(X2 - 3) -5.8542×10-3*(X3 - 800)-6.3455×10-3*(X1- 30)2+ 1.2419×10-3*(X1- 30)*(X3- 800) X1：2040 ；X2：2.04.0；X3：700900Y 的理論值為39.08，在39.08±0.2的范圍內(nèi)均可認為是最值。參考結(jié)果與程序I：ZM=? 39.08G=21X1= 40.00001 X2= 3.428573 X3= 8

26、42.8571 Y= 38.88525X1= 40.00001 X2= 3.428573 X3= 852.3809 Y= 38.94777X1= 40.00001 X2= 3.428573 X3= 861.9047 Y= 39.01029X1= 40.00001 X2= 3.428573 X3= 871.4284 Y= 39.07282X1= 40.00001 X2= 3.428573 X3= 880.9522 Y= 39.13534X1= 40.00001 X2= 3.428573 X3= 890.4761 Y= 39.19786X1= 40.00001 X2= 3.428573 X3= 8

27、99.9999 Y= 39.26038X1= 40.00001 X2= 3.523811 X3= 861.9047 Y= 38.93628X1= 40.00001 X2= 3.523811 X3= 871.4284 Y= 38.99881X1= 40.00001 X2= 3.523811 X3= 880.9522 Y= 39.06133X1= 40.00001 X2= 3.523811 X3= 890.4761 Y= 39.12385X1= 40.00001 X2= 3.523811 X3= 899.9999 Y= 39.18637X1= 40.00001 X2= 3.61905 X3= 87

28、1.4284 Y= 38.9248X1= 40.00001 X2= 3.61905 X3= 880.9522 Y= 38.98732X1= 40.00001 X2= 3.61905 X3= 890.4761 Y= 39.04984X1= 40.00001 X2= 3.61905 X3= 899.9999 Y= 39.11236X1= 40.00001 X2= 3.714288 X3= 880.9522 Y= 38.91331X1= 40.00001 X2= 3.714288 X3= 890.4761 Y= 38.97583X1= 40.00001 X2= 3.714288 X3= 899.99

29、99 Y= 39.03835X1= 40.00001 X2= 3.809526 X3= 890.4761 Y= 38.90182X1= 40.00001 X2= 3.809526 X3= 899.9999 Y= 38.96435X1= 40.00001 X2= 3.904764 X3= 899.9999 Y= 38.89034Ok 參考程序：10 INPUT"ZM=" ZM20 INPUT"G="G30 S1=(40-20)/G:S2=(4!-2!)/G:S3=(900-700)/G40 FOR X1= 20 TO 40 + S1/2 STEP

30、 S150 FOR X2= 2! TO 4! + S2/2 STEP S260 FOR X3= 700 TO 900 + S3/2 STEP S370 Y1= 39.5715-.7771*(X2 - 3) -.0058542*(X3 - 800)-.0063455*(X1- 30)280 Y2= 1.2419E-03*(X1- 30)*(X3- 800) 90 Y=Y1+Y2100 D1=ZM-.2:D2=ZM+.2110 IF Y< D1 OR Y>D2 THEN 140120 PRINT tab(1) "X1="X1;tab(17)"X2=&quo

31、t;X2;tab(32)"X3="X3;130 PRINT tab(47)"Y="Y140 NEXT X3, X2,X1150 END參考結(jié)果與程序II：ZM=? 0.2G=21X1= 40.00001 X2= 3.428573 X3= 842.8571 Y= 38.88525X1= 40.00001 X2= 3.428573 X3= 852.3809 Y= 38.94777X1= 40.00001 X2= 3.428573 X3= 861.9047 Y= 39.01029X1= 40.00001 X2= 3.428573 X3= 871.4284 Y=

32、 39.07282X1= 40.00001 X2= 3.428573 X3= 880.9522 Y= 39.13534X1= 40.00001 X2= 3.428573 X3= 890.4761 Y= 39.19786X1= 40.00001 X2= 3.428573 X3= 899.9999 Y= 39.26038X1= 40.00001 X2= 3.523811 X3= 861.9047 Y= 38.93628X1= 40.00001 X2= 3.523811 X3= 871.4284 Y= 38.99881X1= 40.00001 X2= 3.523811 X3= 880.9522 Y=

