帮忙做下统计显著性检验和K值的误差以及灵敏度分析

箫剑→残念

function parafit
%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
* Y( e# s4 _. |& D. p4 E1 N% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
+ e, K  [1 G/ Y% A+ M% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
$ j9 j/ Y; [# x  f1 P& y0 Q& a% dLadt = k(7)*C(Hmf);
' F; Q* K2 Y! j% u% V4 d4 q. H* K%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
$ D1 B4 Z3 ^7 g9 @% Eclear all
clc
) d" b0 t" x; w7 Mformat long
) ~: f- \2 f7 A: Q2 w* u; b%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
* O( g5 h* X) ?, A, k, a3 f          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
$ N) b+ f- @5 W! C+ X5 ^          360    0.01855    0.04125    0.09363    0.0239    0.06495];
! z: z' v8 S: m& V% {( uk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
0 ]( \2 ~( q) U8 P' Ilb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
1 U0 Z. k" @3 i) ex0 = [0.25  0  0  0  0];
' Q0 w+ o* y4 a0 E5 dyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
3 L4 h: O: i3 ^  F; ?( H  M% warning off
6 ]3 {' u3 a! x) }, P- c4 [  e% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
fprintf('\n使用函数fmincon()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
1 A# W2 i, q3 S+ N# w9 P, vfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
3 l8 Y' t2 O! \fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
0 R1 \6 a' P$ w! r* ifprintf('  The sum of the squares is: %.1e\n\n',fval)
9 w' u' s0 M  r- hk_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
, G. ^# y8 Y* W. }: j; p    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
3 X, w# l0 i9 |, afprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
' ~' E4 _/ [' ]) ?8 nfprintf('\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))
# n' }2 b6 }# Z8 [# p1 ?fprintf('\tk6 = %.11f\n',k(6))
6 W- ~$ A7 z6 a" H7 Rfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
7 |+ ^- l/ j9 B, }" gfprintf('\tk9 = %.11f\n',k(9))
) x6 c2 }# ]- E8 R, M( q$ j6 ffprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
* y* v% N+ _* G: Xk_ls = k;
output
warning off
* {$ |! c+ y9 W" X: L% 以函数fmincon()估计得到的结果为初值，使用函数lsqnonlin()进行参数估计
. {* G  W9 [0 W, G1 y- nk0 = k_fm;
4 ?+ ]9 t  ?! S4 G5 T# l8 i[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\n以fmincon()的结果为初值，使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
: Y: n1 `- w# U5 a, @) P1 pfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
% v& s+ T* B' l% p% t, o" d+ X- cfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
2 x7 }" a/ V4 B* Ufprintf('\tk9 = %.11f\n',k(9))
3 z# U! k' u/ u+ Tfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
; V- ?& X/ Q* ]6 goutput
7 _; I5 x$ W% Q" P* Ztspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
* l  Q6 e& [, a( j, efigure;
+ z# [' a9 o3 J! A, Nplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
) W# E/ y( W  ?7 \' O- D+ Q' {% Q' Vfigure;plot(t,x(:,2:5));
p=x(:,1:5)
hold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
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function f = ObjFunc7LNL(k,x0,yexp)
+ H. l: d4 J1 ?. t, Vtspan = [0 15 30 45 60 90 120 180 240 300 360];
1 @  O/ Q/ ]' {$ L8 P[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
% R) \1 {2 }! P- y3 U; Q% Pf2 = y(:,3) - yexp(:,3);
: K4 B% k- |) o  \/ Kf3 = y(:,4) - yexp(:,4);
' |* a9 w1 l6 ]7 t% Jf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
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9 N3 P) J+ t! A& k* bfunction f = ObjFunc7Fmincon(k,x0,yexp)
: z2 o1 N; J- G# I) Utspan = [0 15 30 45 60 90 120 180 240 300 360];
( }% b9 ?3 H, y( x, q4 Q" t[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
; c# a1 |1 e3 z! _y(:,3:6) = x(:,2:5);
, M: f8 y7 c, y6 pf =  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) ;
% ~# I7 |: V! ?3 I- F5 v
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function dxdt = KineticEqs(t,x,k)
1 _. j8 I4 \9 q2 j/ bdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
; H2 H8 o  f& BdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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蒙的一比 大哥