试验设计及数据挖掘技术课程设计答案.docx
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试验设计及数据挖掘技术课程设计答案
试验设计及数据挖掘技术课程设计
一、均匀设计试验方案的构造(10/每小项,共20分)
已知一试验有四个因素,他们的试验范围及因素水平见表1:
表1、因素水平表
NO.
1
2
3
4
5
6
7
8
9
10
11
12
X1
200
250
300
350
400
450
500
550
600
650
700
750
X2
200
250
300
350
400
450
X3
80
85
90
95
X4
120
125
130
135
140
145
150
155
160
165
170
1、请给出12拟水平的因素水平表
解答:
12拟水平的因素水平表
NO.
1
2
3
4
5
6
7
8
9
10
11
12
X1
200
250
300
350
400
450
500
550
600
650
700
750
X2
200
200
250
250
300
300
350
350
400
400
450
450
X3
80
80
80
85
85
85
90
90
90
95
95
95
X4
120
125
130
135
140
145
150
155
160
165
170
170
2、请给出12拟水平的试验方案
答:
U12*(124)试验方案表
NO.
1
2
3
4
5
6
7
8
9
10
11
12
X1
200
250
300
350
400
450
500
550
600
650
700
750
X2
300
450
300
450
250
400
250
400
200
350
200
350
X3
90
80
95
85
80
90
85
95
90
80
95
85
X4
165
150
135
120
170
155
140
125
170
160
145
130
二、回归分析建模(15分/每小项,共30分)
表2、试验方案及结果
No.
X1
X2
X3
X4
X5
Y
1
15
40
25
45
160
527
2
20
60
35
55
150
453
3
25
100
20
40
140
481
4
30
20
30
55
130
432
5
35
40
40
40
120
614
6
40
80
20
50
160
557
7
45
100
30
35
150
682
8
50
20
40
50
140
562
9
55
60
25
35
130
556
10
60
80
35
45
120
538
表2为一个试验的试验方案及结果,请对表2的数据进行数据中心化的回归分析建模并对所得的回归方程进行F显著性检验,要求如下:
1、用一次项加交叉项的模型建模,如有不显著项须手动剔除之(请保留5个变量项),请拷贝手动剔除后的参数及方程,最后对方程及其系数进行F显著性检验。
答:
一次项加交叉项模型
Y=A0+A1X1+A2X2+A3X3+A4X4+A5X5+A3X1*X2+A7X1*X3+A8X1*X4+A9X1*X5+A10X2*X3+A11X2*X4+A12X2*X5+A13X3*X4+A14X3*X5+A15X4*X5
运行参数:
N,M,B1,T216,10,5,1
剔除不显著项后参考结果
I=1B=1.83073684210526F=20.2398323973374
I=3B=5.70982456140351F=45.1033140286443
I=4B=-7.95789473684211F=102.79706467838
I=5B=3.19361403508772F=50.3929461717992
I=13B=-.712142857142857F=30.3293440491617
BO=547.321428571429F=41.5373305221118R=.990507014808526S=15.3002889140086FO=1.54
JYY*Y-Y*A/%
1527541.453007518797-14.4530075187971-2.74250617054974
2453460.582706766917-7.5827067669174-1.67388670351377
3481471.5213032581469.478696741854491.97062302325457
4432422.0758145363419.9241854636592.29726515362477
5614611.36716791982.63283208020027.428800013061934
6557554.4899749373442.5100250626565.450632865827019
7682672.5670426065169.432957393483661.38313158262224
8562551.90726817042610.09273182957381.79585975615193
9556562.845864661654-6.84586466165422-1.23127062259968
10538553.18984962406-15.1898496240602-2.82339212343127
----------------------------------------------------------------------------
>回归方程:
Y*=547.321428571429+(1.83073684210526)*(X1-37.5)+(5.70982456140351)*(X3-30)+(-7.95789473684211)*(X4-45)+(3.19361403508772)*(X5-140)+(-.712142857142857)*(X3-30)*(X4-45)
对方程各项的F显著性检验
查表得F1,8(0.01)=11.3
F1=20.23>11.3,所以方程有变量的各项通过了a=0.01的F检验
对回归方程总的F显著性检验
f1=6-1=5,f2=10-6=4,查表得F5,4(0.01)=15.5F=41.53>15.5
所以方程通过了a=0.01的F检验
2、二次全模型(一次项,二次项加上交叉项)建模,如有不显著须手动剔除之(请保留5个变量项),请拷贝手动剔除后的参数及方程,最后对方程其系数进行F显著性检验。
解答:
二次全模型
Y=A0+A1X1+A2X2+A3X3+A4X4+A5X5+A6X12+A7X22+A8X32+A9X42+A10X52+A11X1*X2+A12X1*X3+A13X1*X4+A14X1*X5+A15X2*X3+A16X2*X4+A17X2*X5+A18X3*X4+A19X3*X5+A20X4*X5
运行参数:
N,M,B1,T221,10,5,2
剔除不显著项后参考结果
I=1B=1.83073684210526F=20.2398323973374
I=3B=5.70982456140351F=45.1033140286443
I=4B=-7.95789473684211F=102.79706467838
I=5B=3.19361403508772F=50.3929461717992
I=18B=-.712142857142857F=30.3293440491617
