Regression of my Experimental data for Ternary mixture into Non-randomness two liquid model (NRTL) thermodynamic model

Dear all,

I am trying to regress my experimental data for ternary mixture using NRTL multicomponent model. can you please help me out with this. I couldn't able to get the good fitting, the reason for this i don't know. hence if you could please change my code and modify it so that i can get the perfect fitting than it would be so gratefulness of yours.

Please note that consider the "Equation" i have written is correct. And if you have time then you can even write whole equation by your logic as well.

clear all;
clc;

alpha=0.3;
%% where, Xd(:,1)= Temperature, xd(:,2)=Mole fraction of 1, xd(:,3)=Mole fraction of 3, xd(:,4)=Psat of component 1, xd(:,5)=Psat of component 2
%% where, Psat of Component 3rd is negligible and hence Activity in below equation
%% yd is Experimental data
%% a is the parameters to be found out by regression
xd(:,1)=[313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15;313.15;318.15;323.15;328.15;333.15;338.15;343.15;348.15;353.15;358.15;363.15;368.15;373.15;378.15;383.15;388.15;393.15;398.15;403.15];
length(xd(:,1))

xd(:,2)=[0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.476;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.526;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.596;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.353;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.524;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.595;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.436;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.454;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.592;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.274;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.519;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182;0.182];
length(xd(:,2))

xd(:,3)=[0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.275;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.249;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.212;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.276;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.235;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.366;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.376;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.281;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.533;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.378;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818;0.818];
length(xd(:,3))

xd(:,4)=[7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36;7.39;9.6;12.36;15.77;19.96;25.05;31.22;38.61;47.43;57.89;70.21;84.64;101.45;120.94;143.43;169.24;198.73;232.31;270.36];
length(xd(:,4))

xd(:,5)=[0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316;0.091;0.129;0.181;0.252;0.345;0.47;0.632;0.844;1.117;1.466;1.908;2.466;3.164;4.031;5.102;6.417;8.021;9.967;12.316];
length(xd(:,5))

yd=[2.4;2.8;3.2;4.0;4.7;5.5;6.7;8.6;9.9;11.9;13.6;15.6;17.9;19.6;22.2;26.0;27.8;30.7;32.9;2.3;2.7;3.3;4.2;5.0;6.2;7.6;9.4;11.4;13.2;14.9;16.9;19.0;21.1;23.8;26.4;28.9;30.9;33.1;2.7;3.2;4.0;4.9;5.9;7.5;9.2;10.8;12.5;15.7;18.6;20.9;23.9;26.9;30.9;34.1;38.0;41.3;43.9;2.3;2.6;2.9;3.2;3.7;4.3;5.0;6.1;7.2;8.4;9.4;10.1;11.2;11.9;12.6;13.8;15.2;16.4;17.8;2.3;2.5;3.1;3.8;4.8;5.9;7.1;8.6;10.2;12.4;15;17.4;19.7;21.4;24.3;27.8;30.1;32.1;35;2.8;3.2;4.2;5.3;6.6;8.2;10.2;12.4;15.4;17.8;20.4;23.5;27.0;30.0;34.0;37.4;39.6;43.1;47.3;2.1;2.6;3.1;3.8;4.7;5.6;7.2;8.3;9.9;11.7;13.3;14.4;16.7;17.9;19.0;21.0;22.2;23.5;25.0;2.1;2.5;3.0;3.6;4.6;5.9;7.0;8.0;9.0;10.5;12.1;13.6;14.8;16.7;18.6;20.5;21.8;23.8;26.5;2.6;3.5;4.0;5.1;6.6;8.3;9.8;11.4;13.5;14.9;16.9;18.0;20.3;21.8;25.3;27.8;30.1;32.8;35.0;1.9;2.3;2.7;3.2;3.7;4.2;4.8;5.7;6.7;7.7;9.2;10.4;11.1;12.4;14.3;16.3;17.7;19.2;20.1;2.8;3.7;4.9;6.1;7.6;9.0;11.2;13.8;17.0;20.8;25.2;29.7;34.0;37.5;41.0;44.2;47.5;49.8;52.0;2.1;2.6;3.6;4.4;5.6;6.9;8.1;9.0;10.6;12.2;14.2;17.0;20.0;23.3;26.3;29.0;31.0;35.1;38.9];
length(yd)

