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qj2006

½ð³æ (ÖøÃûдÊÖ)

[ÇóÖú] matlab ¶àÔªº¯ÊýÄâºÏ ÒÑÓÐ1È˲ÎÓë

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y=A/(3*137.8)+A/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5
x=[298,473,673,873,1073];
y=[1.51941,1.47,1.38,1.32,1.28];
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qj2006: ½ð±Ò+20, ¡ï¡ï¡ï¡ï¡ï×î¼Ñ´ð°¸ 2014-09-05 10:36:21
Ò»¡¢MATLAB´úÂëºÍ½á¹ûÈçÏ£¬Í¼Ðνá¹û¼û¸½Í¼1¡£
CODE:
function feixianxingnihe_3
clear all;clc
format long


data=[298,1.51941000000000;473,1.47000000000000;673,1.38000000000000;873,1.32000000000000;1073,1.28000000000000];
xspan=data(:,1);    %xµÄÊý¾Ý£¬ÔÚ´ËÊäÈë
Texp=data(:,2);    %TµÄÊý¾Ý£¬ÔÚ´ËÊäÈë

k0=[10 10];
lb=-[1 1]*1e9;
ub=[1 1]*1e9;


%-------------------------------------------------------------------------

% ʹÓú¯Êýlsqnonlin()½øÐвÎÊý¹À¼Æ

OPTIONS=optimset('MaxFunEvals',1000);
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc,k0,lb,ub,OPTIONS,xspan,Texp);


fprintf('\n\nÄâºÏ½á¹û:\n')
fprintf('\n\t²ÎÊý A = %.16f',k(1))
fprintf('\n\t²ÎÊý a = %.16f',k(2))

y=KineticsEqs(xspan,k);
R2=1-sum((Texp-y).^2)./sum((Texp-mean(y)).^2);
fprintf('\n\tÏà¹ØÏµÊý֮ƽ·½R^2 = %.16f',R2);
figure(1)
mm=max(xspan)-min(xspan);
xspan1=min(xspan)-0.05*mm:0.01:max(xspan)+0.05*mm;
plot(xspan1,KineticsEqs(xspan1,k),'b',xspan,Texp,'or'),legend('¼ÆËãÖµ','ʵÑéÖµ','Location','Best')


%-------------------------------------------------------------------------

function f = ObjFunc(k,xspan,Texp)
f=KineticsEqs(xspan,k)-Texp;

%------------------------------------------------------------------------
function xt = KineticsEqs(x,k)
global b
A=k(1);a=k(2);
xt=A/(3*137.8)+A./x.^0.5.*2/a^0.5.*atan((-0.5+0.5*(1+a*137.8./x.^2).^0.5).^0.5)-2*2^0.5/3*A*137.8^0.5./x.^1.5./(1+(1+a*137.8./x.^2).^0.5).^1.5;

CODE:
ÄâºÏ½á¹û:

        ²ÎÊý A = 502.1696785220468100
        ²ÎÊý a = 23729.5421378699030000
        Ïà¹ØÏµÊý֮ƽ·½R^2 = 0.9274532902868037>>

¶þ¡¢Èí¼þ1stOpt¼ÆËã´úÂëºÍ½á¹û
CODE:
¾ù·½²î(RMSE): 0.0241425766168092
²Ð²îƽ·½ºÍ(SSE): 0.0029143200284925
Ïà¹ØÏµÊý(R): 0.963175718167507
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.927707464067493
¾ö¶¨ÏµÊý(DC): 0.927453222207639
¿¨·½ÏµÊý(Chi-Square): 0.00102747119728203
Fͳ¼Æ(F-Statistic): 38.4980600874317

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
a                  502.170022602279
a1                 23730.0107275906

====== ½á¹ûÊä³ö =====

No        ʵ²âÖµy        ¼ÆËãÖµy
1        1.51941        1.5410049
2        1.47        1.4301342
3        1.38        1.3659321
4        1.32        1.3285206
5        1.28        1.3042527

matlab ¶àÔªº¯ÊýÄâºÏ
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MATLAB¡¢MSСÎÊÌâ¡¢ÆÕͨÎÊÌâÇë·¢ÌûÇóÖú£¡Ê±¼ä¾«Á¦ÓÐÏÞ£¬Ë¡²»½ÓÊÜÎÞ³¥Ë½ÐÅÇóÖú¡£
2Â¥2014-07-20 19:57:04
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

qj2006

½ð³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
2Â¥: Originally posted by ÔÂÖ»À¶ at 2014-07-20 19:57:04
Ò»¡¢MATLAB´úÂëºÍ½á¹ûÈçÏ£¬Í¼Ðνá¹û¼û¸½Í¼1¡£

function feixianxingnihe_3
clear all;clc
format long


data=;
xspan=data(:,1);    %xµÄÊý¾Ý£¬ÔÚ´ËÊäÈë
Texp=data(:,2);    %TµÄÊý¾Ý£¬ÔÚ´ËÊäÈë

k0= ...

