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
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
  ?3 ?8 A/ |' ]0 f% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
! T! y; @6 H* p5 Z4 W" W% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
$ A% @6 ~1 x' e: v1 L6 D8 T% dLadt = k(7)*C(Hmf);
3 Z' s5 B( H! U  c%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
clear all
clc
' U" k+ ~0 D" W7 J# D/ i2 H+ C* gformat 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
0 G) X, f9 d) Y0 e) Q          45    0.15105    0.06975    0.02473    0    0.0033
          60    0.13763    0.07397    0.02615    0    0.00428
: w. u, V5 T( O4 g* z0 g/ c          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
+ A$ c7 A8 E; v5 p          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
          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
+ ], m8 p- w2 Z8 G. C# l) }2 |' slb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
2 i, Y) |9 B, l; ?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
% 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')
: N6 Y% [  A  G2 r; p( efprintf('\tk1 = %.11f\n',k(1))
, @9 O3 ~$ R# E+ mfprintf('\tk2 = %.11f\n',k(2))
! _! H1 V8 U0 V8 y7 w, \fprintf('\tk3 = %.11f\n',k(3))
# ~$ ?- Y! V- y$ j5 E3 R1 Q! p# ?fprintf('\tk4 = %.11f\n',k(4))
. x" a" o& q' p) \0 o! D$ ^8 Mfprintf('\tk5 = %.11f\n',k(5))
( V  S* Z. r' mfprintf('\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)
2 E/ I" }7 p. d1 O+ Pk_fm= k;
# y* a, Z3 {5 o5 w( o( u+ o% warning off
% 使用函数lsqnonlin()进行参数估计
& W/ G+ e7 ?: I! I! `3 Z  g" j( z[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
# T* A/ a! \4 J/ Q4 S3 m+ A$ _    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
ci = nlparci(k,residual,jacobian);
/ c+ E" j- h8 Z6 s+ M: Afprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
4 f4 p- b' B1 w* V, `3 t1 l" X5 Gfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
: U8 e6 N$ C1 \: a( S0 Dfprintf('\tk4 = %.11f\n',k(4))
; q: w! L# v' pfprintf('\tk5 = %.11f\n',k(5))
- f3 c/ o" M) X2 U5 ufprintf('\tk6 = %.11f\n',k(6))
" p7 \+ Z3 T0 l& f0 `% Tfprintf('\tk7 = %.11f\n',k(7))
fprintf('\tk8 = %.11f\n',k(8))
( u; I' c% S7 P, bfprintf('\tk9 = %.11f\n',k(9))
( x! b% y( y; o6 D; M& ]( o& j% Jfprintf('\tk10 = %.11f\n',k(10))
# O3 a7 ]" t1 y6 yfprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
warning off
) s% y. W3 C' T3 Z0 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
2 ~; }4 a# l* [k0 = k_fm;
' F/ Y+ S- t6 \/ Y& j[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
- L$ \: z6 o1 U9 ?6 ^9 Xci = 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')
fprintf('\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))
( W0 K8 |1 A1 r3 ^, ]( @fprintf('\tk6 = %.11f\n',k(6))
3 X# e1 W) K- v# N; gfprintf('\tk7 = %.11f\n',k(7))
: K9 s+ ?' o0 Yfprintf('\tk8 = %.11f\n',k(8))
" l' W/ g. f- o9 E. `fprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  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];
  q/ G- Q( _" N+ s6 O[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
; m! i( s% e) j" L# @figure;plot(t,x(:,2:5));
p=x(:,1:5)
# X7 p# c+ j4 R* ^  V5 ghold on
% E! q$ H5 u: f* t8 g0 A6 hplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
  A% C3 f4 g( x9 c  f5 k
1 F. f6 Q1 @$ J4 X- s& `& `7 T( J

$ u4 ^" W9 y1 J. X$ P9 wfunction f = ObjFunc7LNL(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
( Z0 _+ W6 t# u7 w[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
- X* q$ s9 l! f. w3 a( `y(:,3:6) = x(:,2:5);
+ q% B! j1 N0 J/ |f1 = y(:,2) - yexp(:,2);
f2 = y(:,3) - yexp(:,3);
9 L& @7 N" z, j5 a; o- i* \% |3 k' of3 = y(:,4) - yexp(:,4);
: p$ B& C1 g; h3 H1 N; lf4 = y(:,5) - yexp(:,5);
4 g! p: I) C- l: F, |- Zf5 = y(:,6) - yexp(:,6);
( l& W! N" x2 G( O# Nf = [f1; f2; f3; f4; f5];
% ?1 B1 ^6 O$ c* f1 [, z
' H, o+ }' E5 m: k( ^
" _! a* G" |/ v% x0 C/ i" |
function f = ObjFunc7Fmincon(k,x0,yexp)
% X! L- {# k$ b* {0 utspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
) H! D3 P0 t- Ay(:,3:6) = x(:,2:5);
# K4 H; w% v8 p" K0 j' qf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
. v; s( S1 \% C$ F    + sum((y(:,6)-yexp(:,6)).^2) ;

$ Z- Q6 P5 i& i4 t

2 k) H( \, m% C4 ]8 U/ }% M. w1 p
' L' `6 Z8 J/ g  I3 F: B8 u: afunction dxdt = KineticEqs(t,x,k)
dGldt = 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);
' t+ N+ B8 a) B2 _9 FdFadt = 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);
. V5 g; s0 M3 sdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
: ]' p( W: V& D3 M0 v

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