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
2 E: E5 h# {" @! O! ]%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
4 V9 \7 @% ?9 M2 i2 a% 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
1 z4 f( c. P; \* [0 `6 [%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
9 q, h! [- |" B+ d9 V" r9 c: s  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
- `, q) Q/ A% r/ j( R          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
, [+ _+ R3 ~. g          90    0.08115    0.07877    0.07485    0    0.01405
( R3 S3 W) E5 L) P1 }          120    0.0656    0.07397    0.07885    0.00573    0.02143
3 c# j; p( t" d, H; `          180    0.04488    0.0682    0.07135    0.0091    0.03623
3 r6 u: R: X4 {' G5 w$ p          240    0.03653    0.06488    0.08945    0.01828    0.05452
          300    0.02738    0.05448    0.09098    0.0227    0.0597
* |+ X, A5 ]( C- C. M, G  k          360    0.01855    0.04125    0.09363    0.0239    0.06495];
) @' |+ S  g; E" dk0 = [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
x0 = [0.25  0  0  0  0];
yexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
! m* Z% @. l+ U& w* k" Y( @% 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))
fprintf('\tk2 = %.11f\n',k(2))
2 L% y7 e2 Y/ i4 Tfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
& W2 ^8 f9 e4 L+ f1 Z1 \, Dfprintf('\tk5 = %.11f\n',k(5))
5 q- o5 Q4 ~+ Hfprintf('\tk6 = %.11f\n',k(6))
# V: s4 N8 y; d' rfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
% o; b( V$ i" P0 `1 s* u4 X# ^* `( sfprintf('\tk10 = %.11f\n',k(10))
. J+ c4 a* a4 w9 K! K+ ~( ~* Dfprintf('  The sum of the squares is: %.1e\n\n',fval)
& T) c/ ^! {5 m/ {' ?* hk_fm= k;
" ~( q7 G, m, X" f% j7 B+ d% 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);      
* a6 M9 k9 M5 e% b. v( E( B  ^ci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
) C# g3 {7 p9 Ffprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
9 d: V( J7 i; J; [1 F- F: Gfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
. [% x7 T/ J* gfprintf('\tk6 = %.11f\n',k(6))
1 Y6 _7 y. T; Y6 ^" w1 Vfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
( e) m! P& T. c) D9 s8 zfprintf('\tk10 = %.11f\n',k(10))
0 V' {. O0 b/ A' W! w. W! y( ffprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
6 k" E( V# i( {: y4 soutput
warning 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;
. H3 W% j7 }$ h% l% f0 {  k& w[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
) c# \/ k, ?8 m9 ~8 Q: y9 U    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
7 c$ o0 Q6 P2 U/ Yci = 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')
6 M% [( ~3 J, h* s# s( s& Rfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
: d7 E9 m' ]) z0 H" c& B. X, r" ^$ Cfprintf('\tk3 = %.11f\n',k(3))
4 L1 N$ f# L" i* m3 U. \fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
/ ^; z! x% U& C4 X% l% z$ cfprintf('\tk6 = %.11f\n',k(6))
$ A6 z# p% a; H/ H5 Y& j5 cfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
! d- y* y4 I) {. D- gfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
3 _. Q0 |) H% I% \$ w  E' ~: uoutput
# l" f6 B) q5 J0 r+ \* ztspan = [0 15 30 45 60 90 120 180 240 300 360];
' A* @! b5 o, h  D' v[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
; x2 t) e8 Y4 _$ w2 {6 Cfigure;
3 H) `: s! n* U# Y: qplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
" B1 j+ [# I& \$ Y9 K7 |figure;plot(t,x(:,2:5));
p=x(:,1:5)
8 v; \8 _: J9 |( x  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')
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# b" B& L$ Y* y3 W6 v$ H8 p$ ~

- o8 Q; R: _+ o/ xfunction f = ObjFunc7LNL(k,x0,yexp)
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);
5 y) b3 A2 r3 S- Lf1 = y(:,2) - yexp(:,2);
" u* v1 y) k; ]7 ^- S0 Uf2 = y(:,3) - yexp(:,3);
* l, x% z5 y$ I- B6 `4 Q3 Q4 {+ m0 yf3 = y(:,4) - yexp(:,4);
7 G- z0 X4 z3 S0 o) Uf4 = y(:,5) - yexp(:,5);
f5 = y(:,6) - yexp(:,6);
5 r  n* w0 N$ ef = [f1; f2; f3; f4; f5];

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; l# C% W  x) X0 f8 y
function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
* Z& q: n1 F) Fy(:,2) = x(:,1);
& `8 G  ~: P& n  Ny(:,3:6) = x(:,2:5);
f =  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)
+ q; J, J" w) j6 v" PdGldt = 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);
2 J; u$ j. z5 \) ?dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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