课程总练习
1、均匀设计试验方案的构造
已知一试验有四个因素,他们的试验范围及因素水平如下:
X1:1~12;X2:10~20;X3:200~350 ;X4:2000~4000
表1、因素水平表
(1)给出12拟水平的因素水平表
参考答案
表1B、因素拟水平表
(2)给出12拟水平的试验方案
参考答案
表1C、U12(124)试验方案表
2、回归分析建模
请对表2的数据进行逐步回归分析
3
(1)、用一次模型,要求数据中心化处理,寻找出最好的回归方程。
模型:
Y= A
0 + A
1
X
1
+ A
2
X
2
+ A
3
X
3
运行参数:
N,M,B1,T2 4,10,3,1
参考结果:
I= 1 B=-3.866679E-02 F= 4.984817
I= 2 B=-.6733327 F= 15.11584
GG PAUSE AND PRESS ANY KEY FOR GO ON ? 1
BO= 98.10001 F= 7.613494 R= .8276881 S= .3353738 FO= 1.69 G9=1 SHOW THE EQUATION G9=? 1
J Y Y* Y-Y* A/%
1 98.4 98.48667 -8.666992E-0
2 -8.807918E-02
2 97.8 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 97.71333 -1.333618E-02 -1.365014E-02
Y*= 98.10001+(-3.866679E-02)*(X1- 30)+(-.6733327)*(X2- 3)
(2)、用一次模型加上交叉项,要求数据中心化处理,寻找出最好的回归方程。
模型:
Y= A
0 + A
1
X
1
+ A
2
X
2
+ A
3
X
3
+ A
4
X
1
*X
2
+ A
5
X
1
*X
3
+ A
3
X
2
*X
3
运行参数:
N,M,B1,T2 7,10,3,1
参考结果:
I= 1 B=-3.866679E-02 F= 50.02406
I= 2 B=-.6733327 F= 151.6918
I= 4 B= .105 F= 27.74454
I= 5 B= 7.500037E-04 F= 10.8248
I= 6 B=-7.500004E-03 F= 50.18734
GG PAUSE AND PRESS ANY KEY FOR GO ON ?
BO= 98.3625 F= 43.81083 R= .9909929 S= .1058679 FO= 1.69 G9=1 SHOW THE EQUATION G9=? 1
J Y Y* Y-Y* A/%
1 98.4 98.37417 2.583313E-0
2 2.625318E-02
2 97.8 97.7758
3 2.416992E-02 2.471362E-02
3 99.2 99.15501 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 9.916687E-02 .1015014
Y*= 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,要求数据中心化处理,寻找出最好的回归方程。
模型:
Y= A
0 + A
1
X
1
+ A
2
X
2
+ A
3
X
3
+ A
4
X
1
2 + A
5
X
2
2 + A
6
X
3
2
运行参数:
N,M,B1,T2 7,10,3,2
参考结果:
I= 1 B=-3.866679E-02 F= 9.471841
I= 2 B=-.6733327 F= 28.7222
I= 4 B= 3.545463E-03 F= 2.502815
I= 6 B= 6.454537E-05 F= 8.294935
GG PAUSE AND PRESS ANY KEY FOR GO ON ?
BO= 97.60001 F= 9.308587 R= .9389425 S= .2432969 FO= 1.69
G9=1 SHOW THE EQUATION G9=? 1
J Y Y* Y-Y* A/%
1 98.4 98.50258 -.102577
2 -.1042451
2 97.8 97.82924 -2.924347E-02 -.0299013
3 99.2 98.86411 .3358917 .3386006
4 97.3 97.2086
5 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 -2.924347E-02 -2.993191E-02
Y*= 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项,要求数据中心化处理,寻找出最好的回归方程。
模型:
Y= A
0 + A
1
X
1
+ A
2
X
2
+ A
3
X
3
+ A
4
X
1
2 + A
5
X
2
2 + A
6
X
3
2+ A
7
X
1
*X
2
+ A
8
X
1
*X
3
+ A
9
X
2
*X
3
运行参数:
N,M,B,T2 10,10,3,2
参考结果:
I= 1 B=-3.685734E-02 F= 124.0948 I= 2 B=-.6552383 F= 392.1966 I= 3 B= 4.523612E-04 F= 2.392688
I= 5 B=-.2241233 F= 15.17404
I= 6 B= 3.975873E-05 F= 51.82186
I= 9 B=-5.796138E-03 F= 117.4773
GG PAUSE AND PRESS ANY KEY FOR GO ON ?
BO= 97.95531 F= 115.4989 R= .9978425 S= 5.993314E-02 FO= 1.69
G9=1 SHOW THE EQUATION G9=?