33、 39.06133X1= 40.00001 X2= 3.523811 X3= 890.4761 Y= 39.12385X1= 40.00001 X2= 3.523811 X3= 899.9999 Y= 39.18637X1= 40.00001 X2= 3.61905 X3= 871.4284 Y= 38.9248X1= 40.00001 X2= 3.61905 X3= 880.9522 Y= 38.98732X1= 40.00001 X2= 3.61905 X3= 890.4761 Y= 39.04984X1= 40.00001 X2= 3.61905 X3= 899.9999 Y= 39.1

34、1236X1= 40.00001 X2= 3.714288 X3= 880.9522 Y= 38.91331X1= 40.00001 X2= 3.714288 X3= 890.4761 Y= 38.97583X1= 40.00001 X2= 3.714288 X3= 899.9999 Y= 39.03835X1= 40.00001 X2= 3.809526 X3= 890.4761 Y= 38.90182X1= 40.00001 X2= 3.809526 X3= 899.9999 Y= 38.96435X1= 40.00001 X2= 3.904764 X3= 899.9999 Y= 38.8

35、9034Ok 4、配方均勻設計（1）一個飼料的配方由四種主要的成分組成，根據(jù)試驗條件的允許和精度的要求，需要選擇UM21（214）表來安排試驗，請用相應的軟件生成該配方試驗方案表。I、用U21*的1、3、5列生成的結(jié)果如下：MU 21 ( 21 4 )- 1 .7123152 9.419011E-02 5.067718E-02 .1428175 2 .5850867 1.509285E-02 .1999102 .1999102 3 .5080659 .1789612 .2310038 .0819691 4 .4496789 3.379488E-02 .504228 1.229825E

36、-02 5 .4015916 .240791 7.663232E-02 .2809851 6 .3601948 5.574566E-02 .2642174 .3198422 7 .3235568 .3001049 .2598527 .1164857 8 .2905083 8.059454E-02 .583976 4.492123E-02 9 .2602814 .3611556 6.309387E-02 .3154692 10 .2323415 .1081442 .2669463 .3925681 11 .2062995 .4262886 .2361934 .1312185 12 .181862

37、7 .138307 .5988981 8.093218E-02 13 .1588045 .4977789 4.088295E-02 .3025337 14 .1369457 .1710715 .2471368 .4448461 15 .1161412 .5788986 .181524 .1234363 16 9.627259E-02 .2064866 .581034 .1162068 17 7.724118E-02 .6761411 1.761556E-02 .2290021 18 5.896402E-02 .2446572 .2155458 .480833 19 4.137045E-02 .

38、8107098 8.100368E-02 6.691608E-02 20 2.440012E-02 .2857466 .5420276 .1478257 21 8.000374E-03 1.188064E-02 2.333617E-02 .9567828-II、用U21的1、3、4列生成的結(jié)果如下：MU 21 ( 21 4 )- 1 .7123152 .1276317 9.526968E-02 6.478338E-02 2 .5850867 8.224258E-02 5.544514E-02 .2772256 3 .5080659 5.891651E-03 .3818905 .104152 4

39、 .4496789 .2686854 .1005842 .1810516 5 .4015916 .1367264 .4506897 1.099243E-02 6 .3601948 2.327347E-02 .3376246 .2789073 7 .3235568 .3633109 3.727767E-02 .2758547 8 .2905083 .1844587 .3875244 .1375087 9 .2602814 4.542566E-02 .2149002 .4793928 10 .2323415 .4542633 .2910099 2.238538E-02 11 .2062995 .2

40、324695 .2806155 .2806155 12 .1818627 7.128358E-02 .0533467 .693507 13 .1588045 .5509555 .2004038 8.983621E-02 14 .1369457 .2825703 .1520315 .4284525 15 .1161412 .1004018 .6901884 9.326869E-02 16 9.627259E-02 .6621961 .1092642 .1322672 17 7.724118E-02 .3356913 1.397783E-02 .5730897 18 5.896402E-02 .1325688 .5197289 .2887383 19 4.137045E-02 .8107098 .0316971 .1162227 20 2.440012E-02 .3925675 .4858604 9.717208E-02 21 8.000374E-03 .