- 在线时间
- 22 小时
- 最后登录
- 2016-10-27
- 注册时间
- 2014-1-1
- 听众数
- 9
- 收听数
- 0
- 能力
- 0 分
- 体力
- 152 点
- 威望
- 0 点
- 阅读权限
- 20
- 积分
- 88
- 相册
- 0
- 日志
- 0
- 记录
- 0
- 帖子
- 88
- 主题
- 5
- 精华
- 0
- 分享
- 0
- 好友
- 9
升级   87.37% TA的每日心情 | 无聊 2015-10-10 18:19 |
|---|
签到天数: 24 天 [LV.4]偶尔看看III
 |
10体力
function parafit; k2 q6 c* L9 J8 l! S z
% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
+ c% m4 y; w* a) `" F% k6->k6 k7->k7
. H- f% t: j% u9 l9 L( n% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
6 q) Z; j7 I1 [& G. W3 O. N% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
" M5 L$ `6 `; t1 M( E8 X+ u7 y% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);9 a/ h i4 a" w: Y$ P
% dLadt = k(7)*C(Hmf);
& e. g( q- H& Q) O1 v% J. S% a+ R$ r%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);2 H2 X7 O" l/ }/ W
clear all' a: m# D5 I: n2 [, s% S& q5 e
clc, `8 O `2 O* B8 Y# h6 c) m( r
format long! |+ v2 v4 r5 c) S; k
% t/min Glc Fru Fa La HMF/ mol/L
& Q: @. y5 k4 z$ d Kinetics=[0 0.25 0 0 0 03 G( }& F d* j, h
15 0.2319 0.01257 0.0048 0 2.50E-04
0 h. B( o( m6 l- h0 g 30 0.19345 0.027 0.00868 0 7.00E-04; _! I# D% j9 i7 a4 W8 Q
45 0.15105 0.06975 0.02473 0 0.0033# w0 V, L" M0 G' z; a
60 0.13763 0.07397 0.02615 0 0.00428, \; F0 G" o" F. L( S
90 0.08115 0.07877 0.07485 0 0.01405
: K) j2 e- Z1 t9 p 120 0.0656 0.07397 0.07885 0.00573 0.02143
/ a: b) ]; x8 K' w/ e+ ~! p7 h5 @- f 180 0.04488 0.0682 0.07135 0.0091 0.03623
. z8 }: t% ^! I/ b5 e! I6 z 240 0.03653 0.06488 0.08945 0.01828 0.05452
& z4 v; r P' w/ Y 300 0.02738 0.05448 0.09098 0.0227 0.05975 x6 D: C! o2 w9 d0 R
360 0.01855 0.04125 0.09363 0.0239 0.06495];
8 l! {0 g% w7 V, K+ J, H4 Dk0 = [0.0000000005 0.0000000005 0.0000000005 0.00000000005 0.00005 0.0134 0.00564 0.00001 0.00001 0.00001]; % 参数初值- b$ F1 g9 P$ V3 @' W6 h. }8 N
lb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限 J% b+ m l* d8 I# m
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限) N0 x1 x/ @$ ^. L6 w6 G; h
x0 = [0.25 0 0 0 0];$ ?# D# W: y; i$ p! `
yexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]
) Q" h' N: {! u# y# Y" x( Q, r% warning off
& R3 \: L6 Z. _, A0 {' _+ ^% 使用函数 ()进行参数估计% b9 z% e! B, M
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);
0 F, m# x8 |+ O4 {9 m" j. I, Mfprintf('\n使用函数fmincon()估计得到的参数值为:\n')
3 n1 `1 i) Z8 H- S+ K1 Afprintf('\tk1 = %.11f\n',k(1))+ p( w% J. d( E; \7 V: f4 h
fprintf('\tk2 = %.11f\n',k(2))
9 Q: w0 f# M, Qfprintf('\tk3 = %.11f\n',k(3))& a$ [5 b! x. {* ^0 K% i8 c& h