J Y Y* Y-Y* A/%
1 98.4 98.4459 -4.589844E-0
2 -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 -2.175388E-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-02
Y*= 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
- 800)
(5)、用二次模型加上交叉项,要求数据中心化处理,并且剔除不显著项从而寻找出最好的回归方程。
模型:
Y= A
0 + A
1
X
1
+ A
2
X
2
+ A
3
X
3
+ A
4
X
1
2 + A
5
X
2
2 + A
6
X
3
2+ A
7
X
1
*X
2
+ A
8
X
1
*X
3
+ A
9
X
2
*X
3
运行参数:
N,M,B,T2 10,10,3,2
参考结果:
I、
I= 1 B=-3.866679E-02 F= 37.94709
I= 2 B=-.6733327 F= 115.0699
I= 6 B= 5.172763E-05 F= 30.88384
I= 9 B=-5.209428E-03 F= 25.05857
GG PAUSE AND PRESS ANY KEY FOR GO ON ?
BO= 97.78928 F= 41.05093 R= .9851141 S= .1215527 FO= 1.69 G9=1 SHOW THE EQUATION G9=? 1
J Y Y* Y-Y* A/%
1 98.4 98.30526 9.474182E-0
2 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 -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 .1720323
Y*= 97.78928+(-3.866679E-02)*(X1- 30)+(-.6733327)*(X2- 3)+( 5.172763E-05)*(X3- 800)
^ 2+(-5.209428E-03)*(X2- 3)*(X3- 800)
II、对方程各项进行F检验
f1= 1, f2= M-2=10-2=8
F4=25.06>F1,8(0.01)= 11.3 ∴方程各项通过α=0.01的F检验。
III、对整个方程(或者总方程)进行F检验
f1=N*-1= 4, f2=M-N*=10-5=5,F4,5(0.01)= 11.4,
F= 41.05093 >F4,5(0.01)= 11.4,∴总的方程通过α=0.01的F检验。
3、最优化计算
(1)用蒙特卡罗法对下列的方程进行单指标优化计算求出最大值及其对应的参数,并列出原程序
Y = 34.9272 + 1.1785×10-3*(X2-120)^2 + 9.5338×10-2*(X1-6.2)*(X2-120)
+ 5.0045×10-3*(X2-120)*(X3-30)
X1:5.0~7.4;X2:40~200;X3:20~40,实验中Y的最大值为38.09
参考结果与程序:
ZM=? 38
N=? 4000
X1= 6.7514 X2= 167.8 X3= 21.47 Y= 38.0922
X1= 7.281201 X2= 152.6 X3= 30.635 Y= 39.64366
X1= 6.0218 X2= 48.84 X3= 35.365 Y= 40.1932
X1= 6.7178 X2= 189.4 X3= 25.245 Y= 42.37781
X1= 5.2496 X2= 67.8 X3= 25.35 Y= 44.08297
X1= 5.7224 X2= 40.68 X3= 23.98 Y= 48.34332
X1= 7.373 X2= 183.24 X3= 38.255 Y= 49.32518
X1= 5.0174 X2= 51.96 X3= 24.635 Y= 49.8811
X1= 7.310601 X2= 198.08 X3= 30.57 Y= 50.60194
X1= 5.4938 X2= 42.04 X3= 20.105 Y= 51.19925
X1= 6.9032 X2= 199.68 X3= 38.655 Y= 51.20252
X1= 7.358 X2= 198.04 X3= 38.285 Y= 53.956
X1= 5.0768 X2= 42.2 X3= 20.005 Y= 54.28314
X1= 5.0792 X2= 41.84 X3= 20.07 Y= 54.36256
X1= 7.3238 X2= 199.72 X3= 39.59 Y= 54.78419
X1= 7.3988 X2= 199.44 X3= 39.17 Y= 55.08927
S1= 6.000001E-04 S2= .04 S3= .005
Ok
S1= 6.000001E-04 S2= .04 S3= .005
参考程序:
10 INPUT"ZM="; ZM
20 INPUT"N=";N
30 G=20*N
35 S1=(7.4-5)/N:S2=(200-40)/N :S3=(40-20)/N
40 FOR I =1 TO G
50 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 + 0.095338*(X1-6.2)*(X2-120)
130 Y2=0.0050045*(X2-120)*(X3-30)
140 Y=Y1+Y2
150 IF Y< ZM THEN 190
160 IF Y>ZM THEN ZM =Y
170 PRINT TAB(1)"X1=";X1;TAB(16)"X2=";X2;TAB(31)"X3=";X3;
180 PRINT TAB(46)"Y=";ZM
190 NEXT I
200 PRINT "S1=";S1;"S2=";S2;"S3=";S3
210 END
(2)用网格法对下列的方程进行单指标优化求出最逼近理论值的最优参数,并列出原程序Y = 39.5715-0.7771*(X
- 3) -5.8542×10-3*(X3- 800)-6.3455×10-3*(X1- 30)2
2
+ 1.2419×10-3*(X1- 30)*(X3- 800)
