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
5 Q0 s' N! S+ ^% k6->k6 k7->k7
( a( u6 z7 O7 ^7 X% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
+ ~5 u) P$ c5 ]4 J% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
' {% a! D0 \5 z$ x& E7 q% dLadt = k(7)*C(Hmf);
8 |$ @* H( P+ f; r3 s5 M* K- i%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
  V  O+ A; d0 K0 Uclear all
clc
9 w; z6 S* `, c; w- @format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
$ ?; G; S7 o- [+ ]$ [          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
          60    0.13763    0.07397    0.02615    0    0.00428
. ?, J, g' {! }4 _7 _+ _3 A7 y          90    0.08115    0.07877    0.07485    0    0.01405
& {/ m/ [2 a1 I0 h          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
          300    0.02738    0.05448    0.09098    0.0227    0.0597
+ }! E2 v! h! J7 u0 [, \" ?          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
: A. I) `3 x: G. F6 X7 D+ Aub = [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]
' E7 B' d+ u6 }# s( `' ?0 H$ S  i% warning off
. ]2 v- Z- g! x1 o" ~% 使用函数 ()进行参数估计
[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')
) ]; \2 {& N$ O7 @2 ?fprintf('\tk1 = %.11f\n',k(1))
& r3 h6 z, W6 t% u/ ~( i2 Qfprintf('\tk2 = %.11f\n',k(2))
5 A. R) n2 N- H& V( j1 Bfprintf('\tk3 = %.11f\n',k(3))
) k# N7 S+ t& p3 z" @! M; Jfprintf('\tk4 = %.11f\n',k(4))
2 m# i( S  f* B# A/ n/ Ufprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
' E/ w2 e4 F; s: Nfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
& F5 Z0 G3 p+ H/ |  @. u" V3 Wfprintf('\tk9 = %.11f\n',k(9))
! ^0 c& h, z: lfprintf('\tk10 = %.11f\n',k(10))
" Q( ^8 W  j5 i: Cfprintf('  The sum of the squares is: %.1e\n\n',fval)
# t& ?# ?- L% G& s" e; H9 L" vk_fm= k;
2 r* m2 l# F: z4 I! d; N( I4 R% warning off
1 A; x" ?3 f3 \4 H. f* }% 使用函数lsqnonlin()进行参数估计
8 X4 p/ m. X0 u6 \# n& Z0 R5 q1 v[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
6 P" `6 v( ?2 z. d1 T5 O* j    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
; s- m5 y2 t, D3 Gfprintf('\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))
! Q! @8 D( L$ a* Pfprintf('\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))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
5 ]# R  e9 L/ V2 Y$ c* L4 g( W6 noutput
3 Y( o% s! O3 H/ Y! Twarning 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);      
ci = nlparci(k,residual,jacobian);
  a& T  @( ]( }8 A9 o1 Gfprintf('\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')
+ n" j+ v: a( V+ L3 nfprintf('\tk1 = %.11f\n',k(1))
& ]% e) s! j$ j$ _. o! p: D3 {/ {fprintf('\tk2 = %.11f\n',k(2))
8 c. |* \0 ~% xfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
# b" P! N( }9 ]# Q0 `fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
8 y6 C+ T% C- h) h' \fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
5 X$ h. h6 o' p- t" R6 t$ i/ G' ek_fmls = k;
  [4 K3 _( [2 @output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
" F/ o2 u% t% R[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
6 l3 w7 e" ]( d+ ?8 `4 I  a+ k; ~plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
2 @7 _0 V  D) L8 Ifigure;plot(t,x(:,2:5));
p=x(:,1:5)
( g4 g2 A  b0 l3 d. e- Vhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
2 d. p4 V8 O, A2 ~
6 b! y  J5 C  [1 Q' a

# r: V1 I: O/ R; ifunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
5 V; V2 }7 M8 o8 Z% x[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
, Q  o. D6 X- u' I+ Vf2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
/ d& W) k6 x; U  {2 _& D/ qf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
9 d1 r$ B! z6 j4 T1 ?' \  Zf = [f1; f2; f3; f4; f5];



function f = ObjFunc7Fmincon(k,x0,yexp)
6 S5 W' Z; l5 N) P9 `6 Etspan = [0 15 30 45 60 90 120 180 240 300 360];
4 Z* z+ M9 u% {/ J) A[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
: m; v9 d7 t1 N1 z+ ~# hy(:,2) = x(:,1);
3 N1 ~6 b8 h' s6 s5 H  [y(:,3:6) = x(:,2:5);
8 ?" V4 t( M. g  S2 V# d& l% vf =  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) ;
7 X+ [5 t1 D& l


; d+ U# J2 N& V2 M
. ?2 I1 S. j; ?$ F. h! @1 Z( v4 S& pfunction 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);
dLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
! I6 k% _6 {" r9 t, ndxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


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