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СµÜʵÔÚÊÇÒ»Çϲ»Í¨¶Ômatlab£¬²»Òª¹ÖСµÜÌáµÄÎÊÌâ±È½Ïɵ£¬Ò»¸öÊDZ¨´íÖеÄÎÊÌ⣬Õâ¸ö[k,fval,flag] = fmincon(@ObjFunc7FminconÒ»¾äµÄ@ObjFunc7FminconÊÇÔõôÉ趨µÄ£¿ÎÒ¿´ÓеÄÈËд@ObjFunc4Fmincon.
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function parafit
%  
% r1 = k(1)*C(1);
% r2 = k(2)*C(1);
% r3 = k(3)*C(2);
% r4 = k(4)*C(3);
% r5 = k(5)*C(2);
% r6 = k(6)*C(3);
%
% dCAdt = - r1 - r2;
% dCBdt = r1 + r4 - r3 - r5;
% dCCdt = r2 + r3 - r4 ¨C r6 ;
% dCDdt = r5 + r6;
clear all
clc
%        t/min   CA-1     CB-2        CC-3   CD-4   / mol/L
  Kinetics=[0       100    0         0          0      
          10        0.2441  0.1390   0.28.31   0.0171   
          20        0.432  0.1629   0.2370   0.0192   
          30        0.756   0.1992  0.2509    0.0349   
          40        0.522   0.2091   0.2737    0.0531   
          50        0.426    0.1967   0.3231   0.0634   
          60        0.397    0.1803   0.3536   0.0822   
          70        0.431    0.1732   0.3330   0.0945  
          80        0.531   0.1645    0.3310  0.0987];
k0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00000005  0.00000005];         % ²ÎÊý³õÖµ
lb = [0  0  0  0  0  0];                   % ²ÎÊýÏÂÏÞ
ub = [1 1  1  1  1  1];    % ²ÎÊýÉÏÏÞ
x0 = [100  0  0  0];
yexp = Kinetics;                  % yexp: ʵÑéÊý¾Ý[x1        x4        x5        x6]
warning off
% ʹÓú¯Êýfmincon()½øÐвÎÊý¹À¼Æ
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
fprintf('\nʹÓú¯Êýfmincon()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
warning off
% ʹÓú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
warning off
% ÒÔº¯Êýfmincon()¹À¼ÆµÃµ½µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ
k0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\nÒÔfmincon()µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
tspan = [0 : 10 : 80];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('ca-pr','ca-real')
figure;plot(t,x(:,2:5));
hold on
plot(t,yexp(:,3:6),'o');legend('cb-pr','cc-pr','cd-pr','ce-pr','cb-real','cc-real','cd-real','ce-real')
% ------------------------------------------------------------------
function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 : 10 : 80];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;

% ------------------------------------------------------------------
function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0.0 : 10 : 80];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

% ------------------------------------------------------------------
function dxdt = KineticEqs(t,x,k)
r1 = k(1)*x(1);
r2 = k(2)*x(1);
r3 = k(3)*x(2);
r4 = k(4)*x(3);
r5 = k(5)*x(2);
r6 = k(6)*x(3);

dCAdt = - r1 - r2;
dCBdt = r2 + r4 - r3 - r5;
dCCdt = r2 + r3 - r4 - r6;
dCDdt = r5 + r6;

dxdt = [dCAdt; dCBdt; dCCdt; dCDdt];
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llgcty

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2Â¥2015-11-29 21:52:01
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