±±¾©Ê¯ÓÍ»¯¹¤Ñ§Ôº2026ÄêÑо¿ÉúÕÐÉú½ÓÊÕµ÷¼Á¹«¸æ
²é¿´: 1649  |  »Ø¸´: 1

_romantic_Õò

ľ³æ (ÖøÃûдÊÖ)

[ÇóÖú] ³õѧÕßÇóÖú£¬matlabÄ£·Â³ÌÐò ÒÑÓÐ1È˲ÎÓë

function KineticsEst5
% ¶¯Á¦Ñ§ODE·½³ÌÄ£Ð͵IJÎÊý¹À¼Æ

clear all
clc

k0 = [0  0  0  0];         % ²ÎÊý³õÖµ
lb = [ -inf  -inf  -inf  -inf ];                   % ²ÎÊýÏÂÏÞ
ub = [+inf  +inf  +inf  +inf ];    % ²ÎÊýÉÏÏÞ
x0 = [8.5 28.8 27.6];
tspan=[0 0.222 0.333 0.444];
yexp =  [8.5000   28.8000   27.6000
    4.8000   23.2000   35.3000
    4.2000   21.6000   36.5000
    4.0000   21.2000   37.3000];                 % yexp: ʵÑéÊý¾Ý[x1        x2 x3]

% ʹÓú¯Êýfmincon()½øÐвÎÊý¹À¼Æ
[k,fval,flag] = fmincon(@ObjFunc4Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
fprintf('\nʹÓú¯Êýfmincon()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
fprintf('\tk1 = %.4f\n',k(1))
fprintf('\tk2 = %.4f\n',k(2))
fprintf('\tk3 = %.4f\n',k(3))
fprintf('\tk4 = %.4f\n',k(4))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fmincon = k;

% ʹÓú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc4LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\nʹÓú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
Output

% ÒÔº¯Êýfmincon()¹À¼ÆµÃµ½µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ
k0 = k_fmincon;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc4LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\nÒÔfmincon()µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
Output


% ------------------------------------------------------------------
function f = ObjFunc4Fmincon(k,x0,yexp)
tspan = [0.00 : 0.01 : 0.44];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,1:3) = x(:,1:3);
f = sum((y(:,1)-yexp(:,1)).^2) + sum((y(:,2)-yexp(:,2)).^2)   ...
    + sum((y(:,3)-yexp(:,3)).^2) ;

% ÒÔº¯Êýfmincon()¹À¼ÆµÃµ½µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ
k0 = k_fmincon;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc4LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\nÒÔfmincon()µÄ½á¹ûΪ³õÖµ£¬Ê¹Óú¯Êýlsqnonlin()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:\n')
Output

% ------------------------------------------------------------------
function f = ObjFunc4LNL(k,x0,yexp)
tspan = [0.00 : 0.01 : 0.44];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,1:3) = x(:,1:3);
f1 = y(:,1) - yexp(:,1);
f2 = y(:,2) - yexp(:,2);
f3 = y(:,3) - yexp(:,3);
f = [f1; f2; f3];

% ------------------------------------------------------------------
function dxdt = KineticEqs(t,x,k)
dxdt =  ...
[ (k(1)*x(2)- k(1)*x(1))
   (k(1)*x(2)+(k(3)-k(2)-k(4))*x(3))
   (k(3)*x(2)-k(4)*x(3))
   ];
»Ø¸´´ËÂ¥
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

hzlhm

ÖÁ×ðľ³æ (ÖøÃûдÊÖ)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï ¡ï
_romantic_Õò: ½ð±Ò+50, ¡ïÓаïÖú 2022-03-15 11:07:58
³ÌÐòÖеÄÎÊÌ⣺
1¡¢tspan = [0.00 : 0.01 : 0.44]Óëtspan=[0 0.222 0.333 0.444]ûÓжÔÓ¦
2¡¢f = sum((y(:,1)-yexp(:,1)).^2) + sum((y(:,2)-yexp(:,2)).^2)  + sum((y(:,3)-yexp(:,3)).^2)  ºóÃæµÄ´úÂëÊǶàÓàµÄ£¬¼ÆËãµÄ½á¹û²»Ê¹ÓÃ
Ö´Ðнá¹û£º