ллÄ㣬ÎÒÕ⻹ÓÐÒ»×éÊý¾Ý£¬Âé·³ÄãÔÙ¸øÎÒÄâºÏÒ»´Î¡£
²ÉÓùØÏµÊ½£º
y=A/(3*137.8)+A/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5
x=[298,473,673,873,1073];
y=[1.74322,1.6,1.47,1.4,1.37];
3Â¥2014-07-20 20:04:45
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ÔÂÖ»À¶

Ö÷¹ÜÇø³¤ (Ö°Òµ×÷¼Ò)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

ÒýÓûØÌû:
3Â¥: Originally posted by qj2006 at 2014-07-20 20:04:45
ллÄ㣬ÎÒÕ⻹ÓÐÒ»×éÊý¾Ý£¬Âé·³ÄãÔÙ¸øÎÒÄâºÏÒ»´Î¡£
²ÉÓùØÏµÊ½£º
y=A/(3*137.8)+A/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5
x=;
y ...

¾ù·½²î(RMSE): 0.0166330356441843
²Ð²îƽ·½ºÍ(SSE): 0.00138328937370353
Ïà¹ØÏµÊý(R): 0.992803768743302
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.985659323230904
¾ö¶¨ÏµÊý(DC): 0.985526033247728
¿¨·½ÏµÊý(Chi-Square): 0.000442346340380584
Fͳ¼Æ(F-Statistic): 206.195148060588

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
A                  525.805717177879
a1                 7213.56939658239

====== ½á¹ûÊä³ö =====

No        ʵ²âÖµy        ¼ÆËãÖµy
1        1.74322        1.7557642
2        1.6        1.5687255
3        1.47        1.4677259
4        1.4        1.4127136
5        1.37        1.3790017
MATLAB¡¢MSСÎÊÌâ¡¢ÆÕͨÎÊÌâÇë·¢ÌûÇóÖú£¡Ê±¼ä¾«Á¦ÓÐÏÞ£¬Ë¡²»½ÓÊÜÎÞ³¥Ë½ÐÅÇóÖú¡£
4Â¥2014-07-20 20:07:47
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

qj2006

½ð³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
4Â¥: Originally posted by ÔÂÖ»À¶ at 2014-07-20 20:07:47
¾ù·½²î(RMSE): 0.0166330356441843
²Ð²îƽ·½ºÍ(SSE): 0.00138328937370353
Ïà¹ØÏµÊý(R): 0.992803768743302
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.985659323230904
¾ö¶¨ÏµÊý(DC): 0.985526033247728
¿¨·½ÏµÊý(Chi-Square): ...

·Ç³£¸Ðл
5Â¥2014-07-20 20:11:57
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

qj2006

½ð³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
4Â¥: Originally posted by ÔÂÖ»À¶ at 2014-07-20 20:07:47
¾ù·½²î(RMSE): 0.0166330356441843
²Ð²îƽ·½ºÍ(SSE): 0.00138328937370353
Ïà¹ØÏµÊý(R): 0.992803768743302
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.985659323230904
¾ö¶¨ÏµÊý(DC): 0.985526033247728
¿¨·½ÏµÊý(Chi-Square): ...

ÏÖÓÐÒÔÏÂ4×éÊý¾ÝÒª·Ö±ð½øÐÐÄâºÏ,²ÉÓùØÏµÊ½£º
y=A/(3*137.8)+A/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5
x=[298,473,673,873,1073];
1y=[1.74024,1.63,1.49,1.4,1.36];
2y=[1.73395,1.58,1.45,1.37,1.34];
3y=[1.55275,1.51,1.41,1.34,1.3];
4y=[1.55959,1.52,1.42,1.35,1.33];
ÄâºÏÖ®ºó°Ñ´úÂ룬²ÎÊý£¬Í¼·¢¹ýÀ´Ð»Ð»£¡Íò·Ö¸ÐлËÍÄã½ð±Ò20¸ö£¡
6Â¥2014-08-30 21:53:54
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ÔÂÖ»À¶

Ö÷¹ÜÇø³¤ (Ö°Òµ×÷¼Ò)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

ÒýÓûØÌû:
6Â¥: Originally posted by qj2006 at 2014-08-30 21:53:54
ÏÖÓÐÒÔÏÂ4×éÊý¾ÝÒª·Ö±ð½øÐÐÄâºÏ,²ÉÓùØÏµÊ½£º
y=A/(3*137.8)+A/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5
x=;
1y=;
2y=;
3y=;
4y= ...

