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
8 \9 N4 s' d% k' d0 y" Q%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
; l4 q6 A$ ?2 e% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
7 ]9 h9 h5 k  C' n* L  y% 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);
" b# d% y6 W5 j# ~%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
" L" J1 _- X1 {$ ~7 m5 Iclear all
clc
* z) J( ^7 A6 |, o& X5 N5 Cformat long
% ~& B$ S( v- m; P7 f! L$ E6 ~  m%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
( M' Q3 n* ]# I7 S          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
; }. A) ^1 {* m: }' W( z% C$ Z: v          45    0.15105    0.06975    0.02473    0    0.0033
. R4 g' c" Y" O) h- t: k          60    0.13763    0.07397    0.02615    0    0.00428
( p' ?9 W. F* g3 F          90    0.08115    0.07877    0.07485    0    0.01405
7 _% j. _9 H6 a. l/ D* L          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
  ~; U2 O  y4 {- C5 L! k7 E$ Z/ s          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
" x- k7 j7 i5 ~- }, Dk0 = [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]
% warning off
/ p% C- B, l( I. d3 Q- Z% 使用函数 ()进行参数估计
6 x4 X! C3 E/ @9 W6 e[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')
  u# G  c5 A- f8 i* D  z6 D+ Xfprintf('\tk1 = %.11f\n',k(1))
9 ]( e: }: [' r$ x# f0 O5 tfprintf('\tk2 = %.11f\n',k(2))
+ ?( x6 ?! S' W8 K' Tfprintf('\tk3 = %.11f\n',k(3))
! h: d% f) i: Y- [/ p/ b, b# X' Vfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
) o, p. a6 {' ?; v9 T  S! }2 Jfprintf('\tk6 = %.11f\n',k(6))
+ q4 O6 d; _7 E; nfprintf('\tk7 = %.11f\n',k(7))
5 P0 P* r, I) ~1 @fprintf('\tk8 = %.11f\n',k(8))
) Y3 w3 z( ?: z) J5 B  _" k/ ^. e/ tfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
3 r' r6 A; I. ffprintf('  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
5 e' n& I' @3 R6 W/ Y[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
- }0 {8 h! q. H% z# W: p6 a1 q' a    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
' D- e) @, A1 R/ X# v3 Bci = nlparci(k,residual,jacobian);
. w3 w( X- {4 n2 y# L* Q9 y6 nfprintf('\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))
fprintf('\tk4 = %.11f\n',k(4))
5 a. a3 V1 u5 p* a( x9 n8 Wfprintf('\tk5 = %.11f\n',k(5))
8 C9 o7 ~1 Y2 a, [5 c7 R0 lfprintf('\tk6 = %.11f\n',k(6))
8 |) W) p$ Y1 O3 l: {) q# ~* ufprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
( ^7 f. M+ T! a$ s8 w4 Mfprintf('\tk9 = %.11f\n',k(9))
6 q- Z* t6 D+ tfprintf('\tk10 = %.11f\n',k(10))
7 ~( m& H, p- l1 f! B: Q. ~; hfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
( B. X" K5 i" k$ {# sk_ls = k;
( T& |) o% M7 s+ I3 q# A% koutput
$ c8 H6 Q+ d) ^) qwarning 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;
2 {; z# v0 U/ \% e[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
* @2 s  a" |4 U: Q7 p) _! [    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = 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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
; m5 R5 R  C2 A! |; [' y  D9 N) Ffprintf('\tk3 = %.11f\n',k(3))
2 R7 b5 D7 N. f' d" Z5 Sfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
4 m* B8 u2 A+ J1 Gfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
6 x# G8 J; t' A4 ^* J5 _2 ofprintf('\tk8 = %.11f\n',k(8))
2 M8 K& r! |9 T( vfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
2 a3 n8 A0 i) R+ m! t  _k_fmls = k;
output
' ]/ l1 E* @8 p& Xtspan = [0 15 30 45 60 90 120 180 240 300 360];
4 o& N; ?( \6 z. x) ^[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
  b# z( u( ?9 _1 Aplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
  z1 ?% X2 \: l$ _6 {p=x(:,1:5)
hold on
7 w, D& W: B7 T# 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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4 q+ e2 a9 O3 E0 Jfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
# n, T4 @, X/ {2 d/ u[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
: u" X7 o$ z# W) r/ [, By(:,3:6) = x(:,2:5);
8 J* ?7 Z' R! c6 mf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
1 m) p8 c& N( j4 J7 Pf4 = y(:,5) - yexp(:,5);
" ], F. @9 G4 @' x9 Z9 ]' e7 Mf5 = y(:,6) - yexp(:,6);
: G. `! ]- L3 }: R. |8 \f = [f1; f2; f3; f4; f5];

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6 s& v% p7 i/ q5 z+ ]& {function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
1 r6 G4 C$ |+ `8 A: a[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
5 c( E5 o6 u/ w) k' S2 p0 N9 Ny(:,2) = x(:,1);
/ E$ ~; ]! {  F2 |% w4 Ay(:,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)   ...
* u$ t5 ~3 ~0 Q- Y3 E) b( P  q( n    + sum((y(:,6)-yexp(:,6)).^2) ;

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# {) |' c- C  F6 @2 lfunction dxdt = KineticEqs(t,x,k)
! P- o; \+ ?4 e! v0 f" EdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
6 m8 c' b" k! r/ `' g4 rdFrdt = 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);
  P+ g3 k; ~! |7 J& `) c1 OdLadt = k(7)*x(5);
  T9 N6 e, l4 e" @dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
$ V! P* k0 N2 f2 r# Fdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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