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
%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
5 R( F* n: H2 j1 \% h% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
8 C( ~9 c# l" D2 U% 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
6 e, y; |2 o6 C9 T( m3 U7 N+ Oformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
; m! h, J& h4 j1 X  Kinetics=[0    0.25    0           0    0       0
! L: j" [, ~$ P3 P0 p! r: K          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
; q$ h0 Q" I. N          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
          180    0.04488    0.0682    0.07135    0.0091    0.03623
8 ^+ o  D$ [5 `! r; B          240    0.03653    0.06488    0.08945    0.01828    0.05452
8 w( |$ V5 P3 }6 |7 G          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
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
, b" W! ^( M' ]x0 = [0.25  0  0  0  0];
' V5 ~3 |/ m" b! \, {0 n' Lyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
% 使用函数 ()进行参数估计
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
1 I5 H2 p. V# v$ C; w6 gfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
: y# p) Y( r& V: j) C1 O! o/ S# `fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
  i# c* x# P, p3 ~fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
' \# W( B( l2 M8 s0 R7 p2 Wfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
1 ^; V  _8 C7 N9 O/ V/ V2 U# u% warning off
% 使用函数lsqnonlin()进行参数估计
* _3 A9 v! ]3 [; K[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
5 T0 b2 R6 ^4 N' c    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
" }3 I% A, ~% w8 ?8 [& Ifprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
* Y8 c3 I! ^, l8 S9 ofprintf('\tk3 = %.11f\n',k(3))
3 ^' L# _6 ]; Bfprintf('\tk4 = %.11f\n',k(4))
9 B! S* n: x0 j" n+ w. Lfprintf('\tk5 = %.11f\n',k(5))
; g+ x* B+ I: W; sfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
4 ~$ A& {  }4 F2 e+ t( r! U7 |( Gfprintf('\tk9 = %.11f\n',k(9))
8 |  X* S2 z7 D' C# [1 j& a  ~fprintf('\tk10 = %.11f\n',k(10))
4 {( N/ h7 w" k/ ^fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
warning off
1 Q; p: J* j4 ?# H# A- k% 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 Z3 l  y$ M( U$ Q/ kk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
! ~* C( X+ y4 m. S" {    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
) g, T+ X, ~2 B+ Jci = 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')
( \7 e& [* P" t" Vfprintf('\tk1 = %.11f\n',k(1))
" a. P4 B* R& d2 s2 `fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
, C; z/ n- W  Zfprintf('\tk6 = %.11f\n',k(6))
- j. u! b! b7 j: Cfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
4 I  q2 g8 ]7 b, nfprintf('\tk10 = %.11f\n',k(10))
  J" ^# `8 L. hfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
3 C% X+ [0 Y# {k_fmls = k;
7 `9 [( U8 S' ?2 U0 }5 uoutput
" b5 ]& o) g8 I- F2 {tspan = [0 15 30 45 60 90 120 180 240 300 360];
: O: g+ S9 E: C. T1 C% e) B6 ^[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
! w1 R" i# _1 H! Z& xfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
1 q' k0 k/ U2 f" W* {- x$ \figure;plot(t,x(:,2:5));
2 p' r. b- l. v1 H2 op=x(:,1:5)
hold on
' w- @. `6 O5 S& H9 [/ ^plot(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)
5 z. d) M' `: I+ I) ~tspan = [0 15 30 45 60 90 120 180 240 300 360];
- @& U  b) m& R$ T% u4 D6 O% L3 K[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
% ?8 U" W$ s5 \6 B% t2 Q' ^3 y, ?y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
# S- ?; R% m! J& ]! p% [f1 = y(:,2) - yexp(:,2);
; g4 o. p( j6 \' Wf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];



function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
1 z- G3 r9 T8 w% `. f# g6 j( Ey(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
* `7 B# L7 [3 }- C7 i9 Sf =  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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0 [) T6 o) a6 C4 mfunction 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);
7 P/ i1 B1 m2 h! E; o0 e; HdLadt = 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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