µÚÒ»×飺
Variable x,y;
Function y=A1/(3*137.8)+A1/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A1*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5;
Data;
298        1.74024000000000
473        1.63000000000000
673        1.49000000000000
873        1.40000000000000
1073        1.36000000000000


¾ù·½²î(RMSE): 0.0307537469550395
²Ð²îƽ·½ºÍ(SSE): 0.00472896475887301
Ïà¹ØÏµÊý(R): 0.976679183783147
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.953902228035314
¾ö¶¨ÏµÊý(DC): 0.953374176421571
¿¨·½ÏµÊý(Chi-Square): 0.00151939891296933
Fͳ¼Æ(F-Statistic): 62.079067211712

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
a1                 528.632286321485
a                  7309.23339319526

====== ½á¹ûÊä³ö =====

No        ʵ²âÖµy        ¼ÆËãÖµy
1        1.74024        1.7635719
2        1.63        1.5764231
3        1.49        1.4752668
4        1.4        1.4201226
5        1.36        1.3863080


µÚ¶þ×飺
Variable x,y;
Function y=A1/(3*137.8)+A1/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A1*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5;
Data;
298        1.73395000000000
473        1.58000000000000
673        1.45000000000000
873        1.37000000000000
1073        1.34000000000000

¾ù·½²î(RMSE): 0.0180817726996743
²Ð²îƽ·½ºÍ(SSE): 0.00163475251981344
Ïà¹ØÏµÊý(R): 0.992357331948071
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.984773074271095
¾ö¶¨ÏµÊý(DC): 0.984577352758231
¿¨·½ÏµÊý(Chi-Square): 0.000536567599397937
Fͳ¼Æ(F-Statistic): 194.019415042202

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
a1                 514.710671370125
a                  5704.97616409959

====== ½á¹ûÊä³ö =====

No        ʵ²âÖµy        ¼ÆËãÖµy
1        1.73395        1.7468852
2        1.58        1.5480091
3        1.45        1.4425041
4        1.37        1.3859055
5        1.34        1.3516123

µÚÈý×飺

Variable x,y;
Function y=A1/(3*137.8)+A1/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A1*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5;
Data;
298        1.55275000000000
473        1.51000000000000
673        1.41000000000000
873        1.34000000000000
1073        1.30000000000000


¾ù·½²î(RMSE): 0.0295054872943402
²Ð²îƽ·½ºÍ(SSE): 0.00435286890238237
Ïà¹ØÏµÊý(R): 0.952330923708382
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.906934188251261
¾ö¶¨ÏµÊý(DC): 0.906570847157658
¿¨·½ÏµÊý(Chi-Square): 0.00149940028805953
Fͳ¼Æ(F-Statistic): 29.2352531356999

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
a1                 510.648956991685
a                  21291.2744324343

====== ½á¹ûÊä³ö =====

No        ʵ²âÖµy        ¼ÆËãÖµy
1        1.55275        1.5788868
2        1.51        1.4607601
3        1.41        1.3926929
4        1.34        1.3532335
5        1.3        1.3277581


µÚËÄ×飺
Variable x,y;
Function y=A1/(3*137.8)+A1/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A1*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5;
Data;
298        1.55959000000000
473        1.52000000000000
673        1.42000000000000
873        1.35000000000000
1073        1.33000000000000

¾ù·½²î(RMSE): 0.0269603623925428
²Ð²îƽ·½ºÍ(SSE): 0.00363430570168618
Ïà¹ØÏµÊý(R): 0.955014904538155
Ïà¹ØÏµÊý֮ƽ·½(R^2): 0.912053467890022
¾ö¶¨ÏµÊý(DC): 0.911828190854424
¿¨·½ÏµÊý(Chi-Square): 0.0012313365926436
Fͳ¼Æ(F-Statistic): 31.1116349675785

²ÎÊý        ×î¼Ñ¹ÀËã
----------        -------------
a1                 518.480586764386
a                  25383.1634997523

