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yupeifeng

½ð³æ (СÓÐÃûÆø)

[½»Á÷] matlabÇó½â·½³ÌÖеIJÎÊýÒÑÓÐ4È˲ÎÓë

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ʵÑéÊý¾ÝΪ£º£¨t,c£©=£¨0,0.69£©£¨2,0.645£©£¨4,0.635£©£¨8,0.62£©£¨24,0.61£©£¨48,0.61£©.ÆäÖÐtΪʱ¼ä£¬cΪijÀë×ÓµÄŨ¶È¡£
¶¯Á¦Ñ§·½³ÌÄ£ÐÍΪ£º-dc/dt=k*(c0-c)^(1/3)*(c-c~).
ÆäÖÐc0Ϊ³õʼŨ¶È¿ÉÒÔÈ¡0.7£¬c~ΪƽºâŨ¶ÈÈ¡0.61.
ÔõôÑù²ÅÄÜÄâºÏ³ö²ÎÊýkµÄÖµÄØ£¿Ð»Ð»´ó¼Ò¸ø³ö³ÌÐò´úÂ룬ÔٴθÐл
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dbb627

ÈÙÓþ°æÖ÷ (ÖøÃûдÊÖ)

¡ï ¡ï ¡ï ¡ï ¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
fegg7502: ½ð±Ò+4, ¶àл½»Á÷ 2012-07-09 08:07:15
Õâ¸öÆäʵÂÛ̳ÀïÓкܶàÀý×Ó£¬²Î¿¼¾ÍÄÜд³öÀ´¡£
¸øÄãдÁ˸ö
CODE:
function parafit
clear all;
t=[0 2 4 8 24 48];
y=[0.69 0.645 0.635 0.62 0.61 0.61];
y0=0.69;

% Nonlinear least square estimate using lsqnonlin()
beta0=0.5;
lb=[0];ub=[inf];
[beta,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@Func,beta0,lb,ub,[],t,y,y0);         
ci = nlparci(beta,residual,jacobian);
beta;
% result
fprintf('\n Estimated Parameters by Lsqnonlin():\n')
fprintf('\t k = %.4f ¡À %.4f\n',beta(1),ci(1,2)-beta(1))
fprintf('  The sum of the residual squares is: %.1e\n\n',sum(residual.^2))

% plot of fit results
tspan = [0  max(t)];
[tt yc] = ode45(@ModelEqs,tspan,y0,[],beta);
tc=linspace(0,max(t),200);
yca = spline(tt,yc,tc);
plot(t,y,'ro',tc,yca,'r-');
hold on
xlabel('Time');
ylabel('Concentration');
hold off
% =======================================
function f1 = Func(beta,t,y,y0)        % Define objective function
tspan =t;
[tt yy] = ode45(@ModelEqs,tspan,y0,[],beta);
yc= spline(tt,yy,t);
f1=y-yc;
% ==================================
function dydt = ModelEqs(t,y,beta)          % Model equations
dydt = -beta*(0.7-y).^(1/3)*(y-0.61);

The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
2Â¥2012-07-02 17:38:01
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
ÆÕͨ»ØÌû

dbb627

ÈÙÓþ°æÖ÷ (ÖøÃûдÊÖ)

¡ï ¡ï ¡ï ¡ï
fegg7502: ½ð±Ò+4, Ó¦ÖúÖ¸Êý+1, ר¼Ò¿¼ºË, ¶àл½»Á÷ 2012-07-09 08:07:38
½á¹ûÈçÏÂ
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.




Estimated Parameters by Lsqnonlin():
         k = 1.0138 ¡À 0.3000
  The sum of the residual squares is: 1.5e-004


The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
3Â¥2012-07-02 17:39:27
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

yupeifeng

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
3Â¥: Originally posted by dbb627 at 2012-07-02 17:39:27
½á¹ûÈçÏÂ
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.

< ...

