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
, t( |1 |; ~4 ?1 ?) M% v% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
  I/ i# t) ]! G7 W* q& d8 R- `% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
& A4 |/ I: G3 ^+ Y% P1 H3 n' c5 a' o% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
4 r' O% a9 r/ \5 a0 H0 @& R% vclc
! d* `0 M: E. L: x$ }7 Aformat long
* |* I% l0 X4 A$ D: b9 u% \8 m%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
5 b4 }3 [# l1 k- A# R- K" k  v6 c          15    0.2319    0.01257    0.0048    0    2.50E-04
+ ?5 c, q; w: O2 l* a          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
6 U  v0 u4 O/ R% B' I          240    0.03653    0.06488    0.08945    0.01828    0.05452
* o7 n) o- w' T+ `: M6 R8 B9 `" y          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
" ?( [* {2 H" g( Bk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
lb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
# I/ b) O  N8 B: ~7 p* J1 Wub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
1 P; I- F& v- h- `9 I6 R) b8 Cyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
9 [* I3 Q( ]6 Q- j. a$ G5 o% warning off
( `- Y" H9 w, X- F8 d% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
' K# p9 Z% u5 I9 N) l5 b% Efprintf('\n使用函数fmincon()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
  D' h* l" H: J. wfprintf('\tk2 = %.11f\n',k(2))
* A9 g. U8 X5 W# x; Y8 Qfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
- g. T$ X. i; R; n; ^9 k# v4 Nci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
, p' t. I' @3 |; T9 o5 efprintf('\tk1 = %.11f\n',k(1))
; z% v: t9 {9 @: Q2 a- t; |$ c4 mfprintf('\tk2 = %.11f\n',k(2))
% I3 i! p0 d* {" t+ hfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
0 k7 M! N% g, S+ lfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
9 Q+ p$ z/ d- }6 S. o: G' Ufprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
  f: b  S' T! t( ~- u# jwarning off
( X5 G: {# P) r' z8 d8 F% 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
3 g( Q- n# Z3 n) X4 Ek0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
! P; v/ U( Z2 [$ y+ w; _  `2 B    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))
9 ]) P* J+ b( O4 @& ~8 m! w6 Zfprintf('\tk2 = %.11f\n',k(2))
* E2 Z$ U# V! h) Z8 ]6 qfprintf('\tk3 = %.11f\n',k(3))
" k7 N( M/ k/ G7 h) P$ w: sfprintf('\tk4 = %.11f\n',k(4))
+ [# b/ O6 B' L( u2 |# Lfprintf('\tk5 = %.11f\n',k(5))
6 p6 t4 D7 I: ~  G) Y9 pfprintf('\tk6 = %.11f\n',k(6))
+ J! M# t! K' ?fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
0 L4 q0 e1 l" H" X0 kfprintf('\tk10 = %.11f\n',k(10))
5 c6 ?' ^$ y7 F9 e7 E9 \( Y, rfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
. z( u$ r- v  [* Q+ I, @% ~tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
" W: h8 {, T, V/ x. `figure;
! j* A9 d% a2 Jplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
- p, V1 T' i) J  |figure;plot(t,x(:,2:5));
4 g) k/ w. |3 k, B& _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)
5 P. V! j- x5 r" M, ftspan = [0 15 30 45 60 90 120 180 240 300 360];
& Q  `9 W% m( l4 s0 h[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
, G! C3 h8 v& d/ z7 vf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
# M8 i, T- X8 v. {3 Wf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];



function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
5 h- v  F! N) t6 `5 P[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
) {# f  y  I+ [3 w8 Vy(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
( |$ H4 ~' H4 V4 l/ N+ G+ [# X* V    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
/ l, T" V! J/ D- d, S4 e7 k    + sum((y(:,6)-yexp(:,6)).^2) ;

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6 r' c- X  P  d' {
function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
6 p! A; z! u& y4 O8 odFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
; L* H$ V$ P  k2 W$ s/ r+ Q, SdLadt = k(7)*x(5);
3 g$ f9 ~9 B; I$ RdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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