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
6 V/ }) h/ g2 ~%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% p' j4 W' |; t7 t% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
  u" _" l1 d3 B1 N9 P% 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);
: X& q. D6 y: c0 P1 P$ y$ Eclear all
clc
, b8 L$ E) U1 ?' `$ F' vformat long
3 O$ p2 e5 Z. v, U* i# V5 u/ @%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
          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
9 @6 `1 ?7 `# G1 ^+ `; V9 S/ L          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
5 Q/ R" J/ ]: H6 S5 `  L. y5 {          120    0.0656    0.07397    0.07885    0.00573    0.02143
          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
" g; Z- [9 Z5 a' a1 A          300    0.02738    0.05448    0.09098    0.0227    0.0597
- K# B8 b# N- @- i          360    0.01855    0.04125    0.09363    0.0239    0.06495];
4 {' E- ?- z; o/ \5 }/ B' Zk0 = [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
ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
7 h0 N: i9 ?5 {" U6 C0 o% warning off
% n' t- G( n! @8 y# n8 M/ D+ G% \% 使用函数 ()进行参数估计
- ^2 R& T* {2 p$ M3 ^[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))
fprintf('\tk5 = %.11f\n',k(5))
3 y/ B7 x% Z/ E6 ?fprintf('\tk6 = %.11f\n',k(6))
- [6 F" L& r! t$ F3 W/ V6 r2 h4 ?fprintf('\tk7 = %.11f\n',k(7))
; E7 E! g) H, Ofprintf('\tk8 = %.11f\n',k(8))
  y2 r  Z4 i; f7 ^9 {8 h3 ifprintf('\tk9 = %.11f\n',k(9))
* C: R+ d' G( Y  h7 f' Jfprintf('\tk10 = %.11f\n',k(10))
5 M; u+ K# U) U% |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
  P2 c8 \& _. u$ ]3 O7 G' o[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
2 U$ m% o  I1 eci = nlparci(k,residual,jacobian);
6 `9 U* d6 B/ {+ A' q2 @: vfprintf('\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))
) l! D% i4 |  N4 C, d& u! |5 g. kfprintf('\tk4 = %.11f\n',k(4))
6 y- T8 L4 C* |. `& Tfprintf('\tk5 = %.11f\n',k(5))
# w3 v# E3 p* e( F4 q  @  N) cfprintf('\tk6 = %.11f\n',k(6))
2 s1 k# E+ }, s9 _( ~* _) Q3 {$ _fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
" }7 @, U6 V% r* o8 [4 ?; p' Sfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
8 {6 n3 @) p, p( Xoutput
warning 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;
5 j1 s- a, w  s, O+ @8 {5 E! G[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
) Z) O* g3 }  {% R    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
% b- x8 @) ~) ?! K' |" ]; mci = nlparci(k,residual,jacobian);
3 E& O! Z, j  Z* afprintf('\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))
0 p9 o  j; d7 T2 h- d4 `8 Kfprintf('\tk3 = %.11f\n',k(3))
  H4 W1 E' M( D4 Lfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
: T4 u9 f6 G4 A0 S7 Ufprintf('\tk8 = %.11f\n',k(8))
# ]0 K* c8 u* [  cfprintf('\tk9 = %.11f\n',k(9))
: R2 Z' L" k% t1 V% gfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
  T* P, R  H/ Kk_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
2 I9 {4 c2 u% p5 ]0 y% `1 J[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
8 K& T) l' C; j! W4 Cfigure;plot(t,x(:,2:5));
" F9 e3 B9 q7 s7 I  ?8 I, v$ Qp=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')



function f = ObjFunc7LNL(k,x0,yexp)
4 x2 V* N# G6 ^/ Ptspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
2 C" F4 s. z( I! x7 dy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
9 G+ H9 n# ^' d1 g6 M$ ^0 L+ Df1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
& h2 n# F8 l2 B+ Uf = [f1; f2; f3; f4; f5];

: f" I1 s4 E, \8 ?4 g

/ A$ k' U% y: Rfunction f = ObjFunc7Fmincon(k,x0,yexp)
5 H% R, C8 }: y7 I" Z; qtspan = [0 15 30 45 60 90 120 180 240 300 360];
) Q, u- F9 H6 z( Y: c& t/ |# G[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
2 X! {8 `# W6 Ay(:,3:6) = x(:,2:5);
* O+ p, w# Q0 }0 Z& E+ ef =  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) ;


+ C3 e: k* H' W8 k% Y% {
* Y& L9 e& s; ]! e& }! D
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);
6 C4 i" `) B, F5 q, V0 B0 zdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
& R+ p; ^0 W, O5 s( Q' zdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
, Z1 `" ]3 M- [/ ]$ I; ?! ydxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


% f9 F  m' u2 W. v; {5 H# M& v