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
+ U( B2 m0 ?+ S& S. l3 ?+ Y3 E& c# w%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
  f/ M8 ?  ]- o/ P0 l: V3 i- L% 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);
( C' b) f+ ~. q/ G; b4 ?% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
8 O1 ?  F* u- E" `7 l, p. H, [# Uclc
) j# E: O  Z3 g6 w8 kformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
8 \5 B7 S# c% Q% D; Y! e  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
5 j/ Q8 a6 t! g! U7 J3 A1 a          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
          120    0.0656    0.07397    0.07885    0.00573    0.02143
" `6 M$ n7 R! K1 J; S; A: n1 b2 A& t! |          180    0.04488    0.0682    0.07135    0.0091    0.03623
' f( h. O  l1 _( X- c2 X/ V          240    0.03653    0.06488    0.08945    0.01828    0.05452
  L/ C7 M) a: K          300    0.02738    0.05448    0.09098    0.0227    0.0597
1 B8 }. H/ J* |( R+ x% }/ E          360    0.01855    0.04125    0.09363    0.0239    0.06495];
( Z& Q: \" b" t5 `) ?- H1 nk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
/ R, m& \# H" E* S) Elb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
- t# l; |. `% f3 K. p8 Rub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
' E; ^4 K- e. F3 Kyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
- L' P$ q5 t% O% 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')
3 X# h9 H2 v& z* C" d( U- Jfprintf('\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))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
4 ~3 u% ?4 Z3 Jfprintf('\tk8 = %.11f\n',k(8))
# q0 D; D' k: c, U1 H( ifprintf('\tk9 = %.11f\n',k(9))
7 w/ {  s6 c. b) {8 ~: l* yfprintf('\tk10 = %.11f\n',k(10))
9 F; g" {; p* W) I3 Q* M+ [fprintf('  The sum of the squares is: %.1e\n\n',fval)
% [* a" k- _% A2 r/ d- Fk_fm= k;
+ O1 E0 X* \3 K( B$ q% warning off
% 使用函数lsqnonlin()进行参数估计
0 O# Y& T2 V  A/ p4 m[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
& u" B1 \5 y  Q    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
, d) c3 z/ K% e) Oci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
* A" G# G4 ?3 z! w$ f' U7 f+ r0 wfprintf('\tk1 = %.11f\n',k(1))
5 b! w7 ~. H5 G+ f, R+ [$ |3 wfprintf('\tk2 = %.11f\n',k(2))
; D. {( _  _6 l0 Ffprintf('\tk3 = %.11f\n',k(3))
: p) G7 f3 X- k7 S# _2 r7 W4 Afprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
: N6 j' _' f6 c/ Z% Zfprintf('\tk8 = %.11f\n',k(8))
$ H! W' ^6 b0 N' n& Y8 m$ X: ]fprintf('\tk9 = %.11f\n',k(9))
- t5 A* G; e: g( s! R$ Tfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
  P5 P1 r1 O8 q' ]9 awarning 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;
4 j, j5 A# {7 E" L$ r2 L% X[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
6 c3 h) n8 H* B9 xfprintf('\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')
' N& f- {/ q' W$ }7 cfprintf('\tk1 = %.11f\n',k(1))
0 E; X% `8 P# ~  w- T# rfprintf('\tk2 = %.11f\n',k(2))
2 r4 D/ q; Y, t4 C6 g( kfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
1 Q; c& ]! n  N7 l4 C! Gfprintf('\tk5 = %.11f\n',k(5))
8 ?. j& v# a6 a4 Gfprintf('\tk6 = %.11f\n',k(6))
! S6 e; u, T* \2 ^1 jfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
- l& S" }' r& P- l% P. G+ Bfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
6 b! ^5 y4 G2 m, D9 [1 ~tspan = [0 15 30 45 60 90 120 180 240 300 360];
) t' \- s6 t' S* K  H[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
3 S7 d6 R' L0 l2 m6 N/ F; P# P' {figure;
0 `' k6 i4 C7 P! Lplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
- m$ v% s9 G9 I  ~; kp=x(:,1:5)
hold on
3 E' P5 ?1 ]( X0 o2 Q" uplot(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)
2 z9 ?( ?4 i; K2 U; _tspan = [0 15 30 45 60 90 120 180 240 300 360];
8 `' e5 h8 e; I, v6 B& D6 O" ~[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
$ ^8 R% ?0 j' h1 _/ Ty(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
; H+ b- b" U, K' o0 P( L6 o1 Hf3 = y(:,4) - yexp(:,4);
3 M1 g+ h9 B5 n/ bf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
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function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
8 ~8 o0 @: b2 K  X[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
* d: Z7 W. f: ^  F( tf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
( K4 v& e7 Y+ y- I- ?  d$ u3 Z    + sum((y(:,6)-yexp(:,6)).^2) ;
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7 C9 p0 r* J4 u9 [9 bfunction dxdt = KineticEqs(t,x,k)
9 A! x' l* _2 Y- V1 mdGldt = 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);
3 _  o! ~) `) F/ `( H, h$ mdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
# _0 v6 ^; ]. z, ~2 \: T- IdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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