X1:20~40 ;X2:2.0~4.0;X3:700~900
Y 的理论值为39.08,在39.08±0.2的范围内均可认为是最值。
参考结果与程序I:
ZM=? 39.08
G=21
X1= 40.00001 X2= 3.428573 X3= 842.8571 Y= 38.88525
X1= 40.00001 X2= 3.428573 X3= 852.3809 Y= 38.94777
X1= 40.00001 X2= 3.428573 X3= 861.9047 Y= 39.01029
X1= 40.00001 X2= 3.428573 X3= 871.4284 Y= 39.07282
X1= 40.00001 X2= 3.428573 X3= 880.9522 Y= 39.13534
X1= 40.00001 X2= 3.428573 X3= 890.4761 Y= 39.19786
X1= 40.00001 X2= 3.428573 X3= 899.9999 Y= 39.26038
X1= 40.00001 X2= 3.523811 X3= 880.9522 Y= 39.06133
X1= 40.00001 X2= 3.523811 X3= 890.4761 Y= 39.12385
X1= 40.00001 X2= 3.523811 X3= 899.9999 Y= 39.18637
X1= 40.00001 X2= 3.61905 X3= 871.4284 Y= 38.9248
X1= 40.00001 X2= 3.61905 X3= 880.9522 Y= 38.98732
X1= 40.00001 X2= 3.61905 X3= 890.4761 Y= 39.04984
X1= 40.00001 X2= 3.61905 X3= 899.9999 Y= 39.11236
X1= 40.00001 X2= 3.714288 X3= 880.9522 Y= 38.91331
X1= 40.00001 X2= 3.714288 X3= 890.4761 Y= 38.97583
X1= 40.00001 X2= 3.714288 X3= 899.9999 Y= 39.03835
X1= 40.00001 X2= 3.809526 X3= 890.4761 Y= 38.90182
X1= 40.00001 X2= 3.809526 X3= 899.9999 Y= 38.96435
X1= 40.00001 X2= 3.904764 X3= 899.9999 Y= 38.89034
Ok
参考程序:
10 INPUT"ZM="; ZM
20 INPUT"G=";G
30 S1=(40-20)/G:S2=(4!-2!)/G:S3=(900-700)/G
40 FOR X1= 20 TO 40 + S1/2 STEP S1
50 FOR X2= 2! TO 4! + S2/2 STEP S2
60 FOR X3= 700 TO 900 + S3/2 STEP S3
70 Y1= 39.5715-.7771*(X2 - 3) -.0058542*(X3 - 800)-.0063455*(X1- 30)^2 80 Y2= 1.2419E-03*(X1- 30)*(X3- 800)
90 Y=Y1+Y2
100 D1=ZM-.2:D2=ZM+.2
110 IF Y< D1 OR Y>D2 THEN 140
120 PRINT tab(1) "X1=";X1;tab(17)"X2=";X2;tab(32)"X3=";X3;
130 PRINT tab(47)"Y=";Y
140 NEXT X3, X2,X1
150 END
参考结果与程序II:
ZM=? 0.2
G=21
X1= 40.00001 X2= 3.428573 X3= 842.8571 Y= 38.88525
X1= 40.00001 X2= 3.428573 X3= 852.3809 Y= 38.94777
X1= 40.00001 X2= 3.428573 X3= 861.9047 Y= 39.01029
X1= 40.00001 X2= 3.428573 X3= 871.4284 Y= 39.07282
X1= 40.00001 X2= 3.428573 X3= 880.9522 Y= 39.13534
X1= 40.00001 X2= 3.428573 X3= 890.4761 Y= 39.19786
X1= 40.00001 X2= 3.428573 X3= 899.9999 Y= 39.26038
X1= 40.00001 X2= 3.523811 X3= 861.9047 Y= 38.93628
X1= 40.00001 X2= 3.523811 X3= 871.4284 Y= 38.99881
X1= 40.00001 X2= 3.523811 X3= 899.9999 Y= 39.18637
X1= 40.00001 X2= 3.61905 X3= 871.4284 Y= 38.9248
X1= 40.00001 X2= 3.61905 X3= 880.9522 Y= 38.98732
X1= 40.00001 X2= 3.61905 X3= 890.4761 Y= 39.04984
X1= 40.00001 X2= 3.61905 X3= 899.9999 Y= 39.11236
X1= 40.00001 X2= 3.714288 X3= 880.9522 Y= 38.91331
X1= 40.00001 X2= 3.714288 X3= 890.4761 Y= 38.97583
X1= 40.00001 X2= 3.714288 X3= 899.9999 Y= 39.03835
X1= 40.00001 X2= 3.809526 X3= 890.4761 Y= 38.90182
X1= 40.00001 X2= 3.809526 X3= 899.9999 Y= 38.96435
X1= 40.00001 X2= 3.904764 X3= 899.9999 Y= 38.89034
Ok
4、配方均匀设计
(1)一个饲料的配方由四种主要的成分组成,根据试验条件的允许和精度的要求,需要选择UM21(214)表来安排试验,请用相应的软件生成该配方试验方案表。
I、用U21*的1、3、5列生成的结果如下:
MU 21 ( 21 ^ 4 )
