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);
+ g: ~: Q3 l& S- x6 N" @& G! b% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
6 a7 c1 ]# J. C% dLadt = k(7)*C(Hmf);
5 ~' [7 x/ r# `3 H%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
! w0 w  {7 h5 Y! I% a% fclear all
clc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
" D) }+ f% z4 r5 }3 }9 Y  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
# F7 f7 b- D4 c6 b7 H* R; Z          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
5 [/ f( v. [* C. w) p" ?          90    0.08115    0.07877    0.07485    0    0.01405
1 X) `9 ~0 c# |' C  Y8 P) A  W6 H          120    0.0656    0.07397    0.07885    0.00573    0.02143
# G. j) ?3 g+ @; V6 m, N          180    0.04488    0.0682    0.07135    0.0091    0.03623
9 J8 N0 V  j0 q" E          240    0.03653    0.06488    0.08945    0.01828    0.05452
( `) N* s; d& z4 K          300    0.02738    0.05448    0.09098    0.0227    0.0597
; {! g0 Q. T2 }$ C% z          360    0.01855    0.04125    0.09363    0.0239    0.06495];
& h( ^$ x( l2 }- M3 a$ B* |8 Xk0 = [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
x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
) U/ D; \: ?. x& k% warning off
$ @2 D* h/ p+ v7 X, J8 Z0 K% 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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
7 ~7 Y( e% N3 g( dfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
7 `$ v4 ^. |2 i6 o/ Vfprintf('\tk5 = %.11f\n',k(5))
0 z4 M. y+ i; m# x1 V% i: Dfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
5 D/ G3 u% v8 [- F5 G1 Y( B# ffprintf('\tk8 = %.11f\n',k(8))
* A  W" G% B/ `5 G2 F; Ffprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
, h& J2 O7 o5 d" dk_fm= k;
; G( O( s/ d: s% N% warning off
% 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);      
4 {* ~2 D/ t8 z) }* E( |ci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
; E4 ^: R& ]+ t' H0 ]( Ufprintf('\tk1 = %.11f\n',k(1))
" L" ^' x2 C! K, Jfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
( O2 J" z& x: f2 S) ffprintf('\tk4 = %.11f\n',k(4))
" X: x/ x* {% o$ ?" _3 j& v* Pfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
# b4 }2 R, E" L. L- I  sfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
4 x1 _* h/ s. D+ V9 k& [# V( ffprintf('\tk10 = %.11f\n',k(10))
' ]6 s9 {+ s2 R7 b* Gfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
$ L6 y& ^. A& e2 N. H1 }0 X8 v/ u, V/ Aoutput
( {4 \4 y% [1 N! Nwarning 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] = ...
* H& @( }3 X# l1 W+ G    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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
3 t( t2 C4 t( S! g! ?) a) G% afprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
4 P7 G1 O& J4 I! R, j" w( ofprintf('\tk5 = %.11f\n',k(5))
5 m8 x, ?$ G+ Q! j8 y2 K8 ^fprintf('\tk6 = %.11f\n',k(6))
" ^3 z& q8 F5 X% _( S/ z4 P, [, Ifprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
( N" C' O1 P( k4 n7 O3 _7 K! Ffprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
. ?* d: M; o* }( A6 ~6 P- \k_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
9 v: `6 w# L+ _2 ]7 W; J" W. T6 Z[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
; J" j( |; y7 F7 nfigure;plot(t,x(:,2:5));
8 j( @2 j/ S! ]" y8 {0 X7 mp=x(:,1:5)
& m! X2 C9 N  P! chold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')


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function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
5 C/ w9 I" d) g6 M& d[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
( K' w) v! F) w9 c% }y(:,2) = x(:,1);
0 `/ n' M9 v: b# }) \1 gy(:,3:6) = x(:,2:5);
& Z0 G) x' X: {, f8 Af1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
0 l2 J9 X% V* O5 V/ H/ Ff5 = y(:,6) - yexp(:,6);
4 N( M5 h; `. Wf = [f1; f2; f3; f4; f5];

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function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
# q! s4 ^+ G8 w8 m; h[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
0 U/ J; |1 R* c& @; vy(:,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)   ...
$ ]& Q' s$ }* H1 O    + sum((y(:,6)-yexp(:,6)).^2) ;
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" Q4 M5 v+ s' ~
, |' ~$ \. N$ W  Nfunction dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
5 K: ?5 j' X# PdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
* N6 f' `( S5 c' `" x4 V4 TdFadt = 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);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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