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
& v" k5 [3 `$ s; t4 C%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
/ P% M: s1 w  {% 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);
8 w: M0 {/ k2 e" z; g% 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
0 W3 d, f3 ^4 @( j" k) G5 l; A  Kinetics=[0    0.25    0           0    0       0
          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
+ b7 R. X, E/ |; }+ X# x          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
: s0 f) ^. O. i  y          120    0.0656    0.07397    0.07885    0.00573    0.02143
" I  }5 V/ X+ B& |" d( U          180    0.04488    0.0682    0.07135    0.0091    0.03623
& I- C9 ?6 @$ c          240    0.03653    0.06488    0.08945    0.01828    0.05452
7 \0 i7 D2 J! f% B! c          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
" L6 ]* w8 ^; f' Q- c0 `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
0 w) y% y3 u7 n( G6 {7 x* Y3 `ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
" F, S; v6 W+ i8 bx0 = [0.25  0  0  0  0];
4 z4 ^. q! K2 ^- d% [" |yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
( E5 K$ F& R  F0 B4 ]% warning off
% 使用函数 ()进行参数估计
( A% c, [$ [5 r2 h# P( p[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))
4 C5 K- d% U( L* W# |/ Xfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
, I8 G4 O5 P; h+ _2 y0 j$ Sfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
. ?9 }2 r/ p! Z9 k  `6 S& Q8 Vfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
8 u: c& c  f3 Z9 o) ^4 }# [fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
0 w6 F' H, ~6 R( ~$ T0 l* O% 使用函数lsqnonlin()进行参数估计
- w( ?$ _9 R3 P( T) G( w; f[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    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))
+ i8 a) R  v( Zfprintf('\tk2 = %.11f\n',k(2))
# S, n+ o% k& f' }9 ]+ C0 ~* _fprintf('\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))
2 h$ X8 f/ o9 W5 ^0 N7 ]1 o3 qfprintf('\tk8 = %.11f\n',k(8))
( _0 q; p& ?4 o$ \fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
1 Z' R$ w+ g9 m* }1 efprintf('  The sum of the squares is: %.1e\n\n',resnorm)
' {$ Q5 y7 B5 n4 E$ @  Uk_ls = k;
output
: q- y  w5 o0 s; n0 l. o1 x5 Y/ }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
k0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
+ K8 E5 ]( i9 q" W* r    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
& m  X4 q' W  E  Lci = nlparci(k,residual,jacobian);
( X6 S& b% M% r9 p* h  a1 Dfprintf('\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')
5 j) g$ y! m5 R6 g/ {6 j3 rfprintf('\tk1 = %.11f\n',k(1))
: o3 z. a6 `% pfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
# }0 N1 I7 O* M' r" @! r6 p! Kfprintf('\tk5 = %.11f\n',k(5))
1 M8 H; U2 X1 }' s- ^fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
& C; k1 R& d: U) L6 d2 Kfprintf('\tk8 = %.11f\n',k(8))
8 @: G' P. B3 N! r* z  Rfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
% L  E, g6 w9 W" dfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
. K" ?' k9 W9 R6 u: a$ t/ w/ houtput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
# k5 S# }1 F3 y3 Tfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
, O' V3 W0 K8 ?$ R4 z" ]" Dfigure;plot(t,x(:,2:5));
) R# M7 ?6 k0 A0 v+ H0 N: qp=x(:,1:5)
* B) q! v( j$ N0 ^/ e& F6 Zhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
) o5 v: G' ?( ]4 x6 |! P+ Y% z
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1 O" K, P- b6 p0 p/ lfunction f = ObjFunc7LNL(k,x0,yexp)
8 \5 r; J6 S% P. jtspan = [0 15 30 45 60 90 120 180 240 300 360];
& X0 W  S' `- X: P' l[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
9 k. D/ U$ h- t# b0 Jy(:,2) = x(:,1);
$ ?7 w  K! D0 r4 y" d& H2 ey(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
, K% c; K7 t* M* _, w3 B3 Uf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
  s1 g$ A, G# b" f; i; ?/ |f4 = y(:,5) - yexp(:,5);
4 k& f. T8 V/ r) af5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
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function f = ObjFunc7Fmincon(k,x0,yexp)
* Y7 l0 Z0 ]& T% C# a$ `9 L: T, ftspan = [0 15 30 45 60 90 120 180 240 300 360];
[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)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
* i8 g3 B7 ~* z1 ^  V/ J1 N


: L$ T: F: {$ ]3 s! o) }; v, n
function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
9 K& ?+ @! O8 \6 pdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
* t0 S% c& y5 z# o* s7 j, ddFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
6 s2 d% c& U: D: MdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
+ u3 B9 T5 a* ~# M3 z/ {