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
: }( M/ ~4 g5 o+ P" |: q5 e' q%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
2 P3 f* \* I( M( s$ I& h2 ~% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% 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
! P! Y8 M: g0 t3 V# j4 sformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
2 x- C: Q6 v2 f0 f. e          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
- z5 H: M3 L% X* }' h          90    0.08115    0.07877    0.07485    0    0.01405
, N+ d+ p' G: l: C6 L4 L- \% J          120    0.0656    0.07397    0.07885    0.00573    0.02143
, Y! W' H, Z+ b8 u# L/ a& [8 H          180    0.04488    0.0682    0.07135    0.0091    0.03623
  h) t" X* O% m+ m# o  u+ {, }+ m' d          240    0.03653    0.06488    0.08945    0.01828    0.05452
* ?( u  v2 W" m( c+ h          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
- m2 M1 i; K( o% G7 j& Blb = [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
1 c7 z6 a9 b4 Lx0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
! ^* X6 k$ \7 p9 W% 使用函数 ()进行参数估计
$ r8 x) @$ \' b6 ]: x& I1 r[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
; Q8 @' i6 O1 F. }! I/ m: R! g3 sfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
" h& n! H" r6 a6 Y) Vfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
4 @( f0 c* R2 }9 q) x6 T) ~fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
! t8 P* _9 s8 Q8 mfprintf('\tk7 = %.11f\n',k(7))
# n' @  F2 {, b& R, Efprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
  f  o# ^8 d1 ]# r1 R) bfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
( [# m$ J1 W7 m, S) U2 J9 m% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
* A4 l( L' z( D9 g5 Q; |% r    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
7 X* h; v1 n4 k* N( V0 r4 y& R; Aci = 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))
- Q3 k/ Y% f9 I: }9 s; `fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
! A. _1 Q. B' x) h/ g, t& X" bfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
) g" \# b# y. a6 }fprintf('\tk9 = %.11f\n',k(9))
  D# g! @- @6 P# Afprintf('\tk10 = %.11f\n',k(10))
% e8 I' Q% |1 C' J( o; hfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
) o" y! {7 V' F9 W/ O  D% ^. l* wk_ls = k;
output
warning off
( W7 |) h& F$ A2 p. 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
3 L5 Z0 c- R% H0 P( }/ Jk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
8 o; Z, Z6 m$ _2 i4 S    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
8 V% ~0 [8 h. P+ y( R. G' ^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))
5 O, o; Z$ k* {7 V6 @fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
4 s5 K' S7 N# H% b  nfprintf('\tk4 = %.11f\n',k(4))
, c, b1 w+ a- W" p" R! s% D8 d3 Ifprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
2 O8 R/ H* s' }5 E7 Jfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
, k# j. X" C. q4 }# l5 a  Tfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
' s8 P, v- [! X2 U5 O9 F1 E2 |output
! z8 A# D3 j0 ^+ M% u) I0 Etspan = [0 15 30 45 60 90 120 180 240 300 360];
* I2 L2 b% v3 F0 N* i1 E; |[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
$ K9 b2 P2 }. N$ ?figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
* v( j. g9 b2 v9 N1 q% sfigure;plot(t,x(:,2:5));
9 V& b5 `  L6 f9 f0 @2 Wp=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')
3 L4 Q) g+ [6 d& q: Y0 ^) K
" A  f% O  r# ^: W& i3 u/ w- P

function f = ObjFunc7LNL(k,x0,yexp)
4 J# G' P0 v" D, ?% Ttspan = [0 15 30 45 60 90 120 180 240 300 360];
- f. |- Q! P7 I; T" o0 |[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
) b0 f( [, z$ A) Y; \1 cy(:,2) = x(:,1);
; h8 L4 _% U' `: I, X5 ?y(:,3:6) = x(:,2:5);
( {0 i6 u& E2 ]# I9 m1 U4 sf1 = y(:,2) - yexp(:,2);
, h7 }9 h5 ]; E1 H. C( t  k0 Pf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
) Q% P9 U8 \/ m0 H2 D) ]" xf = [f1; f2; f3; f4; f5];


! _. ]/ r  m: g
3 z( p, g9 ^2 Z* `function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
( v, E( W" [, L2 l2 w# G6 F9 I[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
0 t& i& w" Q* h* O/ Z& Yy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
; l& E' S/ s5 e2 k: w9 j6 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)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;



( D7 J1 l% s3 U% u
1 A, I, {+ z4 v, m& a' T! _function 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);
) V: Y0 b6 u3 w' ]1 F, F/ e" BdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
6 u( |6 @/ J1 L/ d% `$ s" ldHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];