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
& D+ d' L, |! P: r& W& a8 p7 @: b%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
& S9 ^% [3 b) K- m0 i) V% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
3 v' g# g% a" J& N% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
. C) P6 u) ~  i& K% a5 b) s8 x% dLadt = k(7)*C(Hmf);
' X3 C/ M7 B! u7 I. U) V; h+ P%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
8 y  X% q) J2 F0 e/ |1 j! Xclear all
clc
. G) T) I/ `: O3 m2 V0 Y* ]format long
2 C# H3 ~: o9 A9 n%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
3 F5 Q5 B3 x" t  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
) A" E+ j  W+ K1 C, b0 i- O) _          30    0.19345    0.027    0.00868    0    7.00E-04
, F* u$ L  R) r' P( Q; I          45    0.15105    0.06975    0.02473    0    0.0033
" K! Z; ]) A; i2 Z- n          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
& ^$ \5 i9 T1 B2 `4 B( d  ^          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
6 d" d* b7 o0 m; A7 plb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
% }9 ]5 Y- g& K+ d& H9 ], i' Sub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
' A+ n0 e. @# n6 d$ j8 [x0 = [0.25  0  0  0  0];
$ s8 Q  z% W: _/ g- xyexp = 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')
fprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
( S9 H* h7 X* z. [fprintf('\tk3 = %.11f\n',k(3))
* O" w+ Z  D2 l" r2 N; H, k$ Qfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
) U$ w! v( B$ mfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
; h8 K3 a$ F: U+ m4 u; C3 c3 ~& ?fprintf('\tk9 = %.11f\n',k(9))
8 M5 u" ?1 z+ r0 C( hfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
# \" l" T  f! G4 g6 _: Uk_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
$ u' O+ X( f# s% q6 E    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')
fprintf('\tk1 = %.11f\n',k(1))
0 K; A5 n$ m  e! W( Afprintf('\tk2 = %.11f\n',k(2))
. D- s: N1 H  C7 N9 y2 D' qfprintf('\tk3 = %.11f\n',k(3))
4 @2 ?" r( U% Y- |  K; O3 d- R2 Qfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
% O( T3 t4 H+ Qfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
$ S0 ^) y- I( o, Hfprintf('\tk10 = %.11f\n',k(10))
# p& ]$ O$ \7 e' I8 m7 O6 y2 f, S) \fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
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
, u3 |; X: l, e4 T/ Ok0 = k_fm;
" K( r) d: U& m( a4 \9 Y$ Z$ c[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
" K, z  s' N) w% D; o    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
+ h% _* x4 h! K1 E8 ?' q/ \) V3 {ci = 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')
2 p  ~  h! N, Nfprintf('\tk1 = %.11f\n',k(1))
4 m& l. s! U: y6 Jfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
7 a' k6 L1 U" X" j& t9 h9 Ofprintf('\tk6 = %.11f\n',k(6))
9 m; Z# C- ~0 Ofprintf('\tk7 = %.11f\n',k(7))
- g* l! {( f, J+ n6 T; Efprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
  B' @8 L/ _" o6 Qfprintf('\tk10 = %.11f\n',k(10))
5 _( ~0 M3 H# x$ n2 R7 vfprintf('  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];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
) {' \5 k: \6 a7 B" cp=x(:,1:5)
& ~3 N- N5 I/ z0 z* F, U- d, Vhold on
. K3 E# T1 e3 qplot(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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/ K! ~: n* P7 z+ z, N+ ]function f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
  R4 R+ E- f$ t$ T4 W; ?- }[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
2 T; w- p8 j9 K8 ?& f3 H( sy(:,2) = x(:,1);
. M* x0 U1 W: U  U% U, |5 Iy(:,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);
f5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];



function f = ObjFunc7Fmincon(k,x0,yexp)
# |' ~4 X" R* W: C$ X! ?tspan = [0 15 30 45 60 90 120 180 240 300 360];
1 V/ Z6 Y5 |' U; y& s% H- h% q$ w7 t[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
) E! g) {* U; Y2 m- e. ?0 n% Py(:,2) = x(:,1);
+ ~' S: n' K& }& l% {y(:,3:6) = x(:,2:5);
. o4 w2 R3 N1 t, tf =  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 J- q$ `3 m. `$ _8 N    + sum((y(:,6)-yexp(:,6)).^2) ;
9 b* N) j. r' E9 E



function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
/ u, h0 }. C: CdFrdt = 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);
& V2 p$ U; v" t1 YdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
) _- z9 U+ k. X1 ], ~8 wdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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