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
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
; ]  j: i: s, e+ z4 a6 X1 s+ z- T% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
, ~8 b  F, H* A) L          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
! b! n, ^2 m) Y9 t1 X8 f          120    0.0656    0.07397    0.07885    0.00573    0.02143
8 }' B, [# h" `: ~          180    0.04488    0.0682    0.07135    0.0091    0.03623
/ b; t0 X$ o( \  Y          240    0.03653    0.06488    0.08945    0.01828    0.05452
( C# R) a% ^! b" d          300    0.02738    0.05448    0.09098    0.0227    0.0597
) r5 P8 |5 a* D" q9 S3 S          360    0.01855    0.04125    0.09363    0.0239    0.06495];
k0 = [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
ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
5 {9 K, O1 k) y* G2 v! e- }x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
$ l: q& S: [" T6 [2 _8 ]% warning off
! f5 f6 o3 r1 _' P! |% {( T% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
+ Y2 |6 C- @. Wfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
! t2 h( q1 `2 v9 B! G/ X: G& O, Ufprintf('\tk1 = %.11f\n',k(1))
0 K3 s( o" g& B% k' [3 \5 _fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
0 ]5 a; ^: u! p6 G+ L# n7 l/ @fprintf('\tk4 = %.11f\n',k(4))
6 W1 w% }; H, j8 h2 h* ~fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
) ^( F* |( ?( O! l3 ofprintf('\tk7 = %.11f\n',k(7))
) }3 w% _7 u# r. g- R. Q% i5 Qfprintf('\tk8 = %.11f\n',k(8))
7 P/ ^4 H9 _& w9 |/ \. tfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
: ?2 f* ?* J; l7 Y  M" J& Dk_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
' T$ _8 [! P& M9 X& F; y. m    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
2 }1 a: n2 j/ o+ Y' g0 |# Dfprintf('\tk2 = %.11f\n',k(2))
, x9 e1 ?* i6 [( }3 rfprintf('\tk3 = %.11f\n',k(3))
: K5 s' [' b9 e8 F8 C0 y  R- ?fprintf('\tk4 = %.11f\n',k(4))
+ P' j( J+ J9 W; Wfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
. b/ N2 Q1 [+ n: W* Z4 yfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
' _$ N4 Q. f" j4 P: k7 Z) Yfprintf('\tk10 = %.11f\n',k(10))
& i& A$ I1 m, o/ C& xfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
$ l; }2 Y2 i! Z; q* Y% vwarning off
% 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
$ O9 G- c/ S) Dk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
$ M  M' s- U& w: i# G; E" Vci = 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')
7 W  z/ P6 E: }5 W3 ~0 ffprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
  M% i. t0 S9 M5 v- Tfprintf('\tk3 = %.11f\n',k(3))
; t, ?3 ~5 m5 L/ M: I1 a8 [fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
6 c9 N( g$ p" c9 `2 l/ Zfprintf('\tk6 = %.11f\n',k(6))
  `8 D) v. k8 |' R( X' ~) Wfprintf('\tk7 = %.11f\n',k(7))
' M( R( G/ Q( M( W2 A5 _5 O3 i0 Efprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
9 Q% D1 [1 `* {fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
$ }. W9 O3 q/ o9 ok_fmls = k;
output
! T. p; A5 l; z+ [" Ptspan = [0 15 30 45 60 90 120 180 240 300 360];
0 d9 A- S  ~0 o& Y3 n# E[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
- B$ P0 h1 R) Ffigure;
5 P  B* G2 C+ R2 j. ^; T+ ^plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
; W' Y. \8 _  h. G' p! ffigure;plot(t,x(:,2:5));
2 P% k5 o! @5 o, `8 ^7 U9 S; Bp=x(:,1:5)
% }# ?+ s2 A9 L2 ]: M! D" r2 u6 Uhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
( c9 u# P/ v) |$ w5 By(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
0 }9 f; n# q- N, U9 {0 pf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
1 q( y# l* n: h0 A4 _f4 = y(:,5) - yexp(:,5);
  M1 @3 [3 l7 q# b1 \f5 = y(:,6) - yexp(:,6);
' l' [: C/ [: O9 W0 e5 |f = [f1; f2; f3; f4; f5];



1 R- O3 o# Y1 y; C. X* c* Yfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
; N# ?" W4 a' g5 ?. C[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
) x6 J2 D) b7 n8 ?) U" o& L6 q    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;


3 q+ N% {( e; \3 l) `

! b1 e3 V9 Y8 _. U9 y" kfunction dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
/ L6 l7 z) r( cdFrdt = 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);
dLadt = k(7)*x(5);
* U0 g7 l- V; t& p1 j: kdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
) d. Q8 j6 @9 X; fdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

2 I3 O$ L1 v+ X# K