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
+ C0 r1 s) v# z. [: n%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
1 w  ?& x. L% Q8 f% x% k6->k6 k7->k7
0 u) o* p8 k7 {( u) I+ L% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
& M1 p' q# \, O  y( H$ Q, T5 {2 I% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
6 `% }% m  ^- y$ F% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
4 G1 I( u; M" p6 {" Tclear all
clc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
2 _3 H0 `- k) w1 r. ]  Kinetics=[0    0.25    0           0    0       0
: b, F1 E; H- ^9 V9 C# {& a          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
$ y; K6 u8 {- h6 N& t          45    0.15105    0.06975    0.02473    0    0.0033
5 H$ J+ ^% W. O0 `5 x          60    0.13763    0.07397    0.02615    0    0.00428
& G3 |5 g4 s. C% Z3 F0 e          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
+ i" [" l- c: z0 {+ L9 a; B& r          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
- t' i6 |" p0 e) F1 e, R; Z          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
0 P7 @' C; ?0 g+ N2 Y. j! uub = [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
+ v. |6 E8 N9 z% c/ m[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
" w6 m' b: o8 |; ]* W5 D8 V; Pfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
2 ^2 ^) }1 b, n/ N3 c( wfprintf('\tk1 = %.11f\n',k(1))
3 @* e7 ^$ E/ S+ P8 ]1 s9 _% X8 Q# |fprintf('\tk2 = %.11f\n',k(2))
+ U+ T6 M* ]/ ?# h0 Nfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
& s, y: `! g( }0 m: U3 J( ufprintf('\tk5 = %.11f\n',k(5))
% v) s5 R- a+ a& `+ Lfprintf('\tk6 = %.11f\n',k(6))
, u5 e# |& V- d9 }( L: cfprintf('\tk7 = %.11f\n',k(7))
  e  @6 h" I* g" Q9 ^fprintf('\tk8 = %.11f\n',k(8))
  i' A* Y& t2 k* V# u* cfprintf('\tk9 = %.11f\n',k(9))
' s- b! X9 n7 T2 T$ r" c. |fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
0 g8 b7 |% J7 Y% ~5 M6 Z) _! A% warning off
) c  Z3 l" b4 E/ a- l% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    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')
8 e9 t2 [! R' x  {fprintf('\tk1 = %.11f\n',k(1))
' H# ?  O" ^* Z( D  _fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
; i9 e  b9 n$ H. h2 ~+ tfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
" p, U7 t( {" sfprintf('\tk9 = %.11f\n',k(9))
1 Q* j9 }& Y" w& `( b9 y. p+ [* d  vfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
! F2 [/ {' F: @7 |/ [# h/ |3 n5 zwarning off
2 R8 H, F- K# j+ R" [0 \" R! D  Y" R$ E% 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;
# N! [; X, B5 m6 Z' Y4 m( |7 M8 `) r" I[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
% Z" h. ?, e  h3 z    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
* A2 Y: S/ R% n3 x) s! S# Uci = 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')
$ q5 \; V2 j+ ]' L  X# u' Wfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
- H( L' S7 ^' v& jfprintf('\tk3 = %.11f\n',k(3))
5 k% B( z! T0 n. Y' d2 Pfprintf('\tk4 = %.11f\n',k(4))
0 w- ?, E' @& a- ~5 {0 Hfprintf('\tk5 = %.11f\n',k(5))
- \- r7 q  I7 d, a6 B6 }4 j; j8 h/ Bfprintf('\tk6 = %.11f\n',k(6))
; V2 k( c6 n0 R- Z, I& ]fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
( N( j! Y5 \  N/ Hfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
  V- e# l. g1 Q! U9 Ck_fmls = k;
output
2 J7 ]. L) X% ^7 Ktspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
% e# e: y2 z9 r. y4 r+ r% rfigure;
- |$ R  g9 m2 W- ?) oplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
# j+ Y- [. {: T* e, R* d3 O( Mhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
, `: u1 N- q" k; ?3 K# \

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function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
3 F, W/ ~" |# T% i; t" f8 m& V[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
3 U0 |# x) ^/ o# ?  H, Ty(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
  z9 n2 v$ E+ [" ^" C  s  i0 `+ {f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
4 Z- t; i& v% Y! m/ U9 o$ i2 Ef4 = y(:,5) - yexp(:,5);
; {" D7 f9 b! @( [6 Qf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];
2 D( u) a: B" T: N  A' u3 ~


+ F* S! D6 F' ?/ ufunction f = ObjFunc7Fmincon(k,x0,yexp)
3 @& F& x2 K" n- n+ M" gtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
& y! x+ c8 k; r& S* U+ Oy(:,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) ;


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function dxdt = KineticEqs(t,x,k)
1 L( p8 l# _" z& v" o8 G  ]dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
$ d( N0 r3 ~; L9 s+ Q' Z) b' edFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
$ \' F2 G  L! A7 }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);
* q, A9 k* ]1 {5 b( u* O/ `6 P" cdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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