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
  W9 m! m! E( M6 H" Y4 B& {* f2 y%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
9 R2 b2 Y+ y+ T& T6 j% Y- E% k% k6->k6 k7->k7
' e1 Y, h) C5 K$ R% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
7 l. h) o9 Z- g9 l" h8 _& ^( {% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
8 k5 \9 G- I, v# D: `7 o3 E% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
' `# U) J' i2 Z4 hclc
format long
# D7 @4 r- d  w# F$ o%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
: q3 R8 T* B  |2 _/ O6 d          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
$ B. X% d2 t% W2 v1 C- S, a! K$ b          45    0.15105    0.06975    0.02473    0    0.0033
' s% q6 d" W4 ]0 M          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
  S# ]  e- r9 x7 {* c" Z' b          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
" k. I% |, \; ?" Z. s+ C          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
ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
' j/ S, W4 c, K' I/ @7 Ax0 = [0.25  0  0  0  0];
0 L/ p( L, h$ c2 Z* ^. Myexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
% c1 U9 r4 y8 O, k5 N% 使用函数 ()进行参数估计
5 d8 Z8 I+ F8 ~' b9 l  [[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')
" i9 I  m9 h* S/ v& v, w' a4 afprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
' a; x: `6 g7 Zfprintf('\tk3 = %.11f\n',k(3))
! c4 d3 `, ]8 I2 ]  W2 z$ I$ [8 Tfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
# Y( W: ^# J* [; Ofprintf('\tk8 = %.11f\n',k(8))
3 N7 S; z/ C1 {  E5 B, Hfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
" g6 @* l0 [. wfprintf('  The sum of the squares is: %.1e\n\n',fval)
- R$ ]2 q7 z0 M9 n* sk_fm= k;
% warning off
' C6 F! g! ]0 c8 g1 n% 使用函数lsqnonlin()进行参数估计
[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')
  L7 A+ ?* a9 n; V; vfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
# o7 m3 G7 b4 j. _; zfprintf('\tk3 = %.11f\n',k(3))
" e" o: f5 I# t: n% I" S& U# j. E) yfprintf('\tk4 = %.11f\n',k(4))
( D- `2 S  Q$ }+ K6 c1 Y; Ffprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
7 X7 W; |4 Z% \7 K& Afprintf('\tk8 = %.11f\n',k(8))
4 d  Q3 G7 e" }fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
* Y3 [9 T$ o6 G  p0 ik_ls = k;
" l4 j* `$ j% ~* E6 R$ I% t0 \: j$ houtput
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] = ...
! g* p* f+ `6 ]# O    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
' d5 f- s  ]) i  s3 \  I, qci = 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))
( {0 s$ m' _8 Q' D" D3 ~; Q; Wfprintf('\tk3 = %.11f\n',k(3))
6 I. [) u. i& o6 P* j5 v* ^fprintf('\tk4 = %.11f\n',k(4))
" Q9 e, a% D' @4 U& ?: O, Z, Cfprintf('\tk5 = %.11f\n',k(5))
" W7 K4 ~1 I7 z. Gfprintf('\tk6 = %.11f\n',k(6))
5 w- I# i+ m; Pfprintf('\tk7 = %.11f\n',k(7))
" B- k' F) o, k5 j0 a& Ufprintf('\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',resnorm)
: c  o+ v' {& y; _" u2 Kk_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
# T5 j  K  n; ?( |[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
" g  w) A. g0 g) M2 B3 Qfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
; b( l2 W7 Y& D' ?' W3 Efigure;plot(t,x(:,2:5));
) W: m/ ]6 |  o5 A& }0 ip=x(:,1:5)
$ c2 B# m4 I7 [; _' Shold on
5 |) Y( G5 y6 }8 n  a$ y) j' eplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



function f = ObjFunc7LNL(k,x0,yexp)
! q8 A) D0 ~5 f; w+ d$ gtspan = [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);
f4 = y(:,5) - yexp(:,5);
# x4 r$ T( N. }- s0 kf5 = y(:,6) - yexp(:,6);
* o  w0 d. l. N2 }& [* q- ?$ ], Gf = [f1; f2; f3; f4; f5];


8 C% ]4 X) M8 M- U& O' D5 R
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);   
3 }% O& c9 ]$ n2 {" fy(:,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)   ...
2 T' [* E5 u% ~9 D- ]1 p    + sum((y(:,6)-yexp(:,6)).^2) ;




function dxdt = KineticEqs(t,x,k)
" s6 ]9 E9 r) W7 CdGldt = 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);
1 f8 E+ e6 I9 }* _- D) a/ jdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
4 G( h9 y. M) X9 ^3 gdLadt = k(7)*x(5);
8 D# F3 O( l! X* R$ F2 ?" u% m% e! M5 ydHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
' G! b  O: s/ A4 Y8 x' W
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