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升级   87.37% TA的每日心情 | 无聊 2015-10-10 18:19 |
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签到天数: 24 天 [LV.4]偶尔看看III
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10体力
function parafit
$ [/ x# A4 ~& b0 v/ {/ F0 n7 j5 |% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4. i- C; T0 N3 T# R, s! C1 e
% k6->k6 k7->k74 V$ ^8 T4 p0 h9 y# o/ [3 T
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
1 ^, H1 R; \9 y/ a3 Q/ `% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);( U9 q" R* [# G- J) O+ A1 f
% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);
8 D7 O ~! Y' W8 y5 @* Q! M* q+ z$ E5 U' ~% dLadt = k(7)*C(Hmf);# L# K3 e) @+ a0 D# r7 J
%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);8 F. v, ^$ c5 n- z; w- M9 F# u! X0 I
clear all
- i6 v( Z# g# d. Gclc) e& T/ Q' N1 I$ r9 h/ ]
format long# y- E/ A8 U" a) N |3 J" |4 j" B
% t/min Glc Fru Fa La HMF/ mol/L
' g8 R: H! s* i; G( i/ @. B$ F7 F Kinetics=[0 0.25 0 0 0 0
* u; [& R/ i6 w5 W; j2 n. V 15 0.2319 0.01257 0.0048 0 2.50E-046 U S) E, F* s" ~$ ^1 e
30 0.19345 0.027 0.00868 0 7.00E-043 R& g6 o/ K) P+ y/ X
45 0.15105 0.06975 0.02473 0 0.0033
0 N" u |5 \5 U 60 0.13763 0.07397 0.02615 0 0.00428
. F+ X0 I, O( y 90 0.08115 0.07877 0.07485 0 0.01405- b X! n2 o% T7 H
120 0.0656 0.07397 0.07885 0.00573 0.02143
: |. Q6 T' l8 T- x- b 180 0.04488 0.0682 0.07135 0.0091 0.03623
4 ?9 i W* l7 V( U1 d) d4 M 240 0.03653 0.06488 0.08945 0.01828 0.05452+ ~( y' [4 V0 V/ S4 s
300 0.02738 0.05448 0.09098 0.0227 0.0597& Z* K# \, x9 j" @: v
360 0.01855 0.04125 0.09363 0.0239 0.06495];6 ?% X: B6 i! w2 _/ I. K+ q
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
4 L0 M6 d$ p# ~* Rlb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限5 {/ [4 j+ C: c- y& f
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限 S0 R0 ]4 p% L: J9 \: n4 U
x0 = [0.25 0 0 0 0];( e0 S3 { b. f% j$ f
yexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]1 e+ p# x5 Z5 ~. T: `+ U# ^
% warning off- i: N* T9 z. c W ~7 e
% 使用函数 ()进行参数估计
2 y3 y8 P5 M8 W[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);+ k" Q1 l# E+ Y% w k8 A# o# w
fprintf('\n使用函数fmincon()估计得到的参数值为:\n'), h6 v7 Z6 b1 y
fprintf('\tk1 = %.11f\n',k(1))% U" u4 @5 ?9 k
fprintf('\tk2 = %.11f\n',k(2))
) k; k0 i# m2 a* T* Y% q. Dfprintf('\tk3 = %.11f\n',k(3))
# v0 S5 h* ]# [9 a9 z+ cfprintf('\tk4 = %.11f\n',k(4))
0 x4 h: [; C: ]6 p; lfprintf('\tk5 = %.11f\n',k(5))4 d9 |: U3 N/ r$ V' C* @
fprintf('\tk6 = %.11f\n',k(6))
. b% }5 z. c% A' O7 Yfprintf('\tk7 = %.11f\n',k(7))
& N3 Y3 j2 A6 w: r; Dfprintf('\tk8 = %.11f\n',k(8))0 ~1 J1 h8 H3 g' h0 P4 F
fprintf('\tk9 = %.11f\n',k(9))7 U; H, M3 J8 ~7 D) c- u P
fprintf('\tk10 = %.11f\n',k(10))# j2 @) _! M# t4 [1 n9 ?
