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);
7 [) Q7 n5 ~4 _9 c% r% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
# Y0 g+ J6 S+ X& j% dLadt = k(7)*C(Hmf);
! b& }) R' X" U" `%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
3 H( `! @2 \1 Y) X4 I& R2 nclear all
2 e) g0 V( Y8 K1 d; Hclc
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
          30    0.19345    0.027    0.00868    0    7.00E-04
* {; e4 l/ A' p          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
* e1 \; K7 L! v+ g" `* T* ~0 t          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
: P2 K' Z$ v, ^0 z  Y, m$ F          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
6 a8 v2 Y( W' u) i3 ~  J. D8 q          300    0.02738    0.05448    0.09098    0.0227    0.0597
          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
$ |* f+ u/ |; t3 R3 kub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
- O+ `; E* [. C. Hx0 = [0.25  0  0  0  0];
/ Q& @: c3 n& ?0 K; a  {( {yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
% 使用函数 ()进行参数估计
% N7 P8 l! ~! `[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
( ^! p6 W8 H7 e& Zfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
" \+ N8 ]4 x& C2 T- X4 {2 v- U0 wfprintf('\tk1 = %.11f\n',k(1))
: a; h- z0 A5 Lfprintf('\tk2 = %.11f\n',k(2))
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))
0 v. T9 Y& w  @. P- p& u: Bfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
3 d5 X3 h  i- zfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
& F% l9 b7 G+ ]# S4 z  ]$ c- \0 B: f: n    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))
fprintf('\tk2 = %.11f\n',k(2))
0 }1 J* Q8 f1 U9 qfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
5 r% a& `% ~0 J9 X% Ufprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
- a$ r: z8 Z2 O! [( yfprintf('\tk7 = %.11f\n',k(7))
0 P+ z8 P/ V4 ?9 Jfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
' V* v2 A% H! S4 s$ w/ Q& S, B, H- Ufprintf('  The sum of the squares is: %.1e\n\n',resnorm)
; p2 b4 _/ f9 C# o7 J. T! wk_ls = k;
' Q/ r8 A$ o( _) r; @+ Ooutput
warning off
) v( q! q  j/ K9 \- q1 Y( @% 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
) V1 M" S# `2 H1 x1 @& c1 K/ ^k0 = k_fm;
6 A. C0 o, E( M1 ]* ^[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
* D# X! [5 h) y9 efprintf('\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')
0 N5 z0 t; K. U  Tfprintf('\tk1 = %.11f\n',k(1))
7 v8 Y5 o# I# d  X3 yfprintf('\tk2 = %.11f\n',k(2))
2 `  z' Z+ C# F' r  E; \fprintf('\tk3 = %.11f\n',k(3))
$ r8 K. p, s6 m  Yfprintf('\tk4 = %.11f\n',k(4))
9 M' W9 ]4 D( w' J- B, Bfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
4 {; C% B: f, v" y2 u1 [fprintf('\tk8 = %.11f\n',k(8))
2 k) z! V4 D- b; \4 _, \fprintf('\tk9 = %.11f\n',k(9))
: [" D6 t1 T$ Q2 {$ zfprintf('\tk10 = %.11f\n',k(10))
3 H1 K/ J  s( Y4 t1 zfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
# B9 }' X* w) @7 w+ t' @k_fmls = k;
output
1 y( U% \0 f# c* @  Btspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
0 S% o* k" `1 ~/ Q5 w- `# P0 \plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
( H. y8 ]$ w+ A: M8 R5 ap=x(:,1:5)
) S+ L' |% Z, \4 U. c1 f- ^5 phold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
# d3 S; x$ h! A! m3 f" A
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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);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
( u+ Z5 p! w1 e% w$ p0 M; Cf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

; ^; Q- T( _6 h5 t

function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
0 F6 y( r2 {# x8 y& h/ E/ z[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
+ r" _. L  b. r( Ly(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
: x# P; b! |. g0 c( r    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
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/ `: x$ G- G9 V7 Q4 w( D& {4 Ifunction dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
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);
dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
1 L# t: u+ b8 Q" G9 L0 _0 cdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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蒙的一比 大哥