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
  n$ ^7 ?. t& a% e" ?% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
% 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);
: U/ b1 f! y; r- U0 u9 N, _: u: d/ y$ Uclear all
clc
" H9 S1 c8 y$ A( I; U3 y6 X/ b9 @format 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
9 T& j& [6 l* @0 g5 M1 B3 z          45    0.15105    0.06975    0.02473    0    0.0033
1 c! S' L% W) z% d/ f4 m+ Q          60    0.13763    0.07397    0.02615    0    0.00428
          90    0.08115    0.07877    0.07485    0    0.01405
$ Z# v: L" h" H/ Z( J( y          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
7 E- f0 ^8 i% D6 V1 H, J          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
: @$ h+ Q2 p, i& G, s# f1 rk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
; U. i) Y, V( j7 z4 ylb = [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];
# |$ I7 D* y+ s9 cyexp = 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))
fprintf('\tk3 = %.11f\n',k(3))
% P, G7 B( X+ `& Gfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
) }  `. }, _: K$ L+ {4 ffprintf('\tk6 = %.11f\n',k(6))
2 l1 G4 R- Q% ^  ~, }fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
) R. u1 \; C5 k: x" N0 V; l  Ffprintf('\tk10 = %.11f\n',k(10))
# z" ?, O( R3 Zfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
% 使用函数lsqnonlin()进行参数估计
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
" V- l/ m" i$ `. j9 @% B9 k# U    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
- y( M2 t7 A3 [; lci = nlparci(k,residual,jacobian);
9 w" t& U8 e+ e$ `fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk1 = %.11f\n',k(1))
" Y3 d# S6 N/ }' u3 zfprintf('\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))
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',resnorm)
k_ls = k;
output
8 k6 c' |' W: q# q4 |& pwarning off
0 N+ h2 u7 o' ~' D) p# K% 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;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
3 c  J* v' ]* l: \& ]2 ]    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
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')
, r0 q8 x) b4 E8 n5 Lfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
0 G7 z' e; v( V# @0 cfprintf('\tk3 = %.11f\n',k(3))
6 {# @7 Q+ e* M+ Nfprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
" q) f8 |& n; i0 [( x; sfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
( d) J1 o, [5 u( |: h  m  Kfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
3 \" L. b+ P4 L& h4 [) R7 r3 `  dk_fmls = k;
output
+ T2 `: L! f& E: U/ U8 Z% D: y7 rtspan = [0 15 30 45 60 90 120 180 240 300 360];
: j+ p  p( E- ?' h[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
3 u/ Z/ `; l/ M  F7 p- Mfigure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
. J+ D" ^% K5 ]$ [( _  `% Vfigure;plot(t,x(:,2:5));
; Y/ B0 M) ~# j: X) Q' Cp=x(:,1:5)
9 w# M% a1 B! b  _2 C3 ^5 ^hold on
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
4 Z9 R$ [9 @9 j& u4 X5 @& a
" X- W8 G/ Y; U1 q

function f = ObjFunc7LNL(k,x0,yexp)
8 Y: ~  b4 M4 O* g& d. itspan = [0 15 30 45 60 90 120 180 240 300 360];
, {* E( V6 [# L4 x[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
y(:,3:6) = x(:,2:5);
$ }- Z0 V7 X6 N3 H1 {7 O, Qf1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
f4 = y(:,5) - yexp(:,5);
0 e! R- |/ x' s$ ]& uf5 = y(:,6) - yexp(:,6);
f = [f1; f2; f3; f4; f5];

2 j! [$ Y$ E+ {5 E2 {
6 K' w6 N' p2 e' z0 I4 V& {
function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
( ?# z# @6 z: b1 I& t[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
3 ~+ h; }8 ^5 a4 ty(:,3:6) = x(:,2:5);
, c; u) [! z" c- ~1 p. c2 ^f =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
" b' _9 E$ H# D* M9 R4 f  I    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
    + sum((y(:,6)-yexp(:,6)).^2) ;
1 Q/ ]0 S, ^8 T1 M7 j$ X
/ z& ^8 @5 e) h" D
! }+ _9 d, f  R& [0 `8 s

function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
& _0 H. |; V, O  Y2 PdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
) Z7 X7 S  }0 o7 z0 O% i4 D: [5 YdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
  u1 Z! K4 k7 n1 X) `$ f: UdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
" j7 ^* Z3 D0 w4 ^2 Q8 u" L; vdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

" s8 `0 J' p# F( e1 [