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
: u" D1 X8 o( X  X% Z( x% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
$ X  U( q! o  n% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
- ?: |9 \4 G0 C/ V% g- s% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
) d7 Z) u) m2 }9 [" Y! O% dLadt = k(7)*C(Hmf);
%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
  J8 X% i. F0 j" v. D+ G- P0 Gclear all
clc
  a6 C. _& g1 s$ \, Y9 tformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
          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
6 S0 r' M0 U% `, c( R          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
% k$ P' z4 |- D3 h) t          180    0.04488    0.0682    0.07135    0.0091    0.03623
7 a3 W% w; s: `# l" b+ H          240    0.03653    0.06488    0.08945    0.01828    0.05452
5 Z/ g1 F2 E: z$ {( p" ?          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 k9 O- M* g3 l7 m: Olb = [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];
( r9 @/ Q$ J9 s) T3 W) V7 Byexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
: X0 T4 V* j/ ~% c9 x% warning off
# n6 z& Q/ R4 ]* h2 R% 使用函数 ()进行参数估计
+ }' ?9 a4 I* Y$ F[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
1 f/ C& F0 g. y" a( j2 o1 gfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
* I9 [" u; U" d# C. v* c$ Ifprintf('\tk2 = %.11f\n',k(2))
: ]2 T* o7 B8 `6 Jfprintf('\tk3 = %.11f\n',k(3))
  w) V3 {3 I, b- t$ c3 I0 V1 ?6 c3 i2 bfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
. e8 @6 l, e7 u+ D( xfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
7 V3 ?& r. M  ?! [$ @" i4 s; \% warning off
& f) D( i4 E# A' T% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
% N2 A! s5 P' m3 W" Q. l    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')
3 E3 c* N2 l" C6 `/ Hfprintf('\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))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
; x6 D2 E1 W# ?2 P: ], dfprintf('\tk8 = %.11f\n',k(8))
4 Z' }$ E8 o6 [3 G( F' ufprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
' A+ ?: ?/ |1 _- p( \) z. U7 @k_ls = k;
( p2 Q! c9 b# K( `( E0 p7 i0 Qoutput
' m7 Q! F4 [4 ]7 ~' Jwarning 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
# s* {8 M  h+ M: y+ [3 fk0 = k_fm;
4 D! t1 Q6 S; R& ]7 u) }[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
; x# T$ s7 U  w% b& c1 y: J& b: w    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
, Y. d% p% }2 T" v6 }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')
fprintf('\tk1 = %.11f\n',k(1))
3 e5 S' m  g8 H' {! Q  a2 S7 w- Ifprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
  U5 ?. w0 @/ e: `fprintf('\tk4 = %.11f\n',k(4))
# _, i7 E0 h+ Z5 ^) n2 y- qfprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
" y, m+ N9 U2 c, Q* n9 x* d  L6 p7 wfprintf('\tk7 = %.11f\n',k(7))
8 O+ z( R7 f  l# m1 r, f9 n' Tfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
2 w( w  ~9 \5 o# g6 Mfprintf('\tk10 = %.11f\n',k(10))
2 k; b% {7 d7 W2 n5 gfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
) N& F. s6 @% uoutput
. E* o# a7 e( L# N" \/ _' [1 ytspan = [0 15 30 45 60 90 120 180 240 300 360];
& L# i2 M4 n# X1 Y[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
6 o$ t/ F# v' P$ }9 ?7 Yfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
figure;plot(t,x(:,2:5));
( H6 R7 V. W" x8 J; o. K6 ep=x(:,1:5)
! m- y" G. w8 k: a. M) t( s' ?hold on
5 H5 [1 ^) W4 r6 R2 `plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')



function f = ObjFunc7LNL(k,x0,yexp)
* K3 s" A$ o. h, l4 k# ?7 x2 jtspan = [0 15 30 45 60 90 120 180 240 300 360];
) X$ C, [# n! k[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);
3 _& t. J. h7 u- lf4 = y(:,5) - yexp(:,5);
( c3 s; C4 Z/ tf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];



# l; m+ h, N3 ]5 F* {3 vfunction f = ObjFunc7Fmincon(k,x0,yexp)
- V3 f3 t" v  ztspan = [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);
6 E! h" f) d" Wf =  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) ;


; c% _2 E' ]$ C0 i5 f
2 F5 M) f6 \! S- i
; v4 `" F' Y/ ?7 X' |6 B8 ffunction dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
0 f; i" E- D9 tdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
# u. P% q( ?. P0 d2 F5 b: q9 w# NdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
dLadt = k(7)*x(5);
# D8 E! @9 [# ^$ x# g8 W7 cdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];


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