FitnessFunction = @(a,xd)curvefit_multiobjective_two(a,xd);

options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt','MaxFunEvals',2000000,'MaxIter',200000,'TolX',1e-100,'TolFun',1e-100)
lb = [];
ub = [];

A=0.1;
a0=[A A A A A A A A A A A A]; %% Initial guess values of the paramters to be found out

[a,residuals,resnorm]=lsqcurvefit(FitnessFunction,a0,xd,yd,lb,ub,options)

C=[0 a(1) a(2); a(3) 0 a(4); a(5) a(6) 0] %% Parameters to be found out by regression
D=[0 a(7) a(8); a(9) 0 a(10); a(11) a(12) 0] %% Parameters to be found out by regression

p1=[a(1) a(2) a(3) a(4) a(5) a(6) a(7) a(8) a(9) a(10) a(11) a(12)]

Below is the other function that i have used in it.

You can take below equation granted and move ahead for regressoin and if you suspect something in equation than please look into below equation as well. This below screenshot shows you the equation for your reference purpose.

function yd=curvefit_multiobjective_two(a,xd)
alpha=0.3;

tow11=0;
tow12=(a(1)+(a(7)./(xd(:,1))));
tow13=(a(2)+(a(8)./(xd(:,1))));
tow21=(a(3)+(a(9)./(xd(:,1))));
tow22=0;
tow23=(a(4)+(a(10)./(xd(:,1))));
tow31=(a(5)+(a(11)./(xd(:,1))));
tow32=(a(6)+(a(12)./(xd(:,1))));
tow33=0;


G11=exp(-alpha.*tow11);
G12=exp(-alpha.*tow12);
G13=exp(-alpha.*tow13);
G21=exp(-alpha.*tow21);
G22=exp(-alpha.*tow22);
G23=exp(-alpha.*tow23);
G31=exp(-alpha.*tow31);
G32=exp(-alpha.*tow32);
G33=exp(-alpha.*tow33);

%%%% this a1, a2, ....., a8 are the breaked parts of the NRTL equation (Above shown in screenshot). 
a1=((xd(:,2).*tow11.*G11)+(xd(:,3).*tow21.*G21)+((1-xd(:,2)-xd(:,3)).*tow31.*G31))./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31));

a2=((xd(:,2).*G11)./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31))).*(tow11-(((xd(:,2).*tow11.*G11)+(xd(:,3).*tow21.*G21)+((1-xd(:,2)-xd(:,3)).*tow31.*G31))./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31))));

a3=((xd(:,3).*G12)./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32))).*(tow12-(((xd(:,2).*tow12.*G12)+(xd(:,3).*tow22.*G22)+((1-xd(:,2)-xd(:,3)).*tow32.*G32))./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32))));

a4=(((1-xd(:,2)-xd(:,3)).*G13)./((xd(:,2).*G13)+(xd(:,3).*G23)+((1-xd(:,2)-xd(:,3)).*G33))).*(tow13-(((xd(:,2).*tow13.*G13)+(xd(:,3).*tow23.*G23)+((1-xd(:,2)-xd(:,3)).*tow33.*G33))./((xd(:,2).*G13)+(xd(:,3).*G23)+((1-xd(:,2)-xd(:,3)).*G33))));

a5=((xd(:,2).*tow12.*G12)+(xd(:,3).*tow22.*G22)+((1-xd(:,2)-xd(:,3)).*tow32.*G32))./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32));

a6=((xd(:,2).*G21)./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31))).*(tow21-(((xd(:,2).*tow11.*G11)+(xd(:,3).*tow21.*G21)+((1-xd(:,2)-xd(:,3)).*tow31.*G31))./((xd(:,2).*G11)+(xd(:,3).*G21)+((1-xd(:,2)-xd(:,3)).*G31))));

a7=((xd(:,3).*G22)./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32))).*(tow22-(((xd(:,2).*tow12.*G12)+(xd(:,3).*tow22.*G22)+((1-xd(:,2)-xd(:,3)).*tow32.*G32))./((xd(:,2).*G12)+(xd(:,3).*G22)+((1-xd(:,2)-xd(:,3)).*G32))));

a8=(((1-xd(:,2)-xd(:,3)).*G23)./((xd(:,2).*G13)+(xd(:,3).*G23)+((1-xd(:,2)-xd(:,3)).*G33))).*(tow23-(((xd(:,2).*tow13.*G13)+(xd(:,3).*tow23.*G23)+((1-xd(:,2)-xd(:,3)).*tow33.*G33))./((xd(:,2).*G13)+(xd(:,3).*G23)+((1-xd(:,2)-xd(:,3)).*G33))));

gamma_one=exp(a1+a2+a3+a4);

gamma_two=exp(a5+a6+a7+a8);

yd=(xd(:,2).*gamma_one.*xd(:,4))+(xd(:,3).*gamma_two.*xd(:,5));

end

Please have a look into this code as i am stucked in this code since 2 months (probably it's hard to believe but it's true).

