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);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
5 E( M' I- M' Y* _8 Y" I7 a% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
2 S/ {/ D# E, w7 I) T. D% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
% ?$ |0 \; z7 c: H5 u/ Mclear all
clc
format long
2 V7 r- B. d& Y9 m" c& g%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
( I. G( U5 k, B% |; I  Kinetics=[0    0.25    0           0    0       0
, ?7 a. C9 _! T- U: W) m' b: j          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
3 x' C/ W8 C0 t6 e7 X          120    0.0656    0.07397    0.07885    0.00573    0.02143
* T. t- X  k7 ^8 h% b3 j- F6 n          180    0.04488    0.0682    0.07135    0.0091    0.03623
7 @$ J, s+ W$ u  q5 q) Q          240    0.03653    0.06488    0.08945    0.01828    0.05452
0 d( R1 a: L2 a3 O+ \          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
; g% k0 A# x7 }! I5 Zlb = [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
, c; w3 D0 e$ E" N7 dx0 = [0.25  0  0  0  0];
  ?2 J0 z' b; I7 k6 wyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
0 Y  c- V( u( ^; A% warning off
* [1 j2 [0 e; K, K+ C# [% 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))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
9 r% N2 r4 h4 V- K/ C8 Ffprintf('\tk5 = %.11f\n',k(5))
' z  Q$ b1 d& w0 k  Rfprintf('\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))
  Z6 |4 G  G. H4 R( x( z& z) ^fprintf('  The sum of the squares is: %.1e\n\n',fval)
& P; S) v5 I( ^8 l. P4 wk_fm= k;
% warning off
; Q/ p% y, c& g% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
1 Y+ R* N# N9 f0 u! G' ~* l    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
. l9 d. h- v6 lci = nlparci(k,residual,jacobian);
# Q7 u2 M( n* g; R) Ffprintf('\n\n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))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
6 J8 H- _5 q% I/ hfprintf('\tk5 = %.11f\n',k(5))
& C- S7 Y& Z6 O6 Y. u* _fprintf('\tk6 = %.11f\n',k(6))
4 V$ z# Y( }+ ?, B  j, I' ~" O: x: V4 gfprintf('\tk7 = %.11f\n',k(7))
* s* p1 A, o  x$ S7 n( dfprintf('\tk8 = %.11f\n',k(8))
1 s7 ]+ G+ o+ B( o" k! Vfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
' a( T8 o6 I8 r! ek_ls = k;
output
warning off
# G: X2 W" O  T7 s% 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
: o. N; l+ z0 N" y2 p- Ak0 = k_fm;
[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')
- |) a- l0 B0 P6 Qfprintf('\tk1 = %.11f\n',k(1))
- S+ W5 J! p2 h! ~6 n' Gfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
9 A( m& G. ]4 c1 U) `  @fprintf('\tk5 = %.11f\n',k(5))
- k/ l8 }1 ^1 p8 H3 l  Gfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
. L+ I6 ^0 B: ~6 ?$ b; P. K! V% Wfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
- J9 ]1 c. v# k% a8 J; a# M1 Xfprintf('\tk10 = %.11f\n',k(10))
( @  q6 f; \4 _% G0 L- [- ifprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
5 J" r; `% j; I' t8 l[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
- S% M' @4 ^/ h5 c: S3 P0 C! o& ~figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
6 O9 x6 m0 n% S" ~7 Q6 h  Afigure;plot(t,x(:,2:5));
2 b8 ~' }! t. c& sp=x(:,1:5)
hold 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)
4 w) ]! R$ ]) h- Z5 Z/ a0 n6 R  B3 Etspan = [0 15 30 45 60 90 120 180 240 300 360];
, L- v# q; e* p! R; R[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
3 U* I/ e2 i) s8 o" N1 t& Jy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
- _: d! x% d7 F9 Q: F" sf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
* E% k' q% k% zf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
! c5 @2 n* b# g% B: B* {- @: Q1 wf5 = y(:,6) - yexp(:,6);
9 P! l1 f6 r' @" t. |4 Tf = [f1; f2; f3; f4; f5];

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function f = ObjFunc7Fmincon(k,x0,yexp)
" Q/ k" E: w% S8 M4 A% Z- ntspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
  [( i" a- y: o' Py(:,2) = x(:,1);
. ^* n# c! e3 D0 V0 i* Hy(:,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)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;

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- y4 V" b0 ~" Q: h  V- zfunction 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);
5 `% i/ K6 F+ _+ v4 n6 E8 v  RdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
1 I+ _( p. @5 _- a* R- Ldxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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