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zoe070721

银虫 (小有名气)

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虫号: 2451384
注册: 2013-05-06
专业: 药物分析

[求助] 用lsqnonlin拟合已知活度系数模型，残差大，无法获得最优解，请大神看看代码的问题！已有2人参与

求助各位大神！！！
   小虫妹在拟合已知NRTL模型时（如图片），用matlab中最小二乘法来拟合实验数据，以求得模型中的两个参数△g12,△g21，目标方程设为OF。
编入的代码如下，运行之后，输出如下，感觉残差值比较大，拟合值好像是局部最优解，而不是全局最优；改变初始值，对参数值的影响也很大，
初始值的设置也是个难题。
   请大神看看，问题该如何解决？？？

   另求版内大神是否有高版本1stOp能否代跑一下，给出个初值或者最优解，小虫妹不胜感激，可追加金币！！！

function OF=ObjFunBinary(x) %目标函数
format long
T=[278.15,283.15,288.15,293.15,298.15,303.15,308.15,313.15,318.15];
x1=[0.01217,0.01457,0.01704,0.02085,0.02337,0.02707,0.03041,0.03377,0.03766];

x2=1-x1;
R=8.3145;
H=19.76;
Tm=454.8;
gamma_exp=exp(H/R*(1/Tm-1./T))./x1;
a=x(1);g1=x(2);g2=x(3);%x(1)根据文献一般取0.2、0.3或者0.47
t12=g1./(R*T);
t21=g2./(R*T);
G12=exp(-a.*t12);
G21=exp(-a.*t21);
lngama1=x2.^2.*(t21.*G21.^2./(x1+x2.*G21).^2+t12.*G12./(x2+x1.*G12).^2);
gamma_cal=exp(lngama1);
OF=gamma_cal-gamma_exp;

beta0 = [0.31 2000 8000];  %参数初始值
options.Algorithm = 'levenberg-marquardt';
[beta,resnorm,residual,exitflag,output]=lsqnonlin(@ObjFunBinarynew,beta0,[],[],options)

输出的结果是

Local minimum possible.

lsqnonlin stopped because the final change in the sum of squares relative to
its initial value is less than the default value of the function tolerance.

<stopping criteria details>

beta =

1.0e+04 *

0.000044925534703 1.158249518250641 1.085523151964263

resnorm =

3.233501964174955

residual =

  Columns 1 through 7

  -0.835682305165847 0.375853525304237 0.641305366330478 0.765737066136275 0.366439803004162 0.007880991932048  -0.337551041065019

  Columns 8 through 9

  -0.624403280363090  -0.870680738315109

exitflag =

   3

output =

   iterations: 37
      funcCount: 168
      stepsize: 23.651354916984875
   cgiterations: []
firstorderopt: 0.093957635054323
      algorithm: 'levenberg-marquardt'
      message: 'Local minimum possible.

lsqnonlin stopped because the final change in the sum of squares relative to
its initial value...'

1305562_1333620757_902.jpg

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