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
/ j( j4 I* W- ?9 r: a% k6->k6 k7->k7
+ J/ N- r0 D" g) [% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
8 P+ T# h, n- F0 F& D# p2 q% dFadt = k(2)*C(Glc)+k4*C(Fru)+（k6+k7)*C(Hmf);
+ U5 g- l) Z5 R8 ^& b% dLadt = k(7)*C(Hmf);
$ z- s) }0 y* i6 D%dHmfdt = k(3)*C(Fru)-（k6+k7)*C(Hmf);
8 Q4 P5 n0 k" E' T& iclear all
- E% @: ?& _1 ~clc
: ~$ d, E2 C- Gformat long
%        t/min   Glc    Fru        Fa   La   HMF/ mol/L
  Kinetics=[0    0.25    0           0    0       0
4 X& l3 t# ?0 p; o% p          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
          90    0.08115    0.07877    0.07485    0    0.01405
          120    0.0656    0.07397    0.07885    0.00573    0.02143
  r4 M& B4 j( {: p( p: x- \( b2 Y          180    0.04488    0.0682    0.07135    0.0091    0.03623
          240    0.03653    0.06488    0.08945    0.01828    0.05452
) z" P, z4 c0 ?+ l# t          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
1 B2 g0 e: T* n+ d4 T) ~lb = [0  0  0  0  0  0  0  0  0  0];                  % 参数下限
+ V! E, C5 q# |* M+ H: u5 k1 r1 {ub = [1  1  1  1  1  1  1  1  1  1];    % 参数上限
x0 = [0.25  0  0  0  0];
# o" g$ ?- ]$ t- o7 i' E( tyexp = Kinetics;                 % yexp: 实验数据[x1        x4        x5        x6]
% warning off
; {: s$ o- v. B% 使用函数 ()进行参数估计
0 d9 X$ Q" L; f+ L& C2 J* |[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')
! ~  Z) i3 a- i; J4 ~9 Afprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
9 E5 W4 X# f8 k! j( y% m; Q) y% ^: pfprintf('\tk3 = %.11f\n',k(3))
fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
, J4 i1 [7 b3 k: B1 K3 Q. c  z, S% Dfprintf('\tk7 = %.11f\n',k(7))
( Q$ [+ Q" D$ M: b# F4 lfprintf('\tk8 = %.11f\n',k(8))
/ q3 @2 }4 A/ ufprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
6 _( q* {) S* @2 Q4 p' jfprintf('  The sum of the squares is: %.1e\n\n',fval)
k_fm= k;
% warning off
& [8 v$ X" V* G! k/ @+ v% 使用函数lsqnonlin()进行参数估计
4 p1 J' f9 a8 e2 J! }[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
! s: k8 s, ]8 D" J8 Z3 c    lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);      
9 `: `0 T; P2 d. \, J& xci = nlparci(k,residual,jacobian);
. r* |/ w* e. c, p0 ]: Qfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
3 K. V2 b9 i3 _/ u' k2 j' F' kfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
fprintf('\tk3 = %.11f\n',k(3))
  j. r" j# F) {! ]fprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
7 v2 U+ E" Z5 Wfprintf('\tk8 = %.11f\n',k(8))
fprintf('\tk9 = %.11f\n',k(9))
# C" W5 M5 G/ T7 u* s4 V2 r2 Rfprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
k_ls = k;
% N4 q) `" H8 Voutput
% X$ t! b) j* A! xwarning 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
* C0 Q% F, w# Y) u6 Wk0 = k_fm;
: s- [8 a/ h3 B& p) L[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
' A5 H7 D4 a( B$ `, e    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')
3 v( o- H1 k, ?& _& Rfprintf('\tk1 = %.11f\n',k(1))
fprintf('\tk2 = %.11f\n',k(2))
8 ]2 o; V3 l# q+ G/ lfprintf('\tk3 = %.11f\n',k(3))
# V8 T% o& h: K: d9 Efprintf('\tk4 = %.11f\n',k(4))
fprintf('\tk5 = %.11f\n',k(5))
; ~7 ^( o) y: S2 c: _fprintf('\tk6 = %.11f\n',k(6))
fprintf('\tk7 = %.11f\n',k(7))
7 w: t, C, m& G4 G+ q( q, {fprintf('\tk8 = %.11f\n',k(8))
; I; r6 H2 f: v8 C/ Cfprintf('\tk9 = %.11f\n',k(9))
fprintf('\tk10 = %.11f\n',k(10))
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)
+ m+ K9 N' S+ J, @, ]# W* Ck_fmls = k;
  O" N8 `/ I! v" xoutput
tspan = [0 15 30 45 60 90 120 180 240 300 360];
, [) D2 a3 p! ]$ r+ d# R3 z[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
figure;
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
. c- y4 N' N* xfigure;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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3 a' [8 I5 t0 ]) l( x' j' s. t$ kfunction f = ObjFunc7LNL(k,x0,yexp)
7 i& U+ D/ R0 ztspan = [0 15 30 45 60 90 120 180 240 300 360];
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);   
y(:,2) = x(:,1);
. j. Z9 L" R2 `9 c: c" zy(:,3:6) = x(:,2:5);
f1 = y(:,2) - yexp(:,2);
& }$ T1 y5 Y$ \6 z7 [$ Df2 = y(:,3) - yexp(:,3);
f3 = y(:,4) - yexp(:,4);
/ f. b; C9 i% A; `3 S2 u( {& Hf4 = y(:,5) - yexp(:,5);
( T7 }8 k) B# u; R% |, a% lf5 = y(:,6) - yexp(:,6);
! J" I: t+ x4 o) {" q: j: N0 ~f = [f1; f2; f3; f4; f5];


7 H9 q8 O  }6 N7 T/ {* R2 s$ {
function f = ObjFunc7Fmincon(k,x0,yexp)
tspan = [0 15 30 45 60 90 120 180 240 300 360];
7 b" R% z. j; n: m& _+ ]7 z/ [[t x] = ode45(@KineticEqs,tspan,x0,[],k);   
& k$ Z$ P6 G# u+ i' A% D6 ry(:,2) = x(:,1);
3 _) c( I- T0 S: s+ J8 ]7 ty(:,3:6) = x(:,2:5);
4 Y. X% m# {* Hf =  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) ;
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function dxdt = KineticEqs(t,x,k)
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
9 ~7 A$ V. l$ h# J, \dFrdt = 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);
' u" T1 @( q/ MdLadt = k(7)*x(5);
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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