Ê×ÏȸÐлÕâλ ѧ³¤°¡£¬ÎÒÓе㿴²»¶®°¡£¬Äã°ïÎÒ ·ÖÎöÏÂ˼·£¬²½ÖèÊÇʲô£¿¾ÍÊÇÏÈ×öÉèô¼ÆË㣬
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4Â¥2012-07-02 22:01:21
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dingd

Ìú¸Ëľ³æ (Ö°Òµ×÷¼Ò)

¡ï ¡ï ¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
fegg7502: ½ð±Ò+2, ¶àл½»Á÷ 2012-07-09 08:07:55
1stOptÇó½â£º
CODE:
Constant c0=0.7,cp=0.61;
Variable t,c;
ODEFunction c'=-k*(c0-c)^(1/3)*(c-cp)
Data;
t,c
0,0.69
2,0.645
4,0.635
8,0.62
24,0.61
48,0.61

¾ù·½²î(RMSE): 0.00535058522113925
²Ð²îƽ·½ºÍ(SSE): 0.000143143811043369
Ïà¹ØϵÊý(R): 0.955733024504782
Ïà¹ØϵÊý֮ƽ·½(R^2): 0.913425614129058
¾ö¶¨ÏµÊý(DC): 0.852429060780033

²ÎÊý                  ×î¼Ñ¹ÀËã
--------------------        -------------
k        1.02159845408008
5Â¥2012-07-03 08:52:49
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

yupeifeng

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
5Â¥: Originally posted by dingd at 2012-07-03 08:52:49
1stOptÇó½â£º

Constant c0=0.7,cp=0.61;
Variable t,c;
ODEFunction c'=-k*(c0-c)^(1/3)*(c-cp)
Data;
t,c
0,0.69
2,0.645
4,0.635
8,0.62
24,0.61
48,0.61


¾ù·½²î(RMSE): 0.00535058522113925
...

ÄãºÃ£¬ÎÒ½ñÌìÏÂÔØÁ˸ö1stopt,²»Ôõô»áÓ𡣬Õâ¸öºÍmatlabÒ»ÑùÂð£¿
ã¿ã½Î´À´
6Â¥2012-07-03 09:31:42
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dingd

Ìú¸Ëľ³æ (Ö°Òµ×÷¼Ò)

¡ï ¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
fegg7502: ½ð±Ò+1, ¶àл½»Á÷ 2012-07-09 08:08:09
±ÈMatlab¼òµ¥°¡£¬ÓÅ»¯ÄâºÏ·½Ãæ¸üÊÇԶʤMatlab£¡
7Â¥2012-07-03 09:45:41
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

yupeifeng

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
7Â¥: Originally posted by dingd at 2012-07-03 09:45:41
±ÈMatlab¼òµ¥°¡£¬ÓÅ»¯ÄâºÏ·½Ãæ¸üÊÇԶʤMatlab£¡

²»Ì«»áÓã¬Ôõôȥ¶¨ÒåÄÄЩÁ¿£¬ÔõôÔËÐÐÄØ£¿
ã¿ã½Î´À´
8Â¥2012-07-03 09:49:46
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

yupeifeng

½ð³æ (СÓÐÃûÆø)

ÒýÓûØÌû:
5Â¥: Originally posted by dingd at 2012-07-03 08:52:49
1stOptÇó½â£º

Constant c0=0.7,cp=0.61;
Variable t,c;
ODEFunction c'=-k*(c0-c)^(1/3)*(c-cp)
Data;
t,c
0,0.69
2,0.645
4,0.635
8,0.62
24,0.61
48,0.61


¾ù·½²î(RMSE): 0.00535058522113925
...

ÎÒ°ÑÄãµÄ³ÌÐò¸´Öƺó£¬ÌáʾûÓж¨Òå²ÎÊý£¬ÕâÊÇÔõô»ØÊ°¡
ã¿ã½Î´À´
9Â¥2012-07-03 10:16:30
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dingd

Ìú¸Ëľ³æ (Ö°Òµ×÷¼Ò)

¡ï ¡ï
Сľ³æ: ½ð±Ò+0.5, ¸ø¸öºì°ü£¬Ð»Ð»»ØÌû
fegg7502: ½ð±Ò+1, ¶àл½»Á÷ 2012-07-09 08:08:30
ÄãÓõÄÊÇÍøÉϵÄ1.5PJ°æ°É£¿ÀÏÁ˵㣬ºÃÏñÒ²²»Ö§³Ö΢·Ö·½³Ì¼ÆËã¡£ÓÃа汾ûÎÊÌâ¡£
10Â¥2012-07-03 10:38:35
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
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