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
# ?' k" b7 J# Z+ h3 y/ ~% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
7 d1 s4 ?. O" U7 R; S5 L% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
5 t7 q8 D$ P2 `. `; o" E- s* B- H. M% dLadt = k(7)*C(Hmf);
  G- V  z% C( ?% ~7 y%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
) u" J/ m4 F7 J; i  Mclc
7 K" T( f! b+ x/ f  G/ Jformat long
4 l# q* ^; L: ?/ j%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
3 l+ a* d8 l* F6 H3 a! i  Kinetics=[0    0.25    0           0    0       0
- u" C1 I0 v( D7 }          15    0.2319    0.01257    0.0048    0    2.50E-04
          30    0.19345    0.027    0.00868    0    7.00E-04
' K8 U9 I- h8 U: W          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
' E; _. i% W. J9 S6 O0 q          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
8 t6 \4 n' \0 O# ^% r          300    0.02738    0.05448    0.09098    0.0227    0.0597
% k1 k( a5 a' X5 X  v2 F/ i: t# [' G- 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
( \' W0 D3 o- F4 z% K# _! flb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
) p2 z; q8 A% {  v' ]1 zub = [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]
% warning off
% 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')
) z) [& z5 x/ K1 A& T$ v: zfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
' X7 {' A  {8 A4 j* ~fprintf('\tk6 = %.11f\n',k(6))
* _3 V& A! D1 ~$ B3 A* o' B9 gfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
& V# T* t5 ~% o1 L$ Bfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
" z4 }' Q& i/ m9 B  J, Gk_fm= k;
% warning off
5 b& j$ H! {  f0 f4 ]) y% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
7 `. \& [1 r; G  O5 P" `    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
. C* t, Q$ j' @; @  h# rfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
# ~( E% y# \$ I1 d: k( Xfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
2 a0 X$ [/ D* \fprintf('\tk3 = %.11f\n',k(3))
$ a% w' v4 o+ X) B9 a3 w2 Vfprintf('\tk4 = %.11f\n',k(4))
) t' W+ F& p9 b: L0 e( Ufprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
% `3 f7 v/ I" dfprintf('\tk7 = %.11f\n',k(7))
; |' G4 ]9 r% }7 j+ [" H" d; Jfprintf('\tk8 = %.11f\n',k(8))
, u/ b- c) a8 ~6 `2 [+ R6 c5 lfprintf('\tk9 = %.11f\n',k(9))
$ l4 Q6 H/ p2 t! cfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
7 t. v& _; F: M/ u7 ~1 m* poutput
warning off
, V4 K6 E* c5 S/ U( O' w3 ]% q; r% 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;
  f2 f0 L; G- m[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
$ Q! G0 ~- j8 t" W/ {8 [; G9 j9 Wci = nlparci(k,residual,jacobian);
) ]3 r( g* j* w0 B5 ~+ t1 jfprintf('\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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
; ]- X* [. {1 Xfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
5 r$ G- N% H3 I/ H6 N, l# ]' Mfprintf('\tk5 = %.11f\n',k(5))
% ^3 E: ^- e+ C% V- ], Q3 D/ l7 Wfprintf('\tk6 = %.11f\n',k(6))
! b, {3 ^( s4 l7 @! d) B! Ofprintf('\tk7 = %.11f\n',k(7))
; S7 y: L0 X: E0 z4 Hfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
" @9 p- i7 `3 cfprintf('  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];
4 @0 @- s( H8 J- c: `% ]. Y[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
8 r5 |, b9 A' W  X. Y! o3 Nplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
% R( r6 q- k, _/ C8 ~figure;plot(t,x(:,2:5));
0 y6 W( i( ~3 ~, s/ q: K; dp=x(:,1:5)
* a) L# |0 s: Jhold on
) J6 V  E& E8 K/ R( y# Xplot(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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function f = ObjFunc7LNL(k,x0,yexp)
1 I7 ^* C' A2 [  D% N' o( ftspan = [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);
0 X: ~% o1 F  G3 ^/ p: ^f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
; F: @4 m( f; S3 \% f6 K1 f* L, Af3 = y(:,4) - yexp(:,4);
# f3 t6 }( \2 l# p6 v1 @8 Hf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
2 X3 b* t8 y9 B% g1 c9 x5 Jf = [f1; f2; f3; f4; f5];
8 \) Z" O5 X$ n+ W: t, \
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! Q1 s5 \9 O" u  N; i' F
function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
3 c3 g: _, T! n/ i+ Q& O' m# q[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
3 w. N8 Z  _% r3 x' z0 n. _y(:,2) = x(:,1);
/ m7 c/ g: d! T/ my(:,3:6) = x(:,2:5);
6 o" z+ G4 L8 l. p5 p, C* Rf =  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) ;
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function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
% Y, d7 `! h$ G3 N* |! Q; EdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
. e' t! }% E, s3 ]# }" n* V; F6 z( C8 fdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
) f9 g& e1 q9 Y  O: t0 odHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
1 ?, b! a* v4 ]  `. `
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