1stopt1.5版本非线性带约束拟合问题
小弟在拟合以y为因变量,x与T为自变量的公式时,需对T=343.15时的各参数进行关系约束,由此建议拟合公式及四个约束条件及代码如下。
然而在采用1stopt1.5版本进行拟合时,5个Function均为单独拟合,相互之间无关联,不知道在哪里出了问题,请大神指教,感激不尽!
Parameters p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11;
Variables x,T,y;
Function y/1000=(p10+p11*T)/x+(p1+p2*T+p3*T^2)*x^((p4+p5*T+p6*T^2)+(p7+p8*T+p9*T^2)*log(x)-1);
p10+p11*343.15=0;
p1+p2*343.15+p3*343.15^2=0.183541;
p4+p5*343.15+p6*343.15^2=-0.08951;
p7+p8*343.15+p9*343.15^2=0.147646;
Data;
1000 343.15 2.1896
681 343.15 2.324669604
464 343.15 2.523491379
316 343.15 2.806234177
215 343.15 3.215116279
147 343.15 3.873197279
100 343.15 4.679
68.1 343.15 5.836123348
46.4 343.15 7.283297414
31.6 343.15 9.332911392
21.5 343.15 11.71488372
1000 353.15 2.497
681 353.15 2.688546256
464 353.15 2.94137931
316 353.15 3.288291139
215 353.15 3.826372093
147 353.15 4.748911565
100 353.15 6.0202
68.1 353.15 7.84743025
46.4 353.15 10.37532328
31.6 353.15 13.54303797
21.5 353.15 18.04046512
1000 363.15 3.2409
681 363.15 3.89
464 363.15 4.7945
316 363.15 6.0358
215 363.15 7.7309
46.4 363.15 21.69
1000 373.15 5.3061
681 373.15 6.2859
464 373.15 7.6893
316 373.15 9.6287
215 373.15 12.368
147 373.15 16.217
100 373.15 21.765
68.1 373.15 28.885 返回小木虫查看更多
1.5版本这种拟合模式不能进行约束拟合
Parameters p(1:11);
ConstStr
p10=-p11*343.15,
p1=0.183541-(p2*343.15+p3*343.15^2),
p4=-0.08951-(p5*343.15+p6*343.15^2),
p7=0.147646-(p8*343.15+p9*343.15^2);
Variables x,T,y;
Function
y=1000*((p10+p11*T)/x+(p1+p2*T+p3*T^2)*x^((p4+p5*T+p6*T^2)+(p7+p8*T+p9*T^2)*log(x)-1));
Data;
1000.0 343.15 2.189600000
681.0 343.15 2.324669604
464.0 343.15 2.523491379
316.0 343.15 2.806234177
215.0 343.15 3.215116279
147.0 343.15 3.873197279
100.0 343.15 4.679000000
68.1 343.15 5.836123348
46.4 343.15 7.283297414
31.6 343.15 9.332911392
21.5 343.15 11.714883720
1000.0 353.15 2.497000000
681.0 353.15 2.688546256
464.0 353.15 2.941379310
316.0 353.15 3.288291139
215.0 353.15 3.826372093
147.0 353.15 4.748911565
100.0 353.15 6.020200000
68.1 353.15 7.847430250
46.4 353.15 10.375323280
31.6 353.15 13.543037970
21.5 353.15 18.040465120
1000.0 363.15 3.240900000
681.0 363.15 3.890000000
464.0 363.15 4.794500000
316.0 363.15 6.035800000
215.0 363.15 7.730900000
46.4 363.15 21.690000000
1000.0 373.15 5.306100000
681.0 373.15 6.285900000
464.0 373.15 7.689300000
316.0 373.15 9.628700000
215.0 373.15 12.368000000
147.0 373.15 16.217000000
100.0 373.15 21.765000000
68.1 373.15 28.885000000
迭代数: 135
计算用时(时:分:秒:微秒): 00:01:09:412
优化算法: 麦夸特法(Levenberg-Marquardt) + 通用全局优化法
计算结束原因: 达到收敛判断标准
均方差(RMSE): 0.143327128000764
残差平方和(SSE): 0.739535962354106
相关系数(R): 0.999742568645631
相关系数之平方(R^2): 0.999485203562164
决定系数(DC): 0.999485147132945
卡方系数(Chi-Square): 0.0868738601073464
F统计(F-Statistic): 66011.5230477663
参数 最佳估算
---------- -------------
p2 -1.79923667345413
p3 0.00261744905299964
p5 -0.150906532823741
p6 0.000201789176766557
p8 0.00773410132098305
p9 -1.16317107036071E-5
p11 -0.00248355454494706
====== 结果输出 =====
No 实测值y 计算值y
1 2.1896 2.1087111
2 2.324669604 2.3019955
3 2.523491379 2.5606199
4 2.806234177 2.9030568
5 3.215116279 3.3554599
6 3.873197279 3.9441324
7 4.679 4.7347504
8 5.836123348 5.7896830
9 7.283297414 7.2127303
10 9.332911392 9.1595457
11 11.71488372 11.8619921
12 2.497 2.1378464
13 2.688546256 2.4408786
14 2.94137931 2.8365141
15 3.288291139 3.3562909
16 3.826372093 4.0450670
17 4.748911565 4.9506933
18 6.0202 6.1864126
19 7.84743025 7.8687097
20 10.37532328 10.1918850
21 13.54303797 13.4549796
22 18.04046512 18.1177033
23 3.2409 3.4170941
24 3.89 4.0514167
25 4.7945 4.8858853
26 6.0358 5.9964864
27 7.7309 7.4931441
28 21.69 21.7058258
29 5.3061 5.1221561
30 6.2859 6.2457133
31 7.6893 7.7391854
32 9.6287 9.7512100
33 12.368 12.4991662
34 16.217 16.2352463
35 21.765 21.5191216
36 28.885 28.9869643,
未计算出来的参数可以根据约束公式计算出来
QQ图片20170620094024.png
QQ图片20170620094059.png
QQ图片20170620094126.png
谢谢,之前照着书上的方法调一直不行,现在解决了,十分感谢。