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
6 ^& e! [' C% _6 v- [%  k1->k-1，k2->k1，k3->k2,k4->k3,k5->k4
7 K; S2 q' y9 D: z1 v1 T2 `% k6->k6 k7->k7
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
( U6 L+ L3 }& Q* |6 F# k& r/ Z% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
# K% j# Q/ w2 t% B% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
% dLadt = k(7)*C(Hmf);
8 O* j5 B; I6 }- X6 `% `%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
) N9 b. r$ J& E) ?* sclear all
clc
format long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
, O6 F3 v# c8 y) x4 @  Kinetics=[0    0.25    0           0    0       0
          15    0.2319    0.01257    0.0048    0    2.50E-04
7 W$ k' S& p: ]  U          30    0.19345    0.027    0.00868    0    7.00E-04
6 d1 a0 d; M  Y# m0 s1 J/ N          45    0.15105    0.06975    0.02473    0    0.0033
) |9 {! R9 o2 ?: H& ?; L" u: ^  L% e          60    0.13763    0.07397    0.02615    0    0.00428
9 D& X$ r& F  h, i          90    0.08115    0.07877    0.07485    0    0.01405
3 k: A+ Y  }2 G6 \          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
          300    0.02738    0.05448    0.09098    0.0227    0.0597
          360    0.01855    0.04125    0.09363    0.0239    0.06495];
. t) Z$ N3 f+ s; ]3 I# k3 kk0 = [0.0000000005  0.0000000005  0.0000000005  0.00000000005  0.00005  0.0134  0.00564  0.00001  0.00001  0.00001];        % 参数初值
3 b3 F; ^# B! a3 `% ?/ ilb = [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
) ]+ b: D+ E  Lx0 = [0.25  0  0  0  0];
, F6 {7 Z" Z. [; Y8 Z. zyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
1 W5 q6 C# s) r3 c! I& _: w) N) ~% 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))
! q, {; t5 f: y1 ?/ u% kfprintf('\tk2 = %.11f\n',k(2))
3 }2 m" p# R, Qfprintf('\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))
- s2 I6 ~3 @: U! d2 @fprintf('\tk10 = %.11f\n',k(10))
; I8 _# V7 \( e# c5 {" `  Pfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
, k% r) J, S& w' X! U, ^& x6 \% 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);      
0 W. o' ^4 S4 nci = nlparci(k,residual,jacobian);
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
7 k/ s9 Z" R, H$ u/ B& {3 rfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
7 J. ]+ Y& M4 l" vfprintf('\tk5 = %.11f\n',k(5))
- f- b( ~1 J" pfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
7 r, u) r7 e1 gfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
: l  F0 Y' Q. e( _1 `9 Gfprintf('\tk10 = %.11f\n',k(10))
, X7 u! ]- E- [' E6 g! ufprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
output
3 m3 F" D3 S; @4 E  |+ swarning 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
# V' r, D" G. a, tk0 = k_fm;
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
+ e0 R" O& n' G    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')
; M% t9 Z2 Q  z! ^: bfprintf('\tk1 = %.11f\n',k(1))
' k3 G4 x# }- j' R2 A, Zfprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
5 s8 L' G2 @4 Xfprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
# V% ^% T5 g* G1 Z. H7 \. z" rfprintf('\tk8 = %.11f\n',k(8))
; x: d5 e+ j& B8 i% Rfprintf('\tk9 = %.11f\n',k(9))
( Z# r+ U. R! K  ?fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_fmls = k;
* Z% ^  \  g4 D1 moutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
: v7 j, T8 b, ?- @" Mplot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
2 v# [4 k7 s; u3 U$ ^& n2 {figure;plot(t,x(:,2:5));
p=x(:,1:5)
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')
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function f = ObjFunc7LNL(k,x0,yexp)
7 }4 X$ L* l3 }! r  b+ @" A4 Utspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
- T! w  ~- E2 B# j; dy(:,2) = x(:,1);
( b0 ~2 |# @3 V  V$ ry(:,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];


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& A" f8 b; `# S/ Rfunction f = ObjFunc7Fmincon(k,x0,yexp)
2 F1 f, t5 R  ctspan = [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);
/ C9 _, ?: |/ S0 Bf =  sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2)   ...
3 s. I. |. N/ d; g    + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2)   ...
; r0 k$ o( P) b4 G" a, H0 z3 N, ^    + sum((y(:,6)-yexp(:,6)).^2) ;


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function dxdt = KineticEqs(t,x,k)
1 x$ w% t7 p* ~dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
5 P. Z6 d) |8 T$ ^/ \7 p% K6 tdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
( H/ n1 F$ A2 m6 \dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
9 F) ^+ N1 y" \! n2 mdLadt = k(7)*x(5);
7 N6 }7 J" C* k7 G+ V* fdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];

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