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小木虫论坛-学术科研互动平台 » 计算模拟区 » 计算模拟 » 软件使用与操作 » matlab非线性最优化求解，微分方程组的拟合，参数估计
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zhangholmes

至尊木虫 (著名写手)

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[求助] matlab非线性最优化求解，微分方程组的拟合，参数估计

如题，用微分方程组拟合4组不同温度下的数据，求理论值a和b，并使a和b的值分别与实验值y1和y2的差方和最小。并求此时的各个参数值(k1,k2,k3,k4,k5,k6)，求各位大侠略施援手。

0<k1<30, 0<k2<10, 0<k3<5, 0<k4<20, 0<k5<20, 0<k6<5
t=[0.494660000000000,0.502760000000000,0.618930000000000,0.621470000000000,0.623470000000000,0.819730000000000,0.825080000000000,0.828350000000000];

T=463 K时，
y1= [0.00800000000000000,0.00990000000000000,0.00782000000000000,0.0108400000000000,0.00937000000000000,0.00882000000000000,0.00614000000000000,0.0108200000000000];
y2=[0.0625100000000000,0.0727400000000000,0.0540300000000000,0.0667600000000000,0.0620200000000000,0.0494400000000000,0.0452000000000000,0.0509400000000000];                                    %y1和y2分别为a和b的实验值

T=473 K时，
y1=[0.00829000000000000,0.0107700000000000,0.00938000000000000,0.0172000000000000,0.0128100000000000,0.0139200000000000,0.0108200000000000,0.0179000000000000];
y2=[0.0622600000000000,0.0719200000000000,0.0525700000000000,0.0604900000000000,0.0586200000000000,0.0444300000000000,0.0405900000000000,0.0439200000000000];

T=483 K时，
y1=[0.0169300000000000,0.0229900000000000,0.0188900000000000,0.0313900000000000,0.0265800000000000,0.0258100000000000,0.0194200000000000,0.0293300000000000];
y2=[0.0537100000000000,0.0598300000000000,0.0431500000000000,0.0465000000000000,0.0450300000000000,0.0326700000000000,0.0321200000000000,0.0327000000000000];

T=493 K时，
y1=[0.0328500000000000,0.0418500000000000,0.0330300000000000,0.0512500000000000,0.0424800000000000,0.0389500000000000,0.0300900000000000,0.0443800000000000];
y2=[0.0381700000000000,0.0415400000000000,0.0292800000000000,0.0273400000000000,0.0295700000000000,0.0197800000000000,0.0216900000000000,0.0180800000000000];

pA = 101*(1 - (2 b + a));
pW = 101*(a+ b);

da/dt=k(4).*k(1).*k(2).*k(3).*pA.*pW./(k(1).*k(2).*k(4).*k(5).*pA^2+k(1).*k(2).*k(3).*pA.*pW+k(4)+k(1).*k(2).*k(4).*pA.*pW+k(1).*k(4).*pW;

db/dt=k(6).*k(1).*k(2).*k(4).*k(5).*pA^2./(k(1).*k(2).*k(4).*k(5).*pA^2+k(1).*k(2).*k(3).*pA.*pW+k(4)+k(1).*k(2).*k(4).*pA.*pW+k(1).*k(4).*pW;

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1楼2013-05-12 12:10:33
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dingd

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【答案】应助回帖

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感谢参与，应助指数 +1
csgt0: 金币+1, 谢谢 2013-05-14 15:45:01
1：好好检查下公式，左右括号似乎都不匹配；
2：是要求统一的参数吗（四组数据），如果是哪影响因子T并未在公式里出现。
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2楼2013-05-12 14:34:13
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zhangholmes

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逍遥门主
引用回帖:
2楼: Originally posted by dingd at 2013-05-12 14:34:13
1：好好检查下公式，左右括号似乎都不匹配；
2：是要求统一的参数吗（四组数据），如果是哪影响因子T并未在公式里出现。

谢谢回复，公式最后忘记加了一个括号。不要求统一参数，每组数据都有一组独立的参数，共四组参数。
公式如下：
da/dt=k(4).*k(1).*k(2).*k(3).*pA.*pW./(k(1).*k(2).*k(4).*k(5).*pA^2+k(1).*k(2).*k(3).*pA.*pW+k(4)+k(1).*k(2).*k(4).*pA.*pW+k(1).*k(4).*pW）;

db/dt=k(6).*k(1).*k(2).*k(4).*k(5).*pA^2./(k(1).*k(2).*k(4).*k(5).*pA^2+k(1).*k(2).*k(3).*pA.*pW+k(4)+k(1).*k(2).*k(4).*pA.*pW+k(1).*k(4).*pW）;
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3楼2013-05-12 15:59:36
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