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
% P0 \7 g3 ?: L% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
/ z  L) S- j: m% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
) W* h; K( T5 v5 g0 H# ?% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
0 E: X+ \; e6 g6 f8 o4 w1 }' N* Y%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
format long
7 @6 z! y; D2 l( X: o+ S7 V- C, g%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
: o, t& }1 g5 L. R; Y          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
. ]% M3 }' Q3 n- g2 j1 ~* ^9 z          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
9 O. q: i# k6 C4 E, X  c          90    0.08115    0.07877    0.07485    0    0.01405
& `2 u& }: k0 S8 h. ]9 y, ], X; j3 w          120    0.0656    0.07397    0.07885    0.00573    0.02143
0 V1 A* N- E, F          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
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
6 U9 H/ W: a5 V$ P3 x0 B6 ?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
$ Q! P" [2 A2 B* x. h! Tlb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
% F8 r# x4 r0 H, L7 z5 H4 cub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
! O# W" W8 g3 ^. Ix0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
% 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))
8 c1 X8 Z9 o( w1 _0 ~fprintf('\tk2 = %.11f\n',k(2))
  t! p0 K, P" y. }, l& tfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
* W3 H9 h6 p; Z; Dfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
7 j, p4 [# {! L! J3 Ufprintf('\tk7 = %.11f\n',k(7))
4 F1 ^- ?3 `9 ?# W. ^  O+ R( T7 zfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
5 w; ?/ d" e) [% Z6 W$ s9 Mfprintf('  The sum of the squares is: %.1e\n\n',fval)
2 v9 u9 x, N( u6 ?$ O% g" `k_fm= k;
% warning off
. \" {' a8 s, [& e; B, ~% t% 使用函数lsqnonlin()进行参数估计
+ m0 s  t3 M0 ?0 M  T- M; F) S[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
: z& i7 D& T; o; i$ `4 b    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = 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))
fprintf('\tk2 = %.11f\n',k(2))
1 B" X) G0 {$ p2 f4 _fprintf('\tk3 = %.11f\n',k(3))
: N+ A. ~" U, G" ?* _) W1 I5 r% Zfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
- ]0 n& g( k+ sfprintf('\tk6 = %.11f\n',k(6))
* f/ d# @/ n! o8 gfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
; z0 e3 K1 n6 V% x/ Cfprintf('\tk9 = %.11f\n',k(9))
! W% ~! t3 B9 @7 ?' I- a' Kfprintf('\tk10 = %.11f\n',k(10))
9 a% h0 q( t  f. g- N3 Gfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
* o& p4 e4 Z( C' O* q. \6 Xwarning 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] = ...
$ m" ^. `& }# s! Z    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
" O3 l( @2 u% Mci = nlparci(k,residual,jacobian);
1 x: U" `# Z2 H2 S, ofprintf('\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')
* `! L! l1 D; J4 X' d7 Z8 |* O; G8 |fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
7 N+ M2 ~2 w1 C4 A7 c- sfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
( y" d% r% E- p' P+ n7 Sfprintf('\tk5 = %.11f\n',k(5))
: m: F# d4 J  a; ]2 Mfprintf('\tk6 = %.11f\n',k(6))
/ ?/ f, P- F' D, |fprintf('\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)
* h7 ~! Z. g% U" f+ pk_fmls = k;
0 w* I1 i' W6 V# routput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
: W( ~' X4 F* P9 X5 a  ~, Hplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
& z( m0 Q1 |+ `figure;plot(t,x(:,2:5));
p=x(:,1:5)
hold on
2 Z+ Y& e( Z; T8 }) xplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



! u4 o7 ~2 }: `+ Wfunction f = ObjFunc7LNL(k,x0,yexp)
+ D. f# }% q: Ctspan = [0 15 30 45 60 90 120 180 240 300 360];
& V+ [4 O7 y6 T5 e1 O! o[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
4 W9 y0 l, Z7 |/ q1 K- ^y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
( M, M3 z8 X6 s3 c) p, Q1 lf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
3 m/ q7 m' I" i$ }! t+ B7 o. af5 = y(:,6) - yexp(:,6);
& L4 v  G/ |) ]9 G3 p1 O% k. C& |+ \f = [f1; f2; f3; f4; f5];
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/ D$ b- L, B* K  U  s" f4 l1 `# `
" o" b0 Y# ?  e( i1 |  v) ]6 M5 x7 W
function f = ObjFunc7Fmincon(k,x0,yexp)
' C. `: ~% D( r+ c9 o, p4 \tspan = [0 15 30 45 60 90 120 180 240 300 360];
8 p' }$ g- M% T2 O% E; y[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
9 T- W- T. w# j7 E* _- `- [, W* Wf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
0 m3 x" V( c' O7 y8 u    + sum((y(:,6)-yexp(:,6)).^2) ;

7 O' W( l& M8 ~8 v
# F, z$ \; @# A

4 H. ?$ D* _" q) G1 Z% Ifunction 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);
9 O' w7 P% E1 @' a  tdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
1 r5 b: Z5 I) N% F! v! e$ [dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


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