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
- L/ ~% E$ W8 t; H- t%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
9 U+ A# A) R0 N! g7 W% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
) G; A% V% b3 I% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
8 D8 p4 o5 z" _+ U2 z7 sclear all
clc
format long
# s: T, w: E, ]%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
5 M) J$ H3 ?% u# ]- k6 }& N          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
- t4 R7 D& Q$ {8 y4 O7 C4 y& n" _          90    0.08115    0.07877    0.07485    0    0.01405
$ }1 t8 \. A. J9 K3 Y) D! n' M          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
  |! \# a& G+ Q. U5 e$ v+ h0 q% q          300    0.02738    0.05448    0.09098    0.0227    0.0597
" Z- t1 s, u3 r7 s2 U% K2 d          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
0 x, k: {2 F' {- n+ u% G4 }- px0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
- V& K; Z' u8 C) i% warning off
: z2 b# n5 [6 t! W% @" }5 c8 q% k% 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')
fprintf('\tk1 = %.11f\n',k(1))
, I3 n" I5 e8 t8 b( ?. \7 W/ bfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
; i6 C5 H7 f- F8 Sfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
5 x5 A5 O) n) q4 }fprintf('\tk8 = %.11f\n',k(8))
( J& ?# ~( N* z- N: Q0 jfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
6 ]2 |$ L6 F$ ^6 k. G1 Uk_fm= k;
$ e/ M1 ]0 c0 p0 E; q% warning off
" P, y$ @5 X5 |) C% j% 使用函数lsqnonlin()进行参数估计
- w0 m% {- m" \1 G. i9 V5 l. p[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
7 {6 O, V1 a# d    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 P! p# J& H0 x6 j# D7 ]) Rfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
2 L' f0 L* w; T$ v  q) X0 Dfprintf('\tk5 = %.11f\n',k(5))
4 E( U6 N, x% h* ?( jfprintf('\tk6 = %.11f\n',k(6))
2 a( @9 |) |5 U- Xfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
! j4 j. z& u0 x7 `! z) rfprintf('\tk10 = %.11f\n',k(10))
4 M& @6 s( C( s; c5 rfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
warning off
1 o$ p" b" D' X3 E9 m% 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
9 t; Y4 o" m+ d' R3 ?9 J6 _k0 = k_fm;
) X3 r. T* }5 W* A" Z8 |[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
$ ?/ W% N5 ^; T! M! p: D. yfprintf('\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')
3 w& z2 {8 d, B  P; Ifprintf('\tk1 = %.11f\n',k(1))
* ^# ~) K; r+ bfprintf('\tk2 = %.11f\n',k(2))
- G, o0 n% H, Q: P: P; y" o7 Tfprintf('\tk3 = %.11f\n',k(3))
3 K& Z& W* b" ~$ p5 j5 Gfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
+ i* l, x( Q6 X' pfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
# T+ b* `- g$ t. J4 kfprintf('\tk8 = %.11f\n',k(8))
7 a4 }) o6 E  x  q! Ufprintf('\tk9 = %.11f\n',k(9))
& B0 r& b0 |) y! u3 M$ U$ jfprintf('\tk10 = %.11f\n',k(10))
6 G  ~  Y1 M3 E) q% k  Efprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
) p) S1 m, m  K& H& v$ q8 Toutput
/ g. y1 P5 t# h5 i% F: |tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
9 Z8 z* d' [8 l6 \7 Dfigure;
  J7 }% i4 H5 `9 Oplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
  m3 Q4 ?; c( _; O  d: m5 s8 B/ y4 z: @p=x(:,1:5)
! K. d+ D3 X$ f4 L6 W) o) l! Qhold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')

4 |& W7 U% L% u( j

function f = ObjFunc7LNL(k,x0,yexp)
2 M  H" M) {( _/ r1 L8 C$ Ztspan = [0 15 30 45 60 90 120 180 240 300 360];
3 M' X8 R( z7 X2 T# S, E[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
1 u$ |7 r8 M) y( S) [2 ~. E8 Ry(:,2) = x(:,1);
& t2 {5 t2 r" i% m6 T- Xy(:,3:6) = x(:,2:5);
, v* c2 O- ?) Kf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
2 q+ t7 G9 \  N6 `f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
  _" b3 @/ W: hf = [f1; f2; f3; f4; f5];

8 O" |+ W8 C+ m/ b* P

function f = ObjFunc7Fmincon(k,x0,yexp)
- g, `8 b( ~1 Utspan = [0 15 30 45 60 90 120 180 240 300 360];
5 k6 m% |* x7 @3 `& f! O- G; Q[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
: U. c2 f0 q5 qy(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
* c  [2 ^4 ]0 c  W6 P1 bf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
' r/ p! P! g8 Z( U; _/ u    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;


( G: Q8 v; k6 C0 q. ]
  P. K0 a( f' c* U3 J
, {$ F* E% v' s$ ifunction dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
$ b) C- T" D9 ]7 s5 C' e1 \dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
* v& P) [/ u7 i. P* @7 I1 wdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
3 N1 o6 Y2 c& P, S7 z/ N; VdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
9 j! ^1 z* V, v* I: tdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

: l. @6 K# w  V$ ?/ z1 D2 j7 r1 o$ H- N

董事长之友

蒙的一比 大哥
' D$ ?* a, A3 ^# o% M  p0 h0 }