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
# j% z; n9 q* w  y%  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);
( N9 S" i. g2 H! H4 T: Q" e% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
9 n" d$ Q$ J8 L7 V& I) d% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
$ p0 R6 w% \8 T0 f% g9 m- Xclear all
clc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
# I6 Q9 ~+ D( g          15    0.2319    0.01257    0.0048    0    2.50E-04
6 G; e4 ^. |- N4 S: u  \: [) J! l          30    0.19345    0.027    0.00868    0    7.00E-04
          45    0.15105    0.06975    0.02473    0    0.0033
7 v, w; `: q& k1 c, b" ?          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
! J# P- s( O( s8 @! K          180    0.04488    0.0682    0.07135    0.0091    0.03623
; D  p* S& Q+ S$ O, ~# @) p/ Y          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
3 B! p( i& V1 G2 T5 b8 X4 i! H          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
/ a3 X6 g* ?7 m6 J6 oub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
% N3 I5 ?; E% `/ N( iyexp = 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);
8 |1 G7 V7 V" L5 F  ^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))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
% v& J2 \! o% Y7 j+ nfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
3 e7 ~( _. @- i% gfprintf('\tk7 = %.11f\n',k(7))
. X: ?: o/ _8 t, l6 Hfprintf('\tk8 = %.11f\n',k(8))
& e: |, m. Z! O# ofprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
. k+ S, K- e9 _k_fm= k;
' N! {1 _3 o! Q% warning off
& s) j- G3 L' ?: k' H2 F4 n% 使用函数lsqnonlin()进行参数估计
7 K, |9 f0 Y2 N+ o) E0 E[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
7 i. C$ \, a7 U- {3 s. E5 [. gci = 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))
fprintf('\tk2 = %.11f\n',k(2))
1 m& E  o& j4 B0 S; H) p' ^fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
* [8 L7 v7 ^) h, w+ [fprintf('\tk5 = %.11f\n',k(5))
* X+ H; i5 d2 o+ [fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
$ z$ E) \% c  p% F$ b9 a; Q$ }fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
5 k- z7 c+ E- x1 o2 W! B& ~fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
& I8 S. F- K3 T; ik_ls = k;
output
warning off
1 Z& O5 P& I7 U/ V2 R! @% 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] = ...
    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))
' F: N' ]+ Y  ?2 `7 T$ pfprintf('\tk2 = %.11f\n',k(2))
5 d* Q- u) K" T7 [fprintf('\tk3 = %.11f\n',k(3))
6 S9 B* |4 _8 O9 rfprintf('\tk4 = %.11f\n',k(4))
1 G* I( i9 Z  _fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
2 ^2 \8 x) F+ bfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
+ y: d" _1 h3 Jfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
2 @' t! P  }! Ck_fmls = k;
output
; O  q# v0 ^5 r  n7 ^2 P8 etspan = [0 15 30 45 60 90 120 180 240 300 360];
5 ~( @. D: Y+ V: Y[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
7 d( P7 Z8 A7 z* c) S/ efigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
& Y1 X% X4 d+ \7 s( ~  z% Fhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
9 O! a9 Q7 H. P5 K


7 G4 B# ^( R& w) ~4 V, dfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
0 I6 @+ S% Y, T+ U! G' m9 x0 V[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
; z  f" v/ J, by(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
1 L' a! q1 W$ z9 D  Sf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
9 V5 l5 h6 u/ M9 @f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

0 n2 s/ E  l8 c( F* l$ l
: e/ ?6 B* T, l% r
3 a0 U2 V# e' p; x0 {function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
- n* N1 v* j% P6 ^/ v! Q! z) X1 yy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
# y0 b0 K7 [# G0 |( l- k, c! Wf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
+ H8 _* Q4 J, u+ l# K  B! w5 m3 \9 S) ^    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;


# T6 I# s; f% u/ i( j3 Z" p* }( w
# p' B" E# H; C0 y7 _8 _, E% [
function dxdt = KineticEqs(t,x,k)
) J) O: h" B- J# n/ LdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
) u% x& ?1 o( z* |9 |dFrdt = 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);
2 ]% ^5 Y) [# N' Z% ndLadt = k(7)*x(5);
9 E6 `/ J: l1 I& HdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
% b6 V: q: o0 d* A1 I$ v8 G
; f" t* V: e5 U1 a; ^5 C6 i