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
& R7 r5 y# w9 e3 @  i0 N%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
/ t5 V) i3 X5 V' |" u% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
5 c3 w8 H- }8 V8 G) b$ i) d% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
5 v" |0 Y- K/ A9 e% dLadt = k(7)*C(Hmf);
9 w  {$ m7 }- S& ^4 D  o3 R%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
- a! \! G" ~& Eclc
7 [: M' S/ L. N: F6 T7 W% b$ j; mformat long
5 C; t$ ^- w% Z: z; l6 @%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
6 w0 y  [4 I" Y2 y% A/ h  Kinetics=[0    0.25    0           0    0       0
% z/ J; D8 r2 Y8 d          15    0.2319    0.01257    0.0048    0    2.50E-04
( h& i9 t2 U2 I          30    0.19345    0.027    0.00868    0    7.00E-04
' e( j! E  ^! t/ H          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
" a$ t& W5 B$ v* t- j4 V  c. z          120    0.0656    0.07397    0.07885    0.00573    0.02143
' e- T1 V  |! R. d. K! B! D6 k          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
& j, [5 M9 {* }2 j9 @" _          360    0.01855    0.04125    0.09363    0.0239    0.06495];
, l$ @. y% H( n2 b7 ]. vk0 = [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
7 ^$ D6 k" X8 U: Hx0 = [0.25  0  0  0  0];
% T9 [, d! e! G4 q' |yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
0 ?/ G7 y$ x& B5 w" ]0 y; K% A% warning off
, f) \0 E% x# @* c: v2 ^% 使用函数 ()进行参数估计
8 C' L' q" T9 A8 _' C$ Q* r[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
( i0 [9 Z$ B$ {6 s9 j' ^fprintf('\n使用函数fmincon()估计得到的参数值为:\n')
* N# z8 X0 g6 k) m+ o: zfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
' b. h" T) @) \. ]( ]' `# J) \* Dfprintf('\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))
fprintf('\tk9 = %.11f\n',k(9))
& E4 o7 e7 u! m; W9 w) r  k( {: tfprintf('\tk10 = %.11f\n',k(10))
; i4 [: j( j$ s: ifprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
/ |2 L! t: g" p& [% warning off
. \- J7 |" T* q3 Q8 f% F  n# `4 v0 }% 使用函数lsqnonlin()进行参数估计
$ }2 x( F7 y6 s[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
7 p* W& O  ?' K& S. n) a6 E% ^* _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))
0 ~# K8 i8 M, n. C: Dfprintf('\tk3 = %.11f\n',k(3))
9 t! `( K- @/ cfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
- P4 x8 b+ z7 }" S# }6 Bfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
6 j1 d0 O, V9 ]2 A2 F7 l3 U9 yfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
* _- q# F/ Z7 R" z3 A$ R* Efprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
* t$ C/ }" a0 V, n) p* D4 X  C" bwarning 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
5 ~% Q& {/ @) u0 q3 t/ V: xk0 = k_fm;
; y$ P8 o3 K! f6 h/ P[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
7 ?7 k5 c+ }9 k3 ]    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
9 \& e1 E6 F8 t5 h: ]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')
7 |% c* W) ?$ v  H- Z& O  U# xfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
; ~0 l" S" t1 v4 J. kfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
; O0 @1 Q& X, z8 x% A: U# F& Kfprintf('\tk8 = %.11f\n',k(8))
5 s2 I3 M+ F' F% g8 ]  T! cfprintf('\tk9 = %.11f\n',k(9))
; j  @- J9 B; @6 [, p$ t* D9 F# Wfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
) e5 x  D7 |; L8 }7 }, pk_fmls = k;
output
" h9 N& j0 V( vtspan = [0 15 30 45 60 90 120 180 240 300 360];
6 ]1 t, _+ t5 ][t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
# |3 a+ O2 m4 P' e6 C8 ^, }! G" kplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
  p1 y, g# c0 j$ f7 s2 vfigure;plot(t,x(:,2:5));
$ j& R9 @- T; V! W/ Z. `3 E) ^p=x(:,1:5)
% o1 M8 Y: V2 [0 t1 n/ Ahold on
: k# p: e9 G( |7 s# [) mplot(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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) l6 p$ R% h9 F) Kfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
: p. u) v/ ?/ X6 W9 X# m[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
, s+ h' o' ]! E' L! k! ^y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
- u4 W, s: p* G8 \2 |* Df1 = y(:,2) - yexp(:,2);
5 y3 B9 G# i  c& }f2 = y(:,3) - yexp(:,3);
2 V/ E8 m' d1 ~( g, A+ uf3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
" _8 e8 w/ X' Jf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
+ t% F9 U& ^0 V8 v$ k1 a) H
& Q  }: G7 S5 F. G+ w6 [
0 t' H4 u; s7 \9 V( h
3 S) n8 G7 F" H3 ]+ a  ofunction f = ObjFunc7Fmincon(k,x0,yexp)
+ C- G: g: |$ A& Mtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
8 c# j" |: m7 p; Q$ g* Ty(:,3:6) = x(:,2:5);
7 {. _4 b/ T$ A" c8 N' v! uf =  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) ;


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- ~3 h  C# {# l  s7 \" Z8 afunction 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);
; z: q9 k: {6 a: C, l, ]  i' A5 GdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
: o0 j/ m4 {/ e6 p8 t+ j3 VdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
3 P2 N3 s7 G' e8 {/ }9 Rdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
$ @$ H$ ]" I, O' L. ]