fprintf(' The sum of the squares is: %.1e\n\n',fval)1 R# L* M6 q( T7 C
k_fm= k;) Y! r; }9 P' t% K$ j
% warning off
" l% j& |8 [# S) R6 R% 使用函数lsqnonlin()进行参数估计
3 N& e! z2 j0 j( R3 \[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
" K2 ?+ }$ {5 S* r3 \ lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
2 h% k/ g8 F4 N. ^9 l+ aci = nlparci(k,residual,jacobian);
. g4 S0 W- t N* g Jfprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n'): h: f5 J% ^0 m3 k$ I) ~
fprintf('\tk1 = %.11f\n',k(1))
\3 e! e4 G& B# O8 X; w, _fprintf('\tk2 = %.11f\n',k(2))) G1 }! j! n- x8 B- E& ^
fprintf('\tk3 = %.11f\n',k(3))! X/ p: q0 ]4 T" B5 }; [
fprintf('\tk4 = %.11f\n',k(4))0 G, l8 L8 B+ J3 K6 l
fprintf('\tk5 = %.11f\n',k(5))7 @' Z1 j! l n* Q: X
fprintf('\tk6 = %.11f\n',k(6))+ ^; w; f. q6 g
fprintf('\tk7 = %.11f\n',k(7))3 O" d: b/ Q& u. Q+ C3 X3 _
fprintf('\tk8 = %.11f\n',k(8))
2 d+ q! c- ^8 s( F i/ E. Tfprintf('\tk9 = %.11f\n',k(9))% d! @9 w3 j0 [# y1 T. m
fprintf('\tk10 = %.11f\n',k(10))8 a; ?9 ?' ~* V4 `2 f0 c: ~9 o
fprintf(' The sum of the squares is: %.1e\n\n',resnorm): j+ A/ L U- c) `
k_ls = k;
, P3 t: B, C1 v8 B$ t2 Doutput& q, R! `. B5 i; q3 H e9 k' H; D f
warning off
' U8 v D# B* a6 j: j: `9 ~, h% 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# o, Z1 E, W0 Z) u$ R' C0 l L% N
k0 = k_fm;4 K- C+ m( J+ e" b M6 z
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ... {8 e9 v' U1 ~# C6 P. x9 W
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
, I5 ~$ H; Q# d/ C/ dci = nlparci(k,residual,jacobian);, V# s" Y( s( }! c x8 E& S3 y/ `
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')
+ B6 O! S! ?+ n! {4 o+ Xfprintf('\tk1 = %.11f\n',k(1))2 L: f# v s9 C3 R( l; ]3 a- [
fprintf('\tk2 = %.11f\n',k(2))# e4 ~# f* o& L+ l) R6 d( X- _
fprintf('\tk3 = %.11f\n',k(3))! C6 C; m: d1 @" l/ ~- Q
fprintf('\tk4 = %.11f\n',k(4))
$ r/ e/ M* w6 Hfprintf('\tk5 = %.11f\n',k(5))
; V5 v! w( r' t8 Bfprintf('\tk6 = %.11f\n',k(6))+ O$ W9 D( i4 E! T2 @" q' d
fprintf('\tk7 = %.11f\n',k(7))
: G# ^3 s& Y. A8 D( V% `fprintf('\tk8 = %.11f\n',k(8))! Q' l5 @+ Q( w' O) [
fprintf('\tk9 = %.11f\n',k(9))
) y2 i: e: k: y+ S% ofprintf('\tk10 = %.11f\n',k(10)). D1 b7 K- m) `
fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
4 q0 ?; F7 \ n' x! Uk_fmls = k;6 f. f9 D' B+ W, |* i- z- s
output
' O# P% x) v/ |& S! _0 }tspan = [0 15 30 45 60 90 120 180 240 300 360]; J8 m( |& Z- p+ I# \8 q7 O& Q
[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
! q; ~5 X1 \5 ^& |* A* qfigure;7 W+ X# q. Y) m# [' H& Z0 u' y
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
( c' f4 _. D$ f3 w" U! Rfigure;plot(t,x(:,2:5));
5 x0 l% V. b6 Y% up=x(:,1:5)
( W1 Z4 o9 e, v9 `hold on6 o% A, s2 [/ N/ m$ D- a& x$ M
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')5 D# ?$ |/ L8 \/ p2 e- M5 E
+ Z8 P: E- b) \7 P; |
% c* @2 [% Q# Q: j# n' {" P
( h4 E0 x6 A0 U5 Y( k
function f = ObjFunc7LNL(k,x0,yexp)* e3 r) _, u& z8 g9 k
tspan = [0 15 30 45 60 90 120 180 240 300 360];
/ ^( m- s4 Z, S) Q6 T[t, x] = ode45(@KineticEqs,tspan,x0,[],k); : j) M$ L$ l- E, O7 ^4 d( q
y(:,2) = x(:,1);
g% m G3 Q" gy(:,3:6) = x(:,2:5);
% X0 D# }6 h0 K/ ~: e M) Sf1 = y(:,2) - yexp(:,2);
; I7 O" W5 J; t3 T K( K* ?. `" {f2 = y(:,3) - yexp(:,3);
) \. j' o: D( E0 W- Xf3 = y(:,4) - yexp(:,4);2 A; y1 P: ]3 ~. ^* b2 i: T; U
f4 = y(:,5) - yexp(:,5);9 v/ o1 r, [& }3 L% N: \
f5 = y(:,6) - yexp(:,6);& c; H' R; h1 G4 D4 J
f = [f1; f2; f3; f4; f5];- t2 C' t6 g8 D& }/ Z* A4 |
1 n$ v1 F8 G9 w! P4 D$ X$ i1 ?
" H- A, z1 H3 W
* _9 ?2 h) k# _$ bfunction f = ObjFunc7Fmincon(k,x0,yexp)( S/ l' x1 k$ j8 J# k+ r
tspan = [0 15 30 45 60 90 120 180 240 300 360];
% D/ U$ R: m8 z1 F[t x] = ode45(@KineticEqs,tspan,x0,[],k);
1 l) L4 ^7 z% g& @* A2 @; W3 v7 X/ oy(:,2) = x(:,1);3 s7 m+ I! w; f9 Q" N9 ]( S
y(:,3:6) = x(:,2:5);0 _ i$ `. q; ?7 |
f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
8 f! X2 J4 K, R0 N& w3 M# E, C + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...
. M& t3 X6 L& N$ O$ i* _ + sum((y(:,6)-yexp(:,6)).^2) ;$ q$ O; E% i- a9 v
9 ~# Q* ?5 K4 }
% q, [- y+ l/ D* ]; S- F: y9 L+ L6 m- }
/ P; g, R5 k% [+ o' V
function dxdt = KineticEqs(t,x,k)
2 O) N7 o. @/ X3 d1 cdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
4 L6 G0 u J* }! e, a+ xdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);; Y3 e2 \1 T/ W; o, S1 P6 T# i2 X5 T' L
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);+ h/ u5 i1 Y) D) j
dLadt = k(7)*x(5);
' e& S" Y, n' O3 f5 w! m8 O3 ydHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
7 i) _; {0 L6 W6 E; q! U9 t/ _dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];% C f$ O3 Z4 F( |) Q
/ x* `- p2 }. X' ^( `0 J" r
6 p9 f( L" e( a4 o, r) l |
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