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= ...

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\tÏà¹ØϵÊý֮ƽ·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;

ÄâºÏ½á¹û:

        ²ÎÊý A = 502.1696785220468100
        ²ÎÊý a = 23729.5421378699030000
        Ïà¹ØϵÊý֮ƽ·½R^2 = 0.9274532902868037>>

¾ù·½²î(RMSE): 0.0241425766168092
²Ð²îƽ·½ºÍ(SSE): 0.0029143200284925
Ïà¹ØϵÊý(R): 0.963175718167507
Ïà¹ØϵÊý֮ƽ·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

3Â¥: Originally posted by qj2006 at 2014-07-20 20:04:45
ллÄ㣬ÎÒÕ⻹ÓÐÒ»×éÊý¾Ý£¬Âé·³ÄãÔÙ¸øÎÒÄâºÏÒ»´Î¡£
²ÉÓùØϵʽ£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 ...

4Â¥: Originally posted by ÔÂÖ»À¶ at 2014-07-20 20:07:47
¾ù·½²î(RMSE): 0.0166330356441843
²Ð²îƽ·½ºÍ(SSE): 0.00138328937370353
Ïà¹ØϵÊý(R): 0.992803768743302
Ïà¹ØϵÊý֮ƽ·½(R^2): 0.985659323230904
¾ö¶¨ÏµÊý(DC): 0.985526033247728
¿¨·½ÏµÊý(Chi-Square): ...