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
6 y6 Z5 E& N: r( h% O2 |% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
8 g1 q) t, \/ D2 q% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
9 p8 Z0 F) q$ ^5 m* B2 }" c; ?% 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
  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
          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
! g2 B. m# `" _/ }9 F7 S- T/ D          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
9 R3 ]  T) i, q5 R; z' c          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
- q) ]" \7 e/ T9 m$ N  G; D- c5 U3 Hlb = [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
0 p/ r& i! W9 ]( Qx0 = [0.25  0  0  0  0];
: \+ m! e0 o/ f1 b# Hyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
- n* E1 {7 q1 h9 y- k, T: s# z" S8 m% warning off
( e" r! y+ X: [% 使用函数 ()进行参数估计
[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')
7 c1 w4 v4 @* _3 ofprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
1 `6 B7 S/ R" T" ~) jfprintf('\tk3 = %.11f\n',k(3))
6 A+ x  P0 U6 K8 p( J- v% Qfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
2 O+ P  R7 ~5 n. `$ w6 @7 }0 tfprintf('\tk8 = %.11f\n',k(8))
2 z8 V7 i9 D% A, zfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  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] = ...
( t+ E6 j) q5 d$ U    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
$ ]* j0 r$ o6 t# C' D$ Qfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
" f' f8 |2 V) g9 M% g! t* rfprintf('\tk2 = %.11f\n',k(2))
9 H- K0 \$ p% n- H7 d' D8 P* M! v4 ^% wfprintf('\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))
fprintf('\tk8 = %.11f\n',k(8))
0 O) y* P+ J3 }+ W- ffprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
" n( C1 q, Q! g3 x5 u$ O1 Efprintf('  The sum of the squares is: %.1e\n\n',resnorm)
7 ^. Y- |1 e2 [9 P9 vk_ls = k;
output
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] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
  a/ u4 H6 M0 V; [; E. Sci = 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')
5 B. T$ w. b+ J5 G. l  q" Sfprintf('\tk1 = %.11f\n',k(1))
4 R. ~. F- `0 @4 sfprintf('\tk2 = %.11f\n',k(2))
% S- X  v  d4 h2 {7 W  `8 E' Sfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
8 {: Q7 }$ E% u+ S! i# lfprintf('\tk6 = %.11f\n',k(6))
2 j: z( m+ _8 m% \/ y* Yfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
5 ^  |: J# `- f: x: Qfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
5 }2 \/ |8 A3 q7 _8 T  T( x  bk_fmls = k;
+ N# y: l. i& w8 B$ E% Toutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
2 |* ^7 I- U6 @2 V: ?0 {[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
( Z' Z# Z% ]* i' u+ W+ Mfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
; q3 U/ s4 h2 Zfigure;plot(t,x(:,2:5));
+ E6 b8 \8 b4 Q$ h0 Ap=x(:,1:5)
  F7 [; _* i1 F* O$ V9 g* y) [8 Phold on
/ O+ P, p$ Z" Yplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')

2 M- h- q; |* H2 u

function f = ObjFunc7LNL(k,x0,yexp)
, c  z; M& Y6 [9 u1 v: m: otspan = [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);
/ N, ^! }- I& jf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
# O& A8 A4 K" w% {( gf = [f1; f2; f3; f4; f5];

7 S) J# e, e5 ?/ r3 c
5 w2 ?( \7 {2 @( R* A7 s' G
- P8 |$ |$ T( m, xfunction f = ObjFunc7Fmincon(k,x0,yexp)
% t1 X1 [( H1 R* O7 H5 gtspan = [0 15 30 45 60 90 120 180 240 300 360];
4 e4 k1 E' R9 v7 C1 H& l2 M[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
6 |- p0 S( M0 `. N& n' z2 Yf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
# n) C9 d( j9 k$ J    + sum((y(:,6)-yexp(:,6)).^2) ;
4 Q3 ?; k- N8 g! T/ Y! m2 M- n6 U0 P

8 ]$ _$ Z6 j, E  d1 F; r; T. D
* U% K' J" a% O1 u, N  W
function 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);
1 U: _0 C7 r' D0 g) N2 o) odLadt = k(7)*x(5);
& ]4 L# |! T& L' NdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
& Y& t: b5 S+ E: Y8 N% R, e% Ydxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

8 Y$ |1 ~9 A  s6 T" o0 ]

董事长之友

蒙的一比 大哥