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
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% l( h; v$ `3 A, h% P# `% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
4 H/ @4 B- i! q; O4 H% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
1 u' \1 g& Q; k3 V% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
( E" E3 m" @7 A! fclear all
clc
& b4 ?" A9 O3 Sformat long
( ]; v8 |* O% P: Y( U8 [- L: y%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
6 V3 |5 |# c$ ^% `3 o' m0 ?  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
          45    0.15105    0.06975    0.02473    0    0.0033
4 x( m6 K- G+ G& n          60    0.13763    0.07397    0.02615    0    0.00428
5 o+ E. x, n7 ?& F& T+ [          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
2 M$ x9 ^/ }1 X! ?" q          180    0.04488    0.0682    0.07135    0.0091    0.03623
1 _4 @2 X, R: x          240    0.03653    0.06488    0.08945    0.01828    0.05452
& |* a5 i  C( m, Q          300    0.02738    0.05448    0.09098    0.0227    0.0597
% `: P1 Z. `  P, l! K8 N          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
- n. F9 G2 j6 |) q" J" ~0 B' @! wlb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
1 L0 q% h3 D! S% H4 ?$ Q1 W+ b+ bub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
" w* f( F6 T$ Y7 A) Z8 T6 B' Zx0 = [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
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
; _( }8 l$ C+ G+ S' ~; s5 X0 Ffprintf('\n使用函数fmincon()估计得到的参数值为:\n')
8 u2 Q3 L* U$ T! r" [4 @- \0 }! Bfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
$ q! S4 M& \: g# Nfprintf('\tk3 = %.11f\n',k(3))
! B8 \% d1 _( Z, qfprintf('\tk4 = %.11f\n',k(4))
5 Q6 l; ?1 Z  Q! c5 _fprintf('\tk5 = %.11f\n',k(5))
9 X9 e( S/ P7 f( H1 P9 m3 Ofprintf('\tk6 = %.11f\n',k(6))
) Z  m, Z, R5 {* k6 @2 `; ?) N' g4 Ifprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
; R  n+ @5 K% G. }/ B; L! Vfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
8 ^$ g, |5 L( P, \) V" _k_fm= k;
4 X  u; u/ s1 t, ?% warning off
. n1 ~  u: ^. ~/ q3 W4 G% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
1 j+ j6 A+ n  y" R    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
: G* i3 z3 k7 M5 p+ @ci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
6 O* [; Y1 o! j$ A2 ofprintf('\tk1 = %.11f\n',k(1))
& K$ S) B- j9 f, Bfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
7 c! |0 U) `" q! n% j% v# Vfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
- @1 [% ]% D0 q5 Vfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
2 m4 N) M. R9 ~+ |6 Mfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
6 S7 E, `8 \0 t+ Ofprintf('  The sum of the squares is: %.1e\n\n',resnorm)
' t  `: @5 a. J7 @' L+ R5 bk_ls = k;
& h4 K. M# I4 {4 X( Youtput
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;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
& {. V! h& _* gci = 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')
' t% M$ b5 v4 d0 s! t7 Y0 `* ufprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
- |( G" y& `# b' i" F' tfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
- v2 x0 W. c' U! g4 l9 Z. pfprintf('\tk6 = %.11f\n',k(6))
# @$ G$ l; T/ K4 O* [% mfprintf('\tk7 = %.11f\n',k(7))
% q9 G3 J( v! Y$ ~. Wfprintf('\tk8 = %.11f\n',k(8))
1 \/ V$ K' @6 M% [$ |8 dfprintf('\tk9 = %.11f\n',k(9))
5 ?4 m3 }1 o2 ^7 n: a7 R2 Z# r) G% pfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
7 D# {" }1 P$ e4 c- Otspan = [0 15 30 45 60 90 120 180 240 300 360];
8 j0 q) y" u' {) n8 p( u[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
( R7 c9 r& l' K- u: s) X! Oplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
- b2 V$ p) G! e5 ^figure;plot(t,x(:,2:5));
p=x(:,1:5)
hold on
' j4 n6 F7 b1 P4 H0 T( Hplot(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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9 C* \* v5 a$ }* {# q  V& a; \
) i* Q3 k' e- \: f2 S0 Mfunction f = ObjFunc7LNL(k,x0,yexp)
' H  u; e' s5 n3 gtspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
% o6 v: q$ b) D, ky(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
# Y: p1 s- a# ]! pf1 = y(:,2) - yexp(:,2);
' y5 i/ [  T. z) w9 I0 Hf2 = y(:,3) - yexp(:,3);
! a) H0 ~$ E( ^2 Z! c# M  Pf3 = y(:,4) - yexp(:,4);
3 f. \4 ~3 G6 z" r- p. H: Ef4 = y(:,5) - yexp(:,5);
: z7 B& O! z* Q* U& G) rf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];


7 y. Z1 q+ e2 E# q
2 x  X1 X$ Z* f6 g5 T( l9 Gfunction f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
$ l( f+ d: m/ x: V) ky(:,2) = x(:,1);
y(:,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)   ...
4 ^/ P! J6 B. w  q7 f2 U    + sum((y(:,6)-yexp(:,6)).^2) ;


+ a0 Y1 u8 _% @, s0 s

function 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);
$ ?/ h2 n' a& f  b9 a* }( [dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
/ y9 c% S# k. s% |5 D- GdLadt = k(7)*x(5);
7 z& t9 x+ q  jdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
+ `' a2 q2 V+ g' |# jdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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