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
% E1 Y8 S; F: |2 T# g( r0 l%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
" B+ V  x! d" X2 A+ Y% k6->k6 k7->k7
! q- `" m' [8 F5 j+ F% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
1 N% w4 N! N7 E2 I- l% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
7 R1 S# C+ F# }+ J1 |. X) D% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
5 W1 p3 ^; ?! Aclc
" ?/ c: _6 Y# L9 |8 kformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
+ J# D5 E0 E4 X4 A. U  Kinetics=[0    0.25    0           0    0       0
9 z  E  C; h' N. ]# G' z. Q' `          15    0.2319    0.01257    0.0048    0    2.50E-04
) t) m9 [% V8 x2 I& j8 O# h* e1 ]          30    0.19345    0.027    0.00868    0    7.00E-04
; e- }* F# P- C( z          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
/ r% {" L& h) E- s          90    0.08115    0.07877    0.07485    0    0.01405
5 f3 p5 E) M2 v2 u  Z! A! ^- R6 W          120    0.0656    0.07397    0.07885    0.00573    0.02143
" u$ X; `( K6 J! @          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
          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
1 T( ]" t3 D+ [& x: @- Lub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
* d( n2 e0 E2 k  l" K5 Vx0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
0 `$ B% w/ A" X0 S% warning off
/ V/ w, e& N/ s' a+ C% 使用函数 ()进行参数估计
) M1 d, m1 Q- i/ ~[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
' D- w4 e4 D1 x' n2 w3 Qfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
4 v! x% ~7 p6 c+ c; B+ Q- h+ v* hfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
9 Q' P- ^& S8 H/ u3 M. H5 R! xfprintf('\tk3 = %.11f\n',k(3))
, h+ s# q: _  p! ~fprintf('\tk4 = %.11f\n',k(4))
8 ~/ j& A6 [' Q2 Cfprintf('\tk5 = %.11f\n',k(5))
) T$ ~# u. G) K) ?# ]$ A8 ^fprintf('\tk6 = %.11f\n',k(6))
4 y% c  X: L* B% h$ xfprintf('\tk7 = %.11f\n',k(7))
3 o/ x% }" P/ }fprintf('\tk8 = %.11f\n',k(8))
- y/ _6 Q& U9 I$ ufprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
6 k* q- L( t9 ?% k* o6 a( {fprintf('  The sum of the squares is: %.1e\n\n',fval)
3 o" s0 l4 B4 a# Jk_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
0 S2 [9 T; L  w. \' J" ^[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
' |. S! d8 U/ }  [0 M5 d  ^& lci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
. V  e) z3 I6 `, n7 Pfprintf('\tk1 = %.11f\n',k(1))
3 }+ R( ^1 N9 j+ }: z8 W" Hfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
9 K( X) z# ^( Y: ^5 [fprintf('\tk7 = %.11f\n',k(7))
" o3 @# b' T( p2 j9 |( \% K* }fprintf('\tk8 = %.11f\n',k(8))
4 N7 [. _6 f- i  n% q* `  V9 e# |fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
6 }1 |" y- Z- H0 I# n4 ak_ls = k;
output
warning off
1 j: Z  Q0 J- R/ f3 ^3 f9 B% 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
0 N7 G; I$ `, g; f9 o- I) j# x% `k0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
. G5 L& ?6 \: T! n) v+ }ci = nlparci(k,residual,jacobian);
3 h2 ]& X3 X9 E8 _% V% }, B# bfprintf('\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')
- H% c7 K% h: f# N0 b  }9 nfprintf('\tk1 = %.11f\n',k(1))
1 ]- M' i. X; R& q1 ?; ifprintf('\tk2 = %.11f\n',k(2))
* Z0 M1 e& ?" x' x4 M+ J# `fprintf('\tk3 = %.11f\n',k(3))
) Z. b! t( H+ |fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
: \5 h( M: E& R% L# Kfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
& p6 g* b, Y* e  yfprintf('\tk9 = %.11f\n',k(9))
7 B9 _( Q5 f- dfprintf('\tk10 = %.11f\n',k(10))
) ~4 M0 m/ A8 A: f- B% t- xfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
  y2 W9 E/ ]8 V; L3 s2 t3 soutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
- }+ ^; M8 n. ][t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
% V* s6 I7 a5 R' E# Vfigure;
8 h4 ]; |2 }$ p  x6 z2 ?2 i) D7 C( Mplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
p=x(:,1:5)
8 \" W+ ?* J/ {- o* Ahold 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 u6 ^! t2 U% q7 L

" e$ M5 c2 ~# h/ `! B6 N- ~% D( B
function f = ObjFunc7LNL(k,x0,yexp)
+ Q- x5 K+ ]2 a2 ~tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
. B1 K, R. w* rf2 = y(:,3) - yexp(:,3);
; N3 K( u( \! \* L0 g$ If3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

$ q! ?2 T! ?3 l+ g2 W/ @$ Z5 h

, O" r: m/ X5 u( u( `$ `function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
3 G7 a6 p' D  P& ^' v8 ^( i1 j% p[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
( y7 I+ L$ A$ E8 G: q3 r( Y, Ny(:,3:6) = x(:,2:5);
) I9 W4 G/ }$ n# t: bf =  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) ;
6 N: ^7 }2 |! e% o


' @; G3 J4 f- D5 B
/ _% L; @8 g# G9 x/ Vfunction 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);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];