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
+ t5 x2 s* O" a6 x, u  ?%  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);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
) _# d: k$ @( _% L# @5 @%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
, t8 l; C5 p$ T2 vclc
: ?; j/ @$ u1 z) k2 Uformat 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
9 L, l8 D0 @) X& K3 A          30    0.19345    0.027    0.00868    0    7.00E-04
0 k3 U) L8 H) k4 d6 h          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
. c7 I1 r( z. G, m, T          120    0.0656    0.07397    0.07885    0.00573    0.02143
# \3 K+ w9 ?$ e, D6 Z* b$ ]) N          180    0.04488    0.0682    0.07135    0.0091    0.03623
' h3 J5 J3 `* j" x          240    0.03653    0.06488    0.08945    0.01828    0.05452
          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
3 z: {- X" ~0 Tub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
6 f/ B' |* Q% m% warning off
% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
+ t5 l% x- @0 h' Y& ?7 Sfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
4 j  i+ J0 R. u2 b( k- @0 G) }fprintf('\tk1 = %.11f\n',k(1))
" ]9 N. \7 R1 f7 ^- y/ o* ^0 Bfprintf('\tk2 = %.11f\n',k(2))
. s0 P% R) t& [! b6 G/ b+ I* Bfprintf('\tk3 = %.11f\n',k(3))
" b8 x- ?0 i# n5 U8 d2 qfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
! C9 N5 [0 }% e2 c" Jfprintf('\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',fval)
k_fm= k;
# c& w/ M( }' E. ~+ G- A% warning off
0 E6 i9 w- N" Y" J- P' g% 使用函数lsqnonlin()进行参数估计
. a6 t3 q: P% \; L$ f* q0 l[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
1 U9 Q/ ~' p5 K' R. f* p    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
% a: a  P* n% Hci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
8 A/ H9 a7 F1 [  H4 Ufprintf('\tk1 = %.11f\n',k(1))
0 K- x8 I( g4 j/ ufprintf('\tk2 = %.11f\n',k(2))
1 u2 u! W' g* O) {/ W; L/ Dfprintf('\tk3 = %.11f\n',k(3))
6 i0 s: Z  P. \  a0 \fprintf('\tk4 = %.11f\n',k(4))
2 h5 c; v0 j; q9 Afprintf('\tk5 = %.11f\n',k(5))
* D: }. Q. Q* e& l0 T3 p! H# [fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\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)
4 B$ k6 C! P1 G" M+ Q. a6 hk_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;
) _3 W' T. e' }* ^- p' z6 `, A[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
! _2 J) A7 Z$ \% Cci = 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')
9 F7 P' G: |' d$ L& q; L( Wfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
, m6 \3 d2 }5 `7 `fprintf('\tk3 = %.11f\n',k(3))
$ E( G- n. L% Mfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
  X; D, e# |4 M% W3 Tfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
4 n4 S, Y6 k8 m* v3 rfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
* d/ |- s- G2 d: @( f; c1 ~tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
. j/ O( E% m$ z' P: c* I$ R! q+ }p=x(:,1:5)
hold on
" Y% w, ]: W! C$ w, V* dplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
0 L" ~; ]. q$ I. o* N


* \4 C2 I) ]; @5 lfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
) w6 e  t& h- l  A[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
, b) ~, v$ r0 J4 O3 @f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
2 M8 ~' B7 b* d: ]# |f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

7 ]2 l) V. w1 ^& O' k" Y  b

8 Z) }0 i) j6 h7 @% E  pfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
+ k1 }' @3 M- b! j  i9 K. x' ny(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
$ I8 S" p" j( l0 @! J: G    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
7 X8 r) b9 g' I; O5 H* b0 _' s    + sum((y(:,6)-yexp(:,6)).^2) ;
2 Z5 m/ H- v# U0 Y1 o



function dxdt = KineticEqs(t,x,k)
; y: |- k0 V8 G* KdGldt = 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);
5 L* c* m# L- @; q5 ^dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
; Q. a* I4 f  q: ?* d0 J9 f7 C