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
0 G. }& i# L* \' i7 `% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
0 y4 \! C$ R: ~1 _% 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);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
! t! `# [) x/ |& S. f: r! Dformat long
8 n8 t1 R4 ?; V! W& Z%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
: ~5 `; V9 e) c9 U5 t+ R6 `  _! Q  Kinetics=[0    0.25    0           0    0       0
# ]1 H0 k& G2 g0 \          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
# O# z5 c  T; X' n* r          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
! F) D. m1 ?2 r1 r% E& Z          120    0.0656    0.07397    0.07885    0.00573    0.02143
" c4 h/ i$ F8 @0 a3 W, v          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
) S6 h+ f. \; x5 L* P0 O8 b! z          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
0 d$ f. Z& W6 E0 u% }ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
# q/ _1 w# E: \5 A6 n0 Gyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
, M/ d/ r+ ^0 D: `7 L9 r6 {/ d- J% 使用函数 ()进行参数估计
: L% p! a; N* R( R. e[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')
4 ^: ~, B( |5 L" C! mfprintf('\tk1 = %.11f\n',k(1))
8 |. C# _" R2 b2 q. Wfprintf('\tk2 = %.11f\n',k(2))
; v# v$ O( @$ b9 q6 Xfprintf('\tk3 = %.11f\n',k(3))
7 V. h/ R* M. o: W* mfprintf('\tk4 = %.11f\n',k(4))
. g$ t3 j2 }8 C. v4 s; B' Bfprintf('\tk5 = %.11f\n',k(5))
; I. p6 w% I+ O8 L5 t7 Z& n$ |& i0 ifprintf('\tk6 = %.11f\n',k(6))
) I) ?0 ?. {* H! h6 h3 pfprintf('\tk7 = %.11f\n',k(7))
* L8 E% V7 s7 \/ J  Zfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
1 F' q  i1 G% xfprintf('\tk10 = %.11f\n',k(10))
0 w; a" {3 u& Nfprintf('  The sum of the squares is: %.1e\n\n',fval)
" |; W4 I4 ~$ qk_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
2 Q) G6 D: k  Q/ u$ g5 U, J    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
- e; h& A* T# {$ \& L% Eci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
) l( {' k* w$ vfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
5 b4 @1 a, C! L3 Xfprintf('\tk3 = %.11f\n',k(3))
5 e6 h( j9 B3 W$ @& jfprintf('\tk4 = %.11f\n',k(4))
& R) D5 o/ l( Z4 A' yfprintf('\tk5 = %.11f\n',k(5))
" Z& z3 V. \* \0 ?fprintf('\tk6 = %.11f\n',k(6))
8 Q- y9 S# l* U, E. C2 xfprintf('\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)
k_ls = k;
output
8 V+ D3 w: v" C2 ~- ?- A1 v" Wwarning off
- R, V/ Q/ f- J% B, T4 I* A4 I4 r% 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] = ...
- E3 ^  f2 G# {9 ^3 f    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
3 U5 f6 Z5 l9 k5 xci = 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))
fprintf('\tk3 = %.11f\n',k(3))
9 p& w- W' R' A% x6 J6 qfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
1 I, a* V; E/ v6 s5 c; e& |) T0 S! Cfprintf('\tk6 = %.11f\n',k(6))
- M  r* h4 L1 [; xfprintf('\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)
7 `" ]) B0 {$ M& p+ C" O' [k_fmls = k;
" X9 T) Y, N  s1 u) T, Doutput
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')
' d- x" S; |! h+ g9 Ffigure;plot(t,x(:,2:5));
6 J, j' |7 v* H5 Q$ k$ p: `2 ~, Yp=x(:,1:5)
$ i; V! Z9 G: D1 I) whold on
) o. u/ c+ u/ Y. n. b& k1 C, j6 Y# ]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];
0 l5 E3 F! ~" @[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
* b  F; x  j/ C/ q, ^9 f  s3 O; {y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
" f, `, b" a5 y+ s  ]* t) Jf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
; p5 Z. b$ b, n7 n; s) J6 p4 cf = [f1; f2; f3; f4; f5];
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: a$ a. B4 s" bfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
8 I) p0 I" A( q2 d9 f3 c! [/ ry(:,2) = x(:,1);
7 X8 ^4 g( d7 P- Y- V' k+ b7 s. ~. Py(:,3:6) = x(:,2:5);
; r3 E- F/ i( u1 J( d1 N; e+ q& @  U8 Jf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
2 T+ m% z: H# n& ^    + sum((y(:,6)-yexp(:,6)).^2) ;
% h, o. @' ?5 ~4 O$ s
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% a- |9 }! n: r* ~( W
% S) P/ n, O4 H: B( C1 x
function dxdt = KineticEqs(t,x,k)
# p6 C5 O% c8 [- K: WdGldt = 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);
6 z: ?! j) I& D' l% Z4 ]& vdLadt = k(7)*x(5);
& D8 U! G. v( m/ DdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
" ?9 T, z8 Z( D6 X1 _! Pdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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