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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 parafit9 C& x) h4 {, x! {: v$ x
% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4/ m+ F% ?; V2 v
% k6->k6 k7->k7
1 z9 m1 l% e( t/ W2 ?6 Z% L$ i+ M% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);( S/ E. E# P( N) ]( y$ ~0 c
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
, a9 D8 Q6 F7 _# A8 S; w) V6 ?% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);6 N8 W$ i" y1 T: T% s) u
% dLadt = k(7)*C(Hmf);
. J( v! C& i- ~2 S%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);
+ [! N; H- d$ `5 e: N P" Rclear all2 K N" \: I! _; o7 r
clc3 G. L9 K# L5 O2 n) b: i2 C
format long
1 `. M5 R$ t+ N5 u1 u% t/min Glc Fru Fa La HMF/ mol/L
7 X2 ?- _3 v: y" q( |8 t2 K+ [, ~- g) v5 A Kinetics=[0 0.25 0 0 0 0) i, T. s" d B1 [9 M6 [
15 0.2319 0.01257 0.0048 0 2.50E-04
0 h* M6 r) P+ T& z* w, Z* k 30 0.19345 0.027 0.00868 0 7.00E-042 C8 _9 h K2 g9 ^; c& p. `
45 0.15105 0.06975 0.02473 0 0.00331 v$ c8 |5 n& s# ]3 A. w
60 0.13763 0.07397 0.02615 0 0.00428
& l. m4 @% g7 @( c 90 0.08115 0.07877 0.07485 0 0.01405$ f( h7 q* D, h7 F2 ?2 X
120 0.0656 0.07397 0.07885 0.00573 0.02143
. i. p6 ?! S Z# [ w3 M 180 0.04488 0.0682 0.07135 0.0091 0.03623
9 p8 c- x: t, x' j 240 0.03653 0.06488 0.08945 0.01828 0.054528 j" f7 O" c, s" {- \% \
300 0.02738 0.05448 0.09098 0.0227 0.0597+ A+ B+ |" E& s
360 0.01855 0.04125 0.09363 0.0239 0.06495];
6 p+ c' [2 n8 v8 D* ^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
' z* K$ w' f1 i; q; D" i5 D4 Blb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限
& S: C0 X7 T2 k; t" v8 q! c! Qub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限
* S, L& F9 `+ Y8 mx0 = [0.25 0 0 0 0];' R L( U* @9 M0 @7 p: s- e
yexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]1 c, I4 i3 P8 e) x) x$ s
% warning off
3 t1 ]0 U! ^1 v7 ]8 Z7 ^% 使用函数 ()进行参数估计6 m( l+ C, l' f* q$ ^: @- w
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
0 ]8 j% M1 q' p( b. ]& P; g3 ofprintf('\n使用函数fmincon()估计得到的参数值为:\n')
' e4 ]" ^8 x$ W0 i8 u. }! Jfprintf('\tk1 = %.11f\n',k(1))
1 v, L; |4 J5 bfprintf('\tk2 = %.11f\n',k(2))* G/ @$ s0 e* y3 o. h) y
fprintf('\tk3 = %.11f\n',k(3))/ [! n7 Q) q+ c% c2 U, N% W9 P
fprintf('\tk4 = %.11f\n',k(4))
+ E$ q5 M* o' A- P* h- o! Vfprintf('\tk5 = %.11f\n',k(5))3 ?" [& K. y* ~0 M: b5 E$ d
fprintf('\tk6 = %.11f\n',k(6)), {/ U* Z& \' Z5 V/ I, A# G" B
fprintf('\tk7 = %.11f\n',k(7))
% ]* g3 P' g' e) E' Wfprintf('\tk8 = %.11f\n',k(8))
$ q4 L8 J* V7 R$ Wfprintf('\tk9 = %.11f\n',k(9))3 z8 y+ A# D+ ^& w- t7 s1 g
fprintf('\tk10 = %.11f\n',k(10))3 ?* Q1 W" U5 {7 z7 M+ A8 J
fprintf(' The sum of the squares is: %.1e\n\n',fval)& h, `. \8 X2 {" y1 s# d; A
k_fm= k;* P5 p- o7 p ]4 @
% warning off/ v% T$ g+ N# K2 F$ N% y* t5 c( \
% 使用函数lsqnonlin()进行参数估计
' J& F( d/ g/ D1 p; J0 q( t5 F' d[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...+ f( |8 q4 ?( |# I: g' F, q( L
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); , S" P) m, t/ ]3 }( a
ci = nlparci(k,residual,jacobian);
( I x) O) F j3 e6 ~fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')( |4 s4 s; s1 t
fprintf('\tk1 = %.11f\n',k(1))2 {' q7 y3 K. q9 ~4 q
fprintf('\tk2 = %.11f\n',k(2))
! `$ V/ _3 U' X+ ffprintf('\tk3 = %.11f\n',k(3))1 Q% Q- Q0 @. B! q) j. ]
fprintf('\tk4 = %.11f\n',k(4))/ m" b: h0 ?2 U4 }! s
fprintf('\tk5 = %.11f\n',k(5))
$ e6 y+ G; t# B. K5 s: C9 o' hfprintf('\tk6 = %.11f\n',k(6)); v. @; `- |- Q0 ~
fprintf('\tk7 = %.11f\n',k(7))
. g7 B( x; g; a! e$ z3 o( rfprintf('\tk8 = %.11f\n',k(8))/ [/ T% N' w% ]& b
fprintf('\tk9 = %.11f\n',k(9))
! B2 @) ~" M" y8 t# Gfprintf('\tk10 = %.11f\n',k(10))
