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
" l1 J" R( R: s) V1 _% 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);
% dLadt = k(7)*C(Hmf);
, G, V! ]) m" I( S8 ?%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
format long
" i5 x7 S+ P/ v$ G%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
" ]3 g, y4 D. Q. V" x5 ^- Z  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
: x6 O4 A* x+ e9 W- @          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
  I& W: J4 Z# Q) c, Y+ L          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
! e0 b% W7 x% X' l2 A  Y. w  `          120    0.0656    0.07397    0.07885    0.00573    0.02143
% a$ O' P. j4 s& x1 C' ?          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
) ?& I( w. k9 w3 j          360    0.01855    0.04125    0.09363    0.0239    0.06495];
4 |3 Q; Y# _# m( \4 P: ek0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
! O+ F8 g0 f2 A6 P* ?4 Zlb = [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
x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
% 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 G. J9 p7 p" J0 Z% y, q' W& |fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
* {) }/ h: [! u& }fprintf('\tk6 = %.11f\n',k(6))
4 x$ i1 e4 K$ x  yfprintf('\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;
3 e/ N  U" l' g& O! K8 S/ x9 D! O% warning off
, X1 a# d8 Q0 N" Y( Y; w* N) i% 使用函数lsqnonlin()进行参数估计
8 H5 U% C/ }6 S1 v- B[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
/ B, N2 X' @9 q9 f    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))
  r. [2 U. u4 a. C* C6 g# F7 ]fprintf('\tk2 = %.11f\n',k(2))
( h9 S5 x, x( R" F) Z( A! Qfprintf('\tk3 = %.11f\n',k(3))
4 P) d3 |  M- @8 Afprintf('\tk4 = %.11f\n',k(4))
# t" w* o8 U  e0 U7 Sfprintf('\tk5 = %.11f\n',k(5))
8 Z  z+ {  _) p& A7 qfprintf('\tk6 = %.11f\n',k(6))
. h$ d2 q, U4 ^( t- Ffprintf('\tk7 = %.11f\n',k(7))
" [, G. [) M& S5 Bfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
: i& p) t1 x1 o; Qfprintf('\tk10 = %.11f\n',k(10))
1 L* G8 h/ S+ e% I) Y# J9 Xfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
5 I5 ]& t8 X0 l& `( j, `k_ls = k;
. ~- a, ^$ R& f3 @+ d* Loutput
9 F: M4 t9 L2 V8 \3 m5 H8 qwarning 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
- O! L+ V7 S9 {6 j. `0 g9 {k0 = k_fm;
# N( {; d7 m- H$ v[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
6 L- B' ]  ~+ V* M: i4 c* A$ C( y    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
! [$ H3 T6 Q5 u1 l7 y1 lci = nlparci(k,residual,jacobian);
  T6 H7 z+ ?# |7 k" q( Gfprintf('\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))
4 c( j4 I2 c0 L6 w7 y% M! f* tfprintf('\tk3 = %.11f\n',k(3))
0 ]+ ^; v; w% S. p+ Dfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
4 [& {3 P& @+ S3 N8 A" t5 F1 X/ a3 xfprintf('\tk6 = %.11f\n',k(6))
/ S) E3 O" A9 X0 c+ L1 Wfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
  E; T( a; V4 X& @! X4 m9 Q& _) cfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
! D1 D% [; L0 g5 i' Xfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
5 s  t* t1 p. R  P: k# I  nk_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
1 h& R. I* n9 w1 b2 b5 a8 ?+ e3 b- ?[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
; Y6 z- l* L+ D3 f: [' X" X' ~figure;
6 q, `) X' A  n! yplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
4 A5 C. c4 _9 f1 L* I# ~/ lfigure;plot(t,x(:,2:5));
* B  x- ^" d- j" o+ ]' J" x4 |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')

/ j9 f1 o: n9 p! [# N+ Q, T/ P0 ^9 N+ X
) w" y/ a+ O, g9 X3 m
' y" O# K& f2 Cfunction f = ObjFunc7LNL(k,x0,yexp)
  C1 B9 h5 N0 N: d( `tspan = [0 15 30 45 60 90 120 180 240 300 360];
$ |6 ~4 e$ a4 e6 N# k[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
: e/ Q# V; W- O. q; i- G, l1 Cy(:,2) = x(:,1);
* Q$ `& j% F1 C, u" b4 Gy(:,3:6) = x(:,2:5);
; i, R6 C! \8 bf1 = y(:,2) - yexp(:,2);
' a$ J$ @% [4 H1 m/ h5 l2 }6 xf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
/ T5 U8 a3 u" ?. d. i7 m# Uf4 = y(:,5) - yexp(:,5);
! B/ q4 L3 N9 u! Ff5 = y(:,6) - yexp(:,6);
. S$ a; b* U& bf = [f1; f2; f3; f4; f5];

1 W/ M, H$ ~2 }* x

( a/ K' b4 y  ofunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
: ]) P9 n  m; E) d[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
& U0 }# V9 b7 P& e9 `  f: v4 I5 xy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f =  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) ;
+ s+ r% E* V; t) \4 W7 d0 M. y9 |
/ w6 ?# n; l. G6 g* c' t6 N: B

* b8 @6 ^' R& @+ e
function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
3 t& x! O( f  Y. c" v4 S; C: [dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
8 w9 u" E2 r1 ?6 i$ p- qdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
- T7 c/ G/ a) `- odHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
$ k$ p7 ]0 \) t4 Z: Udxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
) }1 a$ i# E4 z4 d* R
5 ]; ^8 D$ f- L9 e
6 o, }5 I; W0 ?' N5 ?