BO=547.321428571429F=41.5373305221118R=.990507014808526S=15.3002889140086FO=1.54
JYY*Y-Y*A/%
1527541.453007518797-14.4530075187971-2.74250617054974
2453460.582706766917-7.5827067669174-1.67388670351377
3481471.5213032581469.478696741854491.97062302325457
4432422.0758145363419.9241854636592.29726515362477
5614611.36716791982.63283208020027.428800013061934
6557554.4899749373442.5100250626565.450632865827019
7682672.5670426065169.432957393483661.38313158262224
8562551.90726817042610.09273182957381.79585975615193
9556562.845864661654-6.84586466165422-1.23127062259968
10538553.18984962406-15.1898496240602-2.82339212343127
----------------------------------------------------------------------------------------------------
>回归方程:
Y*=547.321428571429+(1.83073684210526)*(X1-37.5)+(5.70982456140351)*(X3-30)+(-7.95789473684211)*(X4-45)+(3.19361403508772)*(X5-140)+(-.712142857142857)*(X3-30)*(X4-45)
对方程各项的F显著性检验
查表得F1,8(0.01)=11.3F1=20.23>11.3
所以方程有变量的各项通过了a=0.01的F检验
对回归方程总的F显著性检验
f1=6-1=5,f2=10-6=4,查表得F5,4(0.01)=15.5
F=41.53>15.5所以方程通过了a=0.01的F检验
三、优化计算寻优(10分/每小项,其20分)
一个试验的试验范围及所得的数学模型(回归方程)如下:
Y=90.7893-4.6267E-02*(X1-30)-0.8473*(X2-3)+5.2978E-05*(X3-800)^2
-5.2094E-03*(X2-3)*(X3-800)
X1:
20~40;X2:
2.0~4.0;X3:
700~900,实验得到的最大值为Y=80.2
1、用网格优化法寻优求Y的最大值,给出相应的程序及优化结果
答:
程序10INPUT"ZM=";ZM
20INPUT"G=";G
30S1=(40-20)/G:
S2=(4!
-2!
)/G:
S3=(900-700)/G
40FORX1=20TO40+S1/2STEPS1
50FORX2=2!
TO4!
+S2/2STEPS2
60FORX3=700TO900+S3/2STEPS3
70Y1=90.7893-4.6267E-02*(X1-30)-0.8473*(X2-3)
80Y2=5.2978E-05*(X3-800)^2-5.2094E-03*(X2-3)*(X3-800)
90Y=Y1+Y2
110IFY120PRINTtab
(1)"X1=";X1;tab(17)"X2=";X2;tab(32)"X3=";X3;
130PRINTtab(47)"Y=";Y
140NEXTX3,X2,X1
150END
结果:
ZM=?
80.2
G=21
X1=40.00001X2=4.000003X3=700Y=90.53004
X1=40.00001X2=4.000003X3=709.5238Y=90.38433
X1=40.00001X2=4.000003X3=719.0476Y=90.24822
X1=40.00001X2=4.000003X3=728.5715Y=90.12172
X1=40.00001X2=4.000003X3=738.0952Y=90.00484
X1=40.00001X2=4.000003X3=747.619Y=89.89756
X1=40.00001X2=4.000003X3=757.1428Y=89.79989
X1=40.00001X2=4.000003X3=766.6666Y=89.71184
X1=40.00001X2=4.000003X3=776.1905Y=89.63339
X1=40.00001X2=4.000003X3=785.7143Y=89.56456
X1=40.00001X2=4.000003X3=795.2381Y=89.50533
X1=40.00001X2=4.000003X3=804.7618Y=89.45572
X1=40.00001X2=4.000003X3=814.2856Y=89.41572
X1=40.00001X2=4.000003X3=823.8095Y=89.38532
X1=40.00001X2=4.000003X3=833.3333Y=89.36454
X1=40.00001X2=4.000003X3=842.8571Y=89.35337
X1=40.00001X2=4.000003X3=852.3809Y=89.35181
X1=40.00001X2=4.000003X3=861.9047Y=89.35986
X1=40.00001X2=4.000003X3=871.4284Y=89.37752
X1=40.00001X2=4.000003X3=880.9522Y=89.40479
X1=40.00001X2=4.000003X3=890.4761Y=89.44167
X1=40.00001X2=4.000003X3=899.9999Y=89.48816
2、用蒙特卡罗优化法寻优求Y的最大值,给出相应的程序及优化结果
答:
程序
10INPUT"ZM=";ZM
20INPUT"N=";N
30G=20*N
35S1=(40-20)/N:
S2=(4-2)/N:
S3=(900-700)/N
40FORI=1TOG
50A1=INT(N*RND
(1))
60A2=INT(N*RND
(1))
70A3=INT(N*RND
(1))
90X1=20+A1*S1
100X2=2+A2*S2
110X3=700+A3*S3
120Y1=90.7893-4.6267E-02*(X1-30)-0.8473*(X2-3)
130Y2=5.2978E-05*(X3-800)^2-5.2094E-03*(X2-3)*(X3-800)
140Y=Y1+Y2
150IFY160IFY>ZMTHENZM=Y
170PRINTTAB
(1)"X1=";X1;TAB(16)"X2=";X2;TAB(31)"X3=";X3;
180PRINTTAB(46)"Y=";ZM
190NEXTI
200PRINT"S1=";S1;"S2=";S2;"S3=";S3
210END
结果:
ZM=?
