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
1 z9 m1 l% e( t/ W2 ?6 Z% L$ i+ M% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
, a9 D8 Q6 F7 _# A8 S; w) V6 ?% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
. J( v! C& i- ~2 S%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
+ [! N; H- d$ `5 e: N  P" Rclear all
clc
format long
1 `. M5 R$ t+ N5 u1 u%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
7 X2 ?- _3 v: y" q( |8 t2 K+ [, ~- g) v5 A  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
0 h* M6 r) P+ T& z* w, Z* k          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
& l. m4 @% g7 @( c          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
. i. p6 ?! S  Z# [  w3 M          180    0.04488    0.0682    0.07135    0.0091    0.03623
9 p8 c- x: t, x' j          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];
6 p+ c' [2 n8 v8 D* ^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
' z* K$ w' f1 i; q; D" i5 D4 Blb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
& S: C0 X7 T2 k; t" v8 q! c! Qub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
* S, L& F9 `+ Y8 mx0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
3 t1 ]0 U! ^1 v7 ]8 Z7 ^% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
0 ]8 j% M1 q' p( b. ]& P; g3 ofprintf('\n使用函数fmincon()估计得到的参数值为:\n')
' e4 ]" ^8 x$ W0 i8 u. }! Jfprintf('\tk1 = %.11f\n',k(1))
1 v, L; |4 J5 bfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
+ E$ q5 M* o' A- P* h- o! Vfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
% ]* g3 P' g' e) E' Wfprintf('\tk8 = %.11f\n',k(8))
$ q4 L8 J* V7 R$ Wfprintf('\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
' J& F( d/ g/ D1 p; J0 q( t5 F' d[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
( I  x) O) F  j3 e6 ~fprintf('\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))
! `$ V/ _3 U' X+ ffprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
$ e6 y+ G; t# B. K5 s: C9 o' hfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
. g7 B( x; g; a! e$ z3 o( rfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
! B2 @) ~" M" y8 t# Gfprintf('\tk10 = %.11f\n',k(10))
( V5 n0 N6 ~6 E2 H$ y2 q$ K, Sfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
3 Y9 j5 h$ I* W7 a8 |8 }k_ls = k;
0 o: ?9 P+ A2 E/ d. d* {output
warning off
/ m# ]5 @5 h# k8 ]  `% 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
% c& Z( s1 K. [' k$ g1 O3 T. I; J2 F/ Lk0 = 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')
5 g7 i+ x  h* A3 z9 X$ x# w/ z) zfprintf('\tk1 = %.11f\n',k(1))
$ j  @( a9 o3 Nfprintf('\tk2 = %.11f\n',k(2))
9 s4 m0 M' e. r6 K) H% B4 E- `fprintf('\tk3 = %.11f\n',k(3))
; F2 J1 ]5 E# O" I* b& o" Ifprintf('\tk4 = %.11f\n',k(4))
3 }0 X1 N+ v* b/ o! p) T% e* tfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
' G7 k6 g) n( u5 zfprintf('\tk8 = %.11f\n',k(8))
# X: N( C0 p' R$ l, r* D( D6 Zfprintf('\tk9 = %.11f\n',k(9))
5 U( ^! ~4 F5 q; \) ?# Vfprintf('\tk10 = %.11f\n',k(10))
- C' Z/ u" g  o% b% ^! Vfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
% D9 `' y8 \$ ~output
+ c, J+ x# [8 M6 k" J$ }tspan = [0 15 30 45 60 90 120 180 240 300 360];
0 G( E+ J" l1 s8 k) h: K9 t[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
5 S. }/ @' c5 i* F( ]. r, U, A' Pfigure;plot(t,x(:,2:5));
p=x(:,1:5)
5 t2 N+ p/ Q1 z! |$ y7 ?hold on
& c! m+ I$ R7 X+ G# h! Pplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
5 ?' I  G; i) }. l' S4 B

8 i7 g7 ]6 g$ o2 v
5 e( ~& I: J4 o/ J5 W, Pfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
2 u8 t) [5 V) l+ H[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
; w- d5 S5 ~$ p8 v( l/ g. Vy(:,2) = x(:,1);
/ n$ O' W( j: t- E$ Q" L9 `; d) ly(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
  S' |: O6 S4 I" F# G" q5 Qf3 = y(:,4) - yexp(:,4);
5 p  U+ {+ [- `" af4 = y(:,5) - yexp(:,5);
  u2 P1 X2 p/ L" Lf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];


' k: o9 z( o" k6 p! ^
6 U& g9 f7 J: F5 [* _: Ifunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
+ A1 K. l( v! g4 _$ py(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
; v- @7 m6 K  u% w    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
& C3 R2 L/ B* u7 B; c# u3 D    + sum((y(:,6)-yexp(:,6)).^2) ;
- W: a; l5 ]: w- ^" c' t
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( k9 L4 z4 H' |$ v2 G1 [! a

5 E$ \" U( |9 t1 _function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
! h* m: ~7 `  g4 K+ A' h' TdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
: H+ w1 @) U7 vdFadt = 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);
2 @3 D& U( A: J* w$ Tdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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