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
( P# ]8 @/ D/ [  E; X& `0 W% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
( q( P4 [. W3 J  Y% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
4 I: [6 m  ?9 g  B1 c3 O% dLadt = k(7)*C(Hmf);
5 N7 g7 h* W; |: v" z8 o%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
% R+ u4 L$ N/ P4 R6 {! qclear all
clc
3 B3 L6 p; `) dformat long
9 H% U0 f# b& c! {- n%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
6 K! W1 }/ y# e9 O8 K" k1 T          15    0.2319    0.01257    0.0048    0    2.50E-04
7 @6 W6 S4 o$ t+ I0 B; @; r          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
  S& f, g$ l" h) G# j4 g  {          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
0 o8 f8 C# v: [+ J. x3 U          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
8 R) C( y, o# R          360    0.01855    0.04125    0.09363    0.0239    0.06495];
% F3 b, z3 ^! }: z! S, K& I4 \+ Zk0 = [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
x0 = [0.25  0  0  0  0];
, j& r" ]& p& r) q) Ryexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
% 使用函数 ()进行参数估计
3 K2 X. j6 x: e9 v7 j[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
1 a( n9 a( u! G  `+ u. Q1 w5 pfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
$ o$ x; b; c9 [fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
' t* A8 k& z/ H3 l% Ufprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
2 b: [8 X. \8 z& i! {fprintf('\tk5 = %.11f\n',k(5))
! A! w7 N4 x6 k' o% i7 Vfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
$ k  z( L4 p" Q( ^" qfprintf('\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)
1 Y; o8 j: A& jk_fm= k;
0 U8 [  m8 `* u- }1 |# C% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
3 m! v* A  `+ n/ b( W2 Z; ~8 V: K8 X    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
" T! \; ]2 n  Q1 ~4 T3 yci = nlparci(k,residual,jacobian);
7 b( `2 Q# i- M& rfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
; B+ {/ x5 U3 Z- a% m" Wfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
" J* k) q% X8 Y1 U) B2 I1 G* Yfprintf('\tk5 = %.11f\n',k(5))
. w& {6 d; q1 E- ]! o" Z5 Hfprintf('\tk6 = %.11f\n',k(6))
! y9 I9 k* Z6 `fprintf('\tk7 = %.11f\n',k(7))
* d  e! p8 z# y7 g$ [9 y" X% Ifprintf('\tk8 = %.11f\n',k(8))
& b: K# U, g' @6 S$ ^5 t, t- Xfprintf('\tk9 = %.11f\n',k(9))
+ Q, _0 R1 [* _% J% h4 D$ Vfprintf('\tk10 = %.11f\n',k(10))
$ G: S& I  R4 B3 y4 @fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
: F/ L1 _8 }7 Goutput
warning 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
% f9 ?  {$ P% z, {- n& M% xk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
: Q7 L) j/ W5 \3 a4 l, H7 Cci = 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))
fprintf('\tk4 = %.11f\n',k(4))
. I/ F( h1 O  I! t( ]1 M& a" W) _fprintf('\tk5 = %.11f\n',k(5))
: X2 r( Q8 ]: e$ f0 Ofprintf('\tk6 = %.11f\n',k(6))
; n/ E3 {; i/ B$ h7 |6 nfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
1 t* N5 G  l* l) Ofprintf('\tk10 = %.11f\n',k(10))
9 C& r4 f, I5 `% h. }# |/ dfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
/ l4 C' Y2 n1 ~) v0 F# D6 `$ `tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
8 h' U% o3 b+ t6 u. dfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
* d% B) v8 m' q2 X' a' kfigure;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')

& W# y" M/ h2 e. G: W0 {( R

function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
$ c$ l% [# x7 x; h5 C3 Z$ ~[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
3 i5 H& j) C+ R/ yy(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
1 d! p7 }0 G3 N) B  hf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
# `% P3 A5 `3 d* B" qf = [f1; f2; f3; f4; f5];
) J4 d% V/ t4 ^7 R6 e; \3 X


function f = ObjFunc7Fmincon(k,x0,yexp)
# z  z( l( ^4 k  Itspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
( r6 m3 r$ Z1 x- m; i( C* `y(:,2) = x(:,1);
" D6 }7 v2 k! R. ]9 ?: b- qy(:,3:6) = x(:,2:5);
0 C4 k" I5 T, k' b5 Y0 Qf =  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) ;
2 W1 [7 H& R' {

3 r% u4 ~! ^4 a8 A, u

function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
' O' [( f1 T/ h5 h+ [! P, BdFrdt = 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);
6 ^' t9 h! c' R. e( m/ WdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
4 Q3 f5 K, M. Q5 l5 ndxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
1 _( ~% \4 k8 |. y& l' ^' d