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
* D# E. T, s1 P1 t0 U5 y% k6->k6 k7->k7
7 }, u+ d  J+ y/ M$ P- G. ?: t2 I% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
) }# ^) c  \% r% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
' y! c, p, p" I8 T# @+ y# C7 |" i% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
format long
2 i* G7 I) A# G/ i% T%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
) M8 j. F* n* W$ M0 o2 |; R          15    0.2319    0.01257    0.0048    0    2.50E-04
* C" o- f, }% ^5 `) t7 U7 [          30    0.19345    0.027    0.00868    0    7.00E-04
& I/ ~: g0 }/ k4 k          45    0.15105    0.06975    0.02473    0    0.0033
8 L3 t  A( J1 D2 D  O8 M          60    0.13763    0.07397    0.02615    0    0.00428
$ S7 x2 o5 _5 }1 u1 M* t9 j9 }          90    0.08115    0.07877    0.07485    0    0.01405
- a" b7 D2 @8 y, p4 d          120    0.0656    0.07397    0.07885    0.00573    0.02143
. j( m6 ^5 I# b. o: h: D          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
3 e# U/ o9 n- e8 D          300    0.02738    0.05448    0.09098    0.0227    0.0597
. d, W& R! u+ e+ c2 @          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
$ [" o* g6 ?2 F: `/ Z) `; wlb = [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
+ I5 F/ o" L- @, Rx0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
( s  y( x+ d2 |. c* W2 @% warning off
2 T( g! S. ^* G5 P- ~% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
) W* y4 Y7 W* T5 lfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
2 S/ m/ P/ Z. _& s& Vfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
+ q9 W! B# e# \fprintf('\tk3 = %.11f\n',k(3))
! U8 |8 B, C0 H; W3 @7 hfprintf('\tk4 = %.11f\n',k(4))
/ f6 @! f7 N- r5 Y6 U6 xfprintf('\tk5 = %.11f\n',k(5))
' X( u/ c( J9 m) z: P5 Mfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
' S. r& [. T8 @( Q9 Mfprintf('\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] = ...
/ J3 ]+ C; f8 O( R1 \) [0 Z+ l! s5 M% q    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
7 H, D2 H" S4 e, A: H+ Bci = 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))
" Y& P1 ]! \5 ]8 t: Q* d+ j6 Afprintf('\tk2 = %.11f\n',k(2))
  O# u$ R- d3 W7 E3 @fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
9 R9 J( b! H9 s& ^$ b  f: ?fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
0 H6 N5 ]. u& yfprintf('\tk7 = %.11f\n',k(7))
# x5 H& O" Q( _& g; i& K- Mfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
( Y1 N5 W  U7 A5 a1 Y4 Qfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_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;
; U0 m. M6 X1 _" m' L[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')
8 L% [6 |# r; [fprintf('\tk1 = %.11f\n',k(1))
- c2 ^3 z% j4 j! T9 \) }7 tfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
3 `9 y' _# t; L- a3 kfprintf('\tk5 = %.11f\n',k(5))
* X5 e, i, z" N$ i% M- @8 p; efprintf('\tk6 = %.11f\n',k(6))
) q6 k6 H: q& \fprintf('\tk7 = %.11f\n',k(7))
4 A" B- a0 x9 x# J/ L8 p& Ifprintf('\tk8 = %.11f\n',k(8))
2 S7 p* J! t) y4 I, |% O1 e+ `fprintf('\tk9 = %.11f\n',k(9))
5 t2 z9 m2 s1 B8 @$ D0 @3 G$ Q8 Pfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
0 T# d- c. N( D3 W8 c. Nk_fmls = k;
' G0 z7 z6 l' Woutput
/ f* J5 u; F. Q0 J) Xtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
1 p6 j4 S* _' A# W" H, C. Tfigure;
' K8 G- D7 e7 N- N8 \! Iplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
) f: o0 s: {8 S( ~; ~% m4 D, `0 Sfigure;plot(t,x(:,2:5));
& U/ e  u: Z' e  Ep=x(:,1:5)
6 Y' `0 o$ y3 v- _1 Shold on
0 e  F" }' g& |& Dplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
# {8 ~8 E2 \6 T. g. q# P0 J

& |# W6 z' e2 U" l
3 H7 \. y: I* sfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
3 i, d- @0 W1 l+ {y(:,2) = x(:,1);
7 c) |+ N6 c, ]# c7 Ly(:,3:6) = x(:,2:5);
! I! B9 D! t! r5 j6 v1 B/ P# I& Of1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
% ]# u* R( \) x" `; bf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
& s: b5 P* N; `/ Q$ `6 af5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
/ D" D: ?& t' d6 ^) g

5 |3 X5 A, V0 U9 z
function f = ObjFunc7Fmincon(k,x0,yexp)
! \1 l& F- ?3 N5 F* B; v5 Ntspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
) f5 I) e% b/ l+ x4 Y, w) iy(:,2) = x(:,1);
4 f$ O. a' }- P) c2 l6 O2 Ty(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
/ I- P- m/ j5 D6 j* `    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;


1 z' `0 i& ?3 v& E3 b

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);
dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
" b: _5 u0 y+ M9 f) l* d- ?dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
* p& `# ^, }) ~  Z3 b' \8 x
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