Hoping for a valuable response from all Dear ones.

Thanking you,

Ashish Kundaliya

[Alex Sha]

Hi, Ashish, please check the result below:

Root of Mean Square Error (RMSE): 2.76893927823859
Sum of Squared Residual: 1748.08163765851
Correlation Coef. (R): 0.970896160052148
R-Square: 0.942639353604007

Parameter	Best Estimate
----------	-------------
a1	26.6504023429873
a2	-193.916431332614
a3	-8.41341269811459
a4	-41.3226807885564
a5	-22.8860795710246
a6	7.48475915204028
a7	-8690.59540607362
a8	1044388.71558015
a9	2618.83324625766
a10	17562.5888653521
a11	6762.69315909156
a12	-1396.27141432101

[Ashish Kundaliya]

Dear Alex,

Thank you so much for the direct answers and I appreciate your help. But,

1) I would like to ask you that the results that you have given me is still have lesser Rsquare.

2) After completion of lockdown i again will conduct few more experiments and collect data and add into this file hence, at that time i again have to perform regression.

With supporting this two above statements i would like to ask that can you please send me the full code that so that i can run on my Laptop at any time or if you have done it through any tool box than please guide me through it. Their is no doubt that you are much experienced person and hence i am hoping for your more help on this.

I will be very very grateful to you if you could please extend your helping hands.

[Alex Sha]

Hello, Ashish, the result above was obtained by another software of 1stOpt, the code looks like below, very simple and easy for understanding, the he most notable advantages are that the guess of initial start-values is no longer required.

