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
+ o8 u7 K+ D! L4 z2 T. Y8 g%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
% 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);
5 Z" L' N$ }3 Q2 C: g  T% dLadt = k(7)*C(Hmf);
2 K3 l; f( I2 G) M. z%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
  Q5 p# f( A+ \$ K' bclear all
clc
1 ]+ q3 A1 {0 B$ y* [format long
5 b8 s, T1 `4 q%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
) \& u# Q4 @) P  {5 S% S; H, o* t  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
2 s  Q( w9 l8 _2 `8 W          45    0.15105    0.06975    0.02473    0    0.0033
! w( s& X; W+ [: ~5 C) A          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
) E1 l& V' ?  R7 m          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
% w8 }0 x6 [2 s2 i" n4 U          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
! t+ [+ `' n, T( [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
& q# M2 h6 Z: T! J% |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]
% warning off
% 使用函数 ()进行参数估计
2 v; i$ S- T3 Z5 B[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
& b" H8 ^) f2 O. B9 s" Ufprintf('\n使用函数fmincon()估计得到的参数值为:\n')
! P9 u2 t1 w' f4 hfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
6 E5 U5 }. N/ s, r8 Y/ Ffprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
' \) p# t, Q% N1 u$ k4 K8 G! Kfprintf('\tk8 = %.11f\n',k(8))
+ J9 y3 o: T) _: k9 \! r9 }; Cfprintf('\tk9 = %.11f\n',k(9))
/ V5 a; Y6 `" V3 p+ q7 u8 kfprintf('\tk10 = %.11f\n',k(10))
' S  P- N1 c7 \) L5 _3 S, T' rfprintf('  The sum of the squares is: %.1e\n\n',fval)
( D6 e$ j8 B5 M1 Q8 \k_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
) E" L: O) p- I8 v9 ][k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
/ ^+ Z- z7 Q* Q8 `, u1 W4 [    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
) V+ k6 U7 ?( T0 c- nfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
  V' A) y, p. k! S3 h; q1 C5 r4 c* bfprintf('\tk1 = %.11f\n',k(1))
4 B$ L5 z6 k# k; J, A- Hfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
2 i$ x+ u- x$ P! K; L1 N$ h2 Dfprintf('\tk4 = %.11f\n',k(4))
8 o* v  _; q. d7 c$ \fprintf('\tk5 = %.11f\n',k(5))
" {+ O+ m& c* hfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
8 |' v1 I' h1 i2 K3 q; ?; U* Yfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
! ?! u) w( e8 \, N9 N% Gfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
' C5 o8 \) S% j; b# foutput
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;
/ X$ t3 \8 y2 p* k5 u( v[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
$ e; l6 q/ p) s% j3 }' Z    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
0 T6 r8 L# L6 m# x8 t/ d+ Q" i5 f, Tci = 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')
5 z: g1 V6 V  u6 W  @. Vfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
. J- V4 v6 Z% A$ Q  Yfprintf('\tk5 = %.11f\n',k(5))
3 i4 |" L: g, ~" X1 o; w& r+ x- _fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
" Y1 p/ G& a7 T5 z& k" yfprintf('\tk8 = %.11f\n',k(8))
/ Q% K4 ]+ A1 F' Y/ o6 g& Ufprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
& }( D3 i+ F; N) Q- o0 Hk_fmls = k;
output
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')
; h5 |0 p+ Y8 e) }  w' Wfigure;plot(t,x(:,2:5));
: ]5 T/ Z, q- D6 x% ap=x(:,1:5)
hold on
" s$ B. C0 X7 Q0 oplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



) ^/ ~5 p  x- v, p0 d, R+ mfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
( n$ E; Z- ?- ky(:,3:6) = x(:,2:5);
, y) {6 q* k  u+ O8 Of1 = y(:,2) - yexp(:,2);
+ o# F2 V0 \7 f+ Cf2 = y(:,3) - yexp(:,3);
6 `+ u7 w" C. ^+ V$ df3 = y(:,4) - yexp(:,4);
% t  R/ J; ?. B8 k. v' v4 Tf4 = y(:,5) - yexp(:,5);
7 e) I, x/ _- l; C5 m! af5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
& M: y. i) a. u2 S+ r" K# ^' T


& g- k3 C3 h: Afunction f = ObjFunc7Fmincon(k,x0,yexp)
. f6 g: U" c) J' _$ B3 Xtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
1 n' _! N% I" V2 p: f. `$ ey(:,3:6) = x(:,2:5);
f =  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) ;

1 U4 m9 n* h2 E
/ y) q3 y5 [3 g$ b, M  z- u

4 i% A8 X5 F# f, H' r# V8 _6 Xfunction 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);
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
! @( m4 M0 H, p( R0 l