---------------------------------------------------------------------------------------------------------
1 .712315
2 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-02
5 .401591
6 .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 .1818627 .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 .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列生成的结果如下:
MU 21 ( 21 ^ 4 )
------------------------------------------------------------------------------------------------------
1 .712315
2 .1276317 9.526968E-02 6.478338E-02
2 .5850867 8.224258E-02 5.544514E-02 .2772256
3 .5080659 5.891651E-03 .3818905 .104152
4 .4496789 .2686854 .1005842 .1810516
5 .401591
6 .1367264 .450689
7 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 .2324695 .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 .1676986 .3336457 .4906554
------------------------------------------------------------------------------------------------------
(2)一配方有三个成分,这三个成分的范围如下:
0.6≤X1≤0.78,0.15≤X2≤0.25,0.05≤X3≤0.15,X1 + X2 + X3 = 1 根据试验的要求,请24水平的均匀设计表去生成相应的试验方案表。
RUN
N,S? 24,3
G1=1 RESTRICTED MUD ? G1=? 1
MU 13 ( 13 ^ 3 )
---------------------------------------------------
NO. X1 X2 X3
---------------------------------------------------
1 .7747779 .154840
2 7.038192E-02
2 .755 .1786459 6.635417E-02
3 .7367036 .2029577 6.033876E-02
4 .728016
5 .1681009 .1038826
5 .719598
6 .2278262 5.257528E-02
6 .7114259 .190378
7 9.819534E-02
7 .7034785 .1503199 .1462016
8 .6957386 .2134056 9.085584E-02
9 .6881908 .171062 .1407472
10 .6808214 .2371675 8.201118E-02
11 .6736183 .1926559 .1337258
12 .6596693 .2150702 .1252606
13 .6462699 .2382766 .1154536
---------------------------------------------------
5、用方程绘图
Y= 0.06252 + 0 .251*X3 - 0.06*X3^ 2 + 0.0235*X1*X3
X1:1.0~3.4;X3:0.5~3.5
X1= 3.4 ; X3= 2.7575 时有最优值Y= 0.5185
(1)绘出反映Y与X3关系的曲线图
方程经变换后得:
Y= 0.06252 + 0.3309 *X3 - 0.06*X3^ 2
用该方程作图得图1。
(2)绘出Y 分别为0.51,0.49,0.47,0.45,0.43时的X1,X3交互作用的Y 值等高线图
Y= 0.06252 + 0 .251*X3 - 0.06*X3^ 2 + 0.0235*X1*X3
方程经变换后得:X1= [Y-0.06252 - 0 .251*X3 + 0.06*X3^ 2]/[0.0235*X3]
当Y=0.51,0.49,0.47,0.45,0.43时;
Y-0.06252= 0.44748,0.42748,0.40748,0.38748,0.36748 用上述方程及参数作图得图2。
1.0
1.5
2.0
2.5
3.0
3.5
1.8
2.02.22.42.62.8
3.03.23.4E
D C A B A: Y=0.51B: Y=0.49C: Y=0.47D: Y=0.45E: Y=0.43
X 1
X3 / h
图2. X1X3交互作用Y 等值图
0.5
1.0
1.5
2.0 2.5
3.0 3.5
0.20
0.250.300.350.400.450.50
0.55Y
X 3
图1. X-Y 图
附注
1、课程设计的题目已上传到课程的公用信箱
课程公共信箱:kj2006gxu@https://www.wendangku.net/doc/3418441963.html,,密码:kj2006gxu
2、上机实践的练习题已上传到课程的公用信箱。
3、上机实践及课程调换安排
(1)上机实践时间安排:第13、14周星期四晚上综合楼603#
(2)第12周星期四晚停一次课
4、课程设计上交时间、地址及要求:课程设计要求
(1)交A4的纸质材料,请注明班级,学号,手机号码,email等个人信息(2)图形要求粘贴到word后打印出来
(3)请于2012年12月28日前交到化学化工学院2号化工楼119室
5、联系方式:Tel:138********, Email:liaosen@https://www.wendangku.net/doc/3418441963.html,