ʹÓú¯Êýfmincon()¹À¼ÆµÃµ½µÄ²ÎÊýֵΪ:
        k1 = -0.6403
        k2 = 1.8125
        k3 = 3.6968
        k4 = 1.9950
The sum of the squares is: 4.0
QQ£º2120156492
2Â¥2021-12-27 22:26:21
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
Ïà¹Ø°æ¿éÌø×ª ÎÒÒª¶©ÔÄÂ¥Ö÷ _romantic_Õò µÄÖ÷Ìâ¸üÐÂ
×î¾ßÈËÆøÈÈÌûÍÆ¼ö [²é¿´È«²¿] ×÷Õß »Ø/¿´ ×îºó·¢±í
[¿¼ÑÐ] 285Çóµ÷¼Á +14 AZMK 2026-04-02 14/700 2026-04-02 15:54 by ÉϾÅÌìÀ¿Ô£¨ºÃÔ
[¿¼ÑÐ] 071000ÉúÎïѧµ÷¼Á +6 ÖªÕÑÂû 2026-04-02 6/300 2026-04-02 15:28 by sophie2180
[¿¼ÑÐ] Çóµ÷¼ÁÇóµ÷¼Á +6 121. 2026-04-02 6/300 2026-04-02 15:26 by haironglove
[¿¼ÑÐ] ѧ˶»úе¹¤³Ì303Çóµ÷¼Á +4 ÎÞÃûËùÒÔ½ÐÎâÃ÷ 2026-03-30 4/200 2026-04-02 14:06 by asdfzly
[¿¼ÑÐ] 290Çóµ÷¼Á +3 1314Åõ»¨ 2026-04-02 3/150 2026-04-02 13:34 by Ecowxq666£¡
[¿¼ÑÐ] 272Çóµ÷¼Á£¬½ÓÊÜ¿çרҵµ÷¼Á£¡ +4 ÏÐÓ㬠2026-03-31 4/200 2026-04-02 11:18 by guyan1000
[¿¼ÑÐ] ¿¼Ñе÷¼Á0702 +3 ÷×ÓζÍíϼ 2026-03-28 3/150 2026-04-02 10:10 by jp9609
[¿¼ÑÐ] 354Çóµ÷¼Á +4 lxb598 2026-03-31 5/250 2026-04-02 09:55 by Jaylen.
[¿¼ÑÐ] 295²ÄÁϹ¤³Ìר˶Çóµ÷¼Á +19 1428151015 2026-03-27 19/950 2026-04-01 22:34 by peike
[¿¼ÑÐ] 279Çóµ÷¼Á +7 Īxiao 2026-04-01 7/350 2026-04-01 22:05 by ¿Í¶ûÃÀµÂ
[¿¼ÑÐ] 273Çóµ÷¼Á +19 ÀîÜÆÐÂ1 2026-03-31 19/950 2026-04-01 21:49 by chyhaha
[¿¼ÑÐ] 309Çóµ÷¼Á +19 Ë­²»ÊÇÉÙÄê 2026-03-29 19/950 2026-04-01 15:47 by jp9609
[¿¼ÑÐ] 288×ÊÔ´Óë»·¾³×¨Ë¶Çóµ÷¼Á£¬²»ÏÞרҵ£¬ÓÐѧÉϾÍÐÐ +25 lllllos 2026-03-30 26/1300 2026-04-01 09:52 by Ò»Ö»ºÃ¹û×Ó?
[¿¼ÑÐ] 318Ò»Ö¾Ô¸¼ªÁÖ´óѧÉúÎïÓëÒ½Ò© Çóµ÷¼Á +6 óÆÐÐÖÂÔ¶. 2026-03-28 6/300 2026-04-01 09:28 by oooqiao
[¿¼ÑÐ] Çóµ÷¼Á ÉúÎïѧ 377·Ö +6 zzll03 2026-03-31 6/300 2026-03-31 17:33 by ÌÆãå¶ù
[¿¼ÑÐ] 343Çóµ÷¼Á +8 °®î¿°í 2026-03-28 8/400 2026-03-31 16:12 by ²»³Ôô~µÄ؈
[¿¼ÑÐ] ±¾¿Æ211ÉúÎïҽѧ¹¤³Ì085409Çóµ÷¼Á339·Ö +7 Àï×Óľyy 2026-03-29 7/350 2026-03-31 14:35 by fmesaito
[¿¼ÑÐ] Çóµ÷¼Á +8 11ggg 2026-03-30 8/400 2026-03-31 13:56 by nanaliuyun
[¿¼ÑÐ] Ò»Ö¾Ô¸Î÷µç085401ÊýÒ»Ó¢Ò»299Çóµ÷¼Á Áù¼¶521 +4 °®³Ô´óѼÀæ 2026-03-31 4/200 2026-03-31 11:51 by ²«»÷518
[¿¼ÑÐ] 266Çóµ÷¼Á +11 ÑôÑôÍÛÈû 2026-03-27 12/600 2026-03-27 17:56 by yu221
ÐÅÏ¢Ìáʾ
ÇëÌî´¦ÀíÒâ¼û