====== ½á¹ûÊä³ö =====

No        ʵ²âÖµy        ¼ÆËãÖµy
1        1.55959        1.5836851
2        1.52        1.4725106
3        1.42        1.4079438
4        1.35        1.3702032
5        1.33        1.3456515
matlab ¶àÔªº¯ÊýÄâºÏ-1
¸½Í¼1.jpg


matlab ¶àÔªº¯ÊýÄâºÏ-2
¸½Í¼2.jpg


matlab ¶àÔªº¯ÊýÄâºÏ-3
¸½Í¼3.jpg


matlab ¶àÔªº¯ÊýÄâºÏ-4
¸½Í¼4.jpg

» ±¾ÌûÒÑ»ñµÃµÄºì»¨£¨×îÐÂ10¶ä£©

MATLAB¡¢MSСÎÊÌâ¡¢ÆÕͨÎÊÌâÇë·¢ÌûÇóÖú£¡Ê±¼ä¾«Á¦ÓÐÏÞ£¬Ë¡²»½ÓÊÜÎÞ³¥Ë½ÐÅÇóÖú¡£
7Â¥2014-08-31 09:36:39
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

qj2006

½ð³æ (ÖøÃûдÊÖ)

Ëͺ컨һ¶ä
ÒýÓûØÌû:
7Â¥: Originally posted by ÔÂÖ»À¶ at 2014-08-31 09:36:39
µÚÒ»×飺
Variable x,y;
Function y=A1/(3*137.8)+A1/x^0.5*2/a^0.5*atan((-0.5+0.5*(1+a*137.8/x^2)^0.5)^0.5)-2*2^0.5/3*A1*137.8^0.5/x^1.5/(1+(1+a*137.8/x^2)^0.5)^1.5;
Data;
298        1.74024000000000
473 ...

Íò·Ö¸Ðл!
8Â¥2014-08-31 09:56:11
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

ɽӥHPU

гæ (³õÈëÎÄ̳)

Ëͺ컨һ¶ä
ÒýÓûØÌû:
2Â¥: Originally posted by ÔÂÖ»À¶ at 2014-07-20 19:57:04
Ò»¡¢MATLAB´úÂëºÍ½á¹ûÈçÏ£¬Í¼Ðνá¹û¼û¸½Í¼1¡£

function feixianxingnihe_3
clear all;clc
format long


data=;
xspan=data(:,1);    %xµÄÊý¾Ý£¬ÔÚ´ËÊäÈë
Texp=data(:,2);    %TµÄÊý¾Ý£¬ÔÚ´ËÊäÈë

k0= ...

Çó½ÌÄú¸öÎÊÌ⣬¸ù¾ÝÒ»×éÊý¾Ý£¬ÏÂÃæÕâ¸ö¹ØÏµÊ½¿ÉÒÔÄâºÏ³öϵÊýRºÍkÂ𣿿ÉÒÔ¸øÓè½ð±Ò£¬Ð»Ð»¡£
y=5.2/(5.2+u)*exp(57.2-11*u)*erf((45*R-u*x)/(2*(2.1*R*x)^0.5))+ 5.2/(5.2+u)*exp(57.2-11*u)*erf((45*R+u*x)/(2*(2.1*R*x)^0.5))+
6.4/(R*k)*exp(111.4-k*x)*erf((45*R+5.2*x)/(4.2*R*x)
ÆäÖÐ u=(27.04+8.4*R*k)^0.5
erf(x)ÊÇMATLABÀïµÄÄÚÖÃÓàÎó²îº¯Êý£¬
[x y]=[1        0
2        2.81
3        4.22
4        2.81
5        3.52
5.67        4.92
6.17        2.81
6.67        4.22
7.17        4.92
7.67        5.62
8.17        4.92
8.67        6.33
9.17        5.62
9.67        5.62
10.17        7.03
10.67        6.33
11.17        7.03
11.67        7.73
12.17        4.92
14.17        9.84
15.17        9.84
16.17        14.05
17.17        15.46
18.17        16.86
19.17        16.16
20.17        17.56
21.17        17.56
22.17        16.16
23.17        16.86
24.17        16.16
25.17        16.86
26.17        15.46
27.17        16.86
28.17        18.27
29.17        18.27
30.17        16.16
31.17        12.65
32.17        14.05
33.17        14.75
34.17        14.75
35.17        14.75
36.17        15.46
37.17        13.35
38.17        14.05
];
9Â¥2014-11-07 18:34:46
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qj2006

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9¥: Originally posted by ɽӥHPU at 2014-11-07 18:34:46
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10Â¥2014-11-07 19:20:30
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