Constant alpha=0.3, tow11=0;
ConstStr
tow12=(a1+(a7/(xd1))),
tow13=(a2+(a8/(xd1))),
tow21=(a3+(a9/(xd1))),
tow22=0,
tow23=(a4+(a10/(xd1))),
tow31=(a5+(a11/(xd1))),
tow32=(a6+(a12/(xd1))),
tow33=0,
G11=exp(-alpha*tow11),
G12=exp(-alpha*tow12),
G13=exp(-alpha*tow13),
G21=exp(-alpha*tow21),
G22=exp(-alpha*tow22),
G23=exp(-alpha*tow23),
G31=exp(-alpha*tow31),
G32=exp(-alpha*tow32),
G33=exp(-alpha*tow33),
aa1=((xd2*tow11*G11)+(xd3*tow21*G21)+((1-xd2-xd3)*tow31*G31))/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)),
aa2=((xd2*G11)/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)))*(tow11-(((xd2*tow11*G11)+(xd3*tow21*G21)+((1-xd2-xd3)*tow31*G31))/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)))),
aa3=((xd3*G12)/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)))*(tow12-(((xd2*tow12*G12)+(xd3*tow22*G22)+((1-xd2-xd3)*tow32*G32))/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)))),
aa4=(((1-xd2-xd3)*G13)/((xd2*G13)+(xd3*G23)+((1-xd2-xd3)*G33)))*(tow13-(((xd2*tow13*G13)+(xd3*tow23*G23)+((1-xd2-xd3)*tow33*G33))/((xd2*G13)+(xd3*G23)+((1-xd2-xd3)*G33)))),
aa5=((xd2*tow12*G12)+(xd3*tow22*G22)+((1-xd2-xd3)*tow32*G32))/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)),
aa6=((xd2*G21)/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)))*(tow21-(((xd2*tow11*G11)+(xd3*tow21*G21)+((1-xd2-xd3)*tow31*G31))/((xd2*G11)+(xd3*G21)+((1-xd2-xd3)*G31)))),
aa7=((xd3*G22)/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)))*(tow22-(((xd2*tow12*G12)+(xd3*tow22*G22)+((1-xd2-xd3)*tow32*G32))/((xd2*G12)+(xd3*G22)+((1-xd2-xd3)*G32)))),
aa8=(((1-xd2-xd3)*G23)/((xd2*G13)+(xd3*G23)+((1-xd2-xd3)*G33)))*(tow23-(((xd2*tow13*G13)+(xd3*tow23*G23)+((1-xd2-xd3)*tow33*G33))/((xd2*G13)+(xd3*G23)+((1-xd2-xd3)*G33)))),
gamma_one=exp(aa1+aa2+aa3+aa4),
gamma_two=exp(aa5+aa6+aa7+aa8);
Variable xd(5),yd;
Parameter a(12);
Function yd=(xd2*gamma_one*xd4)+(xd3*gamma_two*xd5);
Data;
xd1=[313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15,313.15,318.15,323.15,328.15,333.15,338.15,343.15,348.15,353.15,358.15,363.15,368.15,373.15,378.15,383.15,388.15,393.15,398.15,403.15];
xd2=[0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.476,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.526,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.596,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.353,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.524,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.595,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.436,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.454,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.592,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.274,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.519,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182,0.182];
xd3=[0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.275,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.249,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.212,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.276,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.235,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.366,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.376,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.281,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.533,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.378,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818,0.818];
xd4=[7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36,7.39,9.6,12.36,15.77,19.96,25.05,31.22,38.61,47.43,57.89,70.21,84.64,101.45,120.94,143.43,169.24,198.73,232.31,270.36];
xd5=[0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316,0.091,0.129,0.181,0.252,0.345,0.47,0.632,0.844,1.117,1.466,1.908,2.466,3.164,4.031,5.102,6.417,8.021,9.967,12.316];
yd=[2.4,2.8,3.2,4.0,4.7,5.5,6.7,8.6,9.9,11.9,13.6,15.6,17.9,19.6,22.2,26.0,27.8,30.7,32.9,2.3,2.7,3.3,4.2,5.0,6.2,7.6,9.4,11.4,13.2,14.9,16.9,19.0,21.1,23.8,26.4,28.9,30.9,33.1,2.7,3.2,4.0,4.9,5.9,7.5,9.2,10.8,12.5,15.7,18.6,20.9,23.9,26.9,30.9,34.1,38.0,41.3,43.9,2.3,2.6,2.9,3.2,3.7,4.3,5.0,6.1,7.2,8.4,9.4,10.1,11.2,11.9,12.6,13.8,15.2,16.4,17.8,2.3,2.5,3.1,3.8,4.8,5.9,7.1,8.6,10.2,12.4,15,17.4,19.7,21.4,24.3,27.8,30.1,32.1,35,2.8,3.2,4.2,5.3,6.6,8.2,10.2,12.4,15.4,17.8,20.4,23.5,27.0,30.0,34.0,37.4,39.6,43.1,47.3,2.1,2.6,3.1,3.8,4.7,5.6,7.2,8.3,9.9,11.7,13.3,14.4,16.7,17.9,19.0,21.0,22.2,23.5,25.0,2.1,2.5,3.0,3.6,4.6,5.9,7.0,8.0,9.0,10.5,12.1,13.6,14.8,16.7,18.6,20.5,21.8,23.8,26.5,2.6,3.5,4.0,5.1,6.6,8.3,9.8,11.4,13.5,14.9,16.9,18.0,20.3,21.8,25.3,27.8,30.1,32.8,35.0,1.9,2.3,2.7,3.2,3.7,4.2,4.8,5.7,6.7,7.7,9.2,10.4,11.1,12.4,14.3,16.3,17.7,19.2,20.1,2.8,3.7,4.9,6.1,7.6,9.0,11.2,13.8,17.0,20.8,25.2,29.7,34.0,37.5,41.0,44.2,47.5,49.8,52.0,2.1,2.6,3.6,4.4,5.6,6.9,8.1,9.0,10.6,12.2,14.2,17.0,20.0,23.3,26.3,29.0,31.0,35.1,38.9];

[Ashish Kundaliya]

Thanks for this assistance. But i found that 1stOpt is a paid version not a free version.! so how will i get that. can you have any idea about it.

I mean if you know any free software similar to 1stOpt then please suggest me that software and share appropriate code for that as well.

Sorry for this much inconvinience from you, but i have no choice other than regression.

[Roei Shapira]

Hi Did you get an answer? Im facing the same problem