( V5 n0 N6 ~6 E2 H$ y2 q$ K, Sfprintf(' The sum of the squares is: %.1e\n\n',resnorm)
3 Y9 j5 h$ I* W7 a8 |8 }k_ls = k;
0 o: ?9 P+ A2 E/ d. d* {output7 e( A9 ~$ s; x$ _
warning off
/ m# ]5 @5 h# k8 ] `% 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
% c& Z( s1 K. [' k$ g1 O3 T. I; J2 F/ Lk0 = k_fm;8 A3 @: j: c% j, j! M/ K! O# T
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...9 E6 E# Y0 |. m' ]* x
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); 4 t9 h/ H9 s1 R1 U" g- `
ci = nlparci(k,residual,jacobian);9 b. `9 Z# H% c9 }- s' U1 L. W
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')
5 g7 i+ x h* A3 z9 X$ x# w/ z) zfprintf('\tk1 = %.11f\n',k(1))
$ j @( a9 o3 Nfprintf('\tk2 = %.11f\n',k(2))
9 s4 m0 M' e. r6 K) H% B4 E- `fprintf('\tk3 = %.11f\n',k(3))
; F2 J1 ]5 E# O" I* b& o" Ifprintf('\tk4 = %.11f\n',k(4))
3 }0 X1 N+ v* b/ o! p) T% e* tfprintf('\tk5 = %.11f\n',k(5))$ H4 W. D5 u2 A
fprintf('\tk6 = %.11f\n',k(6))8 K" {$ E; b% B. b& {
fprintf('\tk7 = %.11f\n',k(7))
' G7 k6 g) n( u5 zfprintf('\tk8 = %.11f\n',k(8))
# X: N( C0 p' R$ l, r* D( D6 Zfprintf('\tk9 = %.11f\n',k(9))
5 U( ^! ~4 F5 q; \) ?# Vfprintf('\tk10 = %.11f\n',k(10))
- C' Z/ u" g o% b% ^! Vfprintf(' The sum of the squares is: %.1e\n\n',resnorm); z7 @% V* e G6 I$ {5 m- F
k_fmls = k;
% D9 `' y8 \$ ~output
+ c, J+ x# [8 M6 k" J$ }tspan = [0 15 30 45 60 90 120 180 240 300 360];
0 G( E+ J" l1 s8 k) h: K9 t[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls); 6 f* ^4 C! [6 m; Z% s. x
figure;8 t9 k: ], @* [9 u
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
5 S. }/ @' c5 i* F( ]. r, U, A' Pfigure;plot(t,x(:,2:5));% o( G( S9 J4 Z" s
p=x(:,1:5)
5 t2 N+ p/ Q1 z! |$ y7 ?hold on
& c! m+ I$ R7 X+ G# h! Pplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
5 ?' I G; i) }. l' S4 B6 v% V- Y' v/ X" G0 ^4 p
8 i7 g7 ]6 g$ o2 v
5 e( ~& I: J4 o/ J5 W, Pfunction f = ObjFunc7LNL(k,x0,yexp)6 N+ X6 Q. p$ c& j( O
tspan = [0 15 30 45 60 90 120 180 240 300 360];
2 u8 t) [5 V) l+ H[t, x] = ode45(@KineticEqs,tspan,x0,[],k);
; w- d5 S5 ~$ p8 v( l/ g. Vy(:,2) = x(:,1);
/ n$ O' W( j: t- E$ Q" L9 `; d) ly(:,3:6) = x(:,2:5);- A. n, U& i+ }" E* H5 [4 X% b
f1 = y(:,2) - yexp(:,2);2 B' N5 h$ M4 p' Z+ W! D2 o; s
f2 = y(:,3) - yexp(:,3);
S' |: O6 S4 I" F# G" q5 Qf3 = y(:,4) - yexp(:,4);
5 p U+ {+ [- `" af4 = y(:,5) - yexp(:,5);
u2 P1 X2 p/ L" Lf5 = y(:,6) - yexp(:,6);5 B# S3 F; r o9 ^; q
f = [f1; f2; f3; f4; f5];4 c+ u/ d2 ?5 B2 M8 D
4 a7 i. d/ t P! b
' k: o9 z( o" k6 p! ^
6 U& g9 f7 J: F5 [* _: Ifunction f = ObjFunc7Fmincon(k,x0,yexp)5 `6 F' R/ y- h2 n+ h {6 x0 O
tspan = [0 15 30 45 60 90 120 180 240 300 360];% `; m/ ~8 n9 m% m( q8 k; p1 u/ k% |
[t x] = ode45(@KineticEqs,tspan,x0,[],k);
+ A1 K. l( v! g4 _$ py(:,2) = x(:,1);6 e6 |1 _+ U$ V7 n
y(:,3:6) = x(:,2:5);! J% A7 `1 W) P# y* v. S6 Q
f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
; v- @7 m6 K u% w + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...
& C3 R2 L/ B* u7 B; c# u3 D + sum((y(:,6)-yexp(:,6)).^2) ;
- W: a; l5 ]: w- ^" c' t
9 L6 _9 {1 ]: ?0 N3 R
( k9 L4 z4 H' |$ v2 G1 [! a+ t2 \9 w5 n: U# e' q" L5 Z) ]
5 E$ \" U( |9 t1 _function dxdt = KineticEqs(t,x,k)1 }) [: A5 ]( u) `1 r. G
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
! h* m: ~7 ` g4 K+ A' h' TdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
: H+ w1 @) U7 vdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);* V, m( _! r' h! I; K6 |
dLadt = k(7)*x(5);, I8 `1 C1 }- {2 j
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
2 @3 D& U( A: J* w$ Tdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
/ V/ n0 p. C/ b& r, t) _$ [
% L7 T; G! b" A! F2 h& Y# |
3 q( x- B1 \4 A |
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