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
4 u+ v! J; x8 |. X; J9 [7 Y' b% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% c$ x1 I9 x) G1 k' Q4 ?% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
; q: W) c1 ?+ Y: p2 [' `1 q; A# e% 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
clc
format long
+ I0 G( c6 q0 H%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
% n- V& Q5 E& W+ j1 n  Kinetics=[0    0.25    0           0    0       0
$ c% B' t% k: S7 n: A9 D  O          15    0.2319    0.01257    0.0048    0    2.50E-04
0 N% L: a% y7 g8 W          30    0.19345    0.027    0.00868    0    7.00E-04
  B  x& N4 b, c* m& O+ K          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
          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
! t9 q5 }4 v; `, U8 O4 T          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
' E' H, d, K$ W  }4 n2 }8 ~1 A" m7 Sk0 = [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
4 b/ k, p" s2 f6 k- v$ o7 Dub = [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]
5 A  L9 z9 e& o# @3 s0 L" U% warning off
' z$ X! n  H" ^- P- s% 使用函数 ()进行参数估计
" U- ?" J7 d" |& |[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
# ]/ Z. S+ ?7 |3 M8 ifprintf('\n使用函数fmincon()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
- C6 p( i4 s6 O+ z- }fprintf('\tk3 = %.11f\n',k(3))
9 [: I, L/ B/ C9 B- y! K$ G# ^fprintf('\tk4 = %.11f\n',k(4))
2 `0 s0 }' s2 L. O- ^fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
+ W3 ?) A8 i% W& w6 j' Kfprintf('\tk7 = %.11f\n',k(7))
) ?) e' B3 e1 I" z0 ~) O9 jfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
9 c7 Y; D# N5 p& J% [8 p$ Lfprintf('  The sum of the squares is: %.1e\n\n',fval)
6 n8 a5 P% y' `6 Q0 w, Kk_fm= k;
% warning off
% 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);
. @3 U) f0 t. }. d+ u7 z4 Mfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
5 }$ E# H0 }6 D" s$ yfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
0 Z. x. A+ x4 p! @& B+ ], M; _/ L+ p$ jfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
* g' X+ e9 _& }# f3 T) M- ufprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
& Z& b& w2 Z; u/ g; B2 b1 v; Efprintf('\tk10 = %.11f\n',k(10))
' P5 Z/ f4 X: g( U; I  g3 i9 [, Sfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
. }% I# Q' `% d% soutput
warning off
% X* U# j9 ^! u& k7 \' l% 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
. J% C7 F, L& v/ o3 s7 s9 b! yk0 = k_fm;
& m( `. ~! M3 h, G8 i$ I& G[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
1 s1 ^, o) K9 T    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
! c  K* O; o4 G4 z3 C" Wci = 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')
; C- k0 d( J+ ^4 W, [& u8 Afprintf('\tk1 = %.11f\n',k(1))
3 l5 Y0 ?# [6 vfprintf('\tk2 = %.11f\n',k(2))
0 M/ a) w$ U1 v3 }1 Z# E4 ~fprintf('\tk3 = %.11f\n',k(3))
/ a# [8 j0 [% m" U3 S. t' J, ?* wfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
. c/ L5 y* ~- ffprintf('\tk8 = %.11f\n',k(8))
& \* R( ?3 r6 U0 }fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
$ h& H" P) k& ?" S8 W! T! }fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
output
tspan = [0 15 30 45 60 90 120 180 240 300 360];
7 x; O' i( o' I: P+ q6 X[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
0 N8 p' B7 _3 r( V( K+ j) _figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
$ F& _) Q7 l% w9 s( |" b& Hp=x(:,1:5)
hold on
0 E( l: F: d6 D5 Lplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
/ Q8 ~- ~) ]; p5 h" G5 I3 i


1 S9 L9 Z/ [5 M, ~. ofunction f = ObjFunc7LNL(k,x0,yexp)
: _2 P4 J3 T% D" itspan = [0 15 30 45 60 90 120 180 240 300 360];
0 f; W. @! o4 A/ ~( N  `% C[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
- N* A* w* f. p2 K# uf5 = y(:,6) - yexp(:,6);
: p* O% y% L8 q. C7 df = [f1; f2; f3; f4; f5];

' R2 ]6 P0 N5 f2 }3 j
, ~' d: o( h% x) r* _( L
function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
1 N1 _; `# N( \! j) o3 J( o[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
! b/ F$ {) L& i% u3 @5 yf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
1 \  k5 F& ~9 r% x, N9 ~7 D: g    + sum((y(:,6)-yexp(:,6)).^2) ;
3 O- Q7 x; N/ F5 w) j& ~

- Q- F" d/ v) \- P' ~

8 Y+ G0 Y# S0 ~8 ]$ g3 @3 n/ ]  _function dxdt = KineticEqs(t,x,k)
0 i1 C9 |& O; OdGldt = 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);
+ W# `+ I  {( C. [dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];