80.2
N=?
4000
X1=22.425X2=3.3035X3=873.75Y=91.05416
X1=29.805X2=2.909X3=721.4Y=91.16546
X1=39.42X2=2.6415X3=891.2Y=91.26818
X1=28.515X2=2.1105X3=853.65Y=92.01277
X1=29.73X2=2.334X3=898.05Y=92.21559
X1=21.985X2=2.214X3=879.55Y=92.48708
X1=21.755X2=2.177X3=884.95Y=92.61462
X1=22.485X2=2.103X3=888.65Y=92.72761
X1=23.5X2=2.0525X3=890.05Y=92.76693
X1=22.59X2=2.06X3=892.6Y=92.83632
X1=21.96X2=2.0805X3=899.45Y=92.94071
X1=23.265X2=2.0305X3=899.15Y=92.94393
X1=20.005X2=2.0265X3=895.45Y=93.04331
X1=20.475X2=2.0335X3=898.55Y=93.05963
X1=20.165X2=2.037X3=899.55Y=93.08471
S1=.005S2=.0005S3=.05
四、配方均匀设计(7.5分/每小项,其15分)
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UM16(164)表来安排试验,请用相应的软件生成该配方试验方案表。
答:
用U16*的1、4、6列生成的结果如下:
N,S?
16,4
G1=1RESTRICTEDMUD?
G1=?
0
MU16(16^4)
------------------------------------------------------------------
NO.X1X2X3X4
------------------------------------------------------------------
1.6850198.14793688.874186E-027.830165E-02
2.5457199.10423381.093894E-02.3391074
3.46139142.586848E-02.3044395.2083007
4.3974645.36436252.232872E-02.2158444
5.3448147.2066106.2943772.1541976
6.29949028.134079E-029.674513E-02.5224239
7.259376.6096999.410238E-023.682267E-02
8.2231919.32136419.962839E-02.3558157
9.1900971.1538066.5125753.1435211
10.15950611.323694E-02.232666.5945909
11.1309934.462566.34293436.350635E-02
12.104238.2428689.224432.4284611
137.899213E-027.500816E-02.76668737.931248E-02
14.0550592.655613.1175394.1717884
15.0322808.3509168.59752731.927508E-02
161.052713E-02.1506065.3932186.4456478
------------------------------------------------------------------
2、一配方有三个成分,这三个成分的范围如下:
0.6≤X1≤0.85,0.10≤X2≤0.25,0.05≤X3≤0.15,X1+X2+X3=1
根据试验的要求,请26水平的均匀设计表去生成相应的试验方案表。
答:
用U26*的1、7列生成的结果如下:
N,S?
26,3
G1=1RESTRICTEDMUD?
G1=?
1
MU11(11^3)
--------------------------------------------------------------------------------
NO.X1X2X3
--------------------------------------------------------------------------------
1.7974918.13669316.581519E-02
2.7728733.13438339.274339E-02
3.7615152.18482575.365908E-02
4.750674.1267407.1225853
5.740285.17963628.007881E-02
6.7206636.1699297.1094068
7.7113526.22851256.013487E-02
8.7023328.1562753.1413919
9.6935784.21704878.937298E-02
10.67678.2020125.1212075
11.6381804.2321676.129652
--------------------------------------------------------------------------------
五、用方程绘图(7.5分/每小项,其15分)(图形要求打印出来)
已知有一试验的试验范围为:
X1:
1.0-4.0,X3:
1.0-3.5,得到的方程及最佳参数如下
Y=0.07