fprintf('\tk4 = %.11f\n',k(4))" n8 G) @1 [" p
fprintf('\tk5 = %.11f\n',k(5))
2 }6 P4 c k1 `* W" r7 O, {" k, ofprintf('\tk6 = %.11f\n',k(6))& u, ^- ?# T y( T& I+ N5 l! e% |
fprintf('\tk7 = %.11f\n',k(7)), |" ~& F% B. s0 X' @5 f4 k7 r% n N
fprintf('\tk8 = %.11f\n',k(8)). H/ J1 O6 d8 i& @0 m
fprintf('\tk9 = %.11f\n',k(9))
5 k% {% j2 t' [$ Q* nfprintf('\tk10 = %.11f\n',k(10))
/ G4 [& o2 M# J4 V) v$ W0 Efprintf(' The sum of the squares is: %.1e\n\n',fval)& C4 y( N& l; [! X. l4 W; O' c! ~
k_fm= k;
3 {) V" j5 S ^" q+ |3 x: M% warning off
% v0 t+ _2 t% n+ U5 M0 D% 使用函数lsqnonlin()进行参数估计( _6 ?) {0 W0 z4 J X& A
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...6 g' Z, ]/ |% B+ N+ A% ~5 Q! E
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); 0 E+ g. M+ b ]- H6 {
ci = nlparci(k,residual,jacobian);
x, m2 w8 e4 L& l" p6 ofprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')6 Y$ A0 ?# w' k, n
fprintf('\tk1 = %.11f\n',k(1))4 U: ]& x: v; v1 z/ _$ e
fprintf('\tk2 = %.11f\n',k(2))4 L/ g, o) d" ~
fprintf('\tk3 = %.11f\n',k(3))& i% T* v, ?+ L1 C( u& y
fprintf('\tk4 = %.11f\n',k(4))
. M. V* G9 ~- @) N/ ~! I2 Lfprintf('\tk5 = %.11f\n',k(5))" F3 ~/ e6 }9 @7 _
fprintf('\tk6 = %.11f\n',k(6))
/ v, S0 j6 ?" l5 f1 w: Efprintf('\tk7 = %.11f\n',k(7))* D3 p+ n, _( P: j4 o& c
fprintf('\tk8 = %.11f\n',k(8))& e" O, I x* B3 e7 p7 U! r
fprintf('\tk9 = %.11f\n',k(9))5 z% Q; f$ T3 e% Y6 w3 B. n
fprintf('\tk10 = %.11f\n',k(10))+ m9 R0 W3 k( u5 N) s
fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
o& }& s% E9 @6 Q/ y+ Y0 X ?k_ls = k; N c6 D3 G3 G6 N3 t
output
1 K: T) o+ x6 d4 ]% Pwarning off7 a0 F" I; R. {; h P" E. S8 T' 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
' G& F' x3 j3 U4 q) P* c* C) Ak0 = k_fm;; }) s3 ` N$ P- K2 a2 H' R
[k,resnorm,residual,exitflag,output,lambda,jacobian] = .../ s; ?" f0 `7 y
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); , a. a; [2 Y# w1 ?
ci = nlparci(k,residual,jacobian);
* t" s- Z. m$ `+ o! ffprintf('\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')
9 R0 g& F9 c3 R2 qfprintf('\tk1 = %.11f\n',k(1))8 _8 y8 z8 E3 L% o
fprintf('\tk2 = %.11f\n',k(2))" d8 F# v$ Q2 O1 h) k
fprintf('\tk3 = %.11f\n',k(3))5 K$ \) C% s/ r1 V. n; ]+ p* ^
fprintf('\tk4 = %.11f\n',k(4))
5 { _) C. F7 vfprintf('\tk5 = %.11f\n',k(5))
' j; @3 ^/ e$ Xfprintf('\tk6 = %.11f\n',k(6))+ u6 C {" P. b, Z
fprintf('\tk7 = %.11f\n',k(7))
% h/ B4 ~5 z& I$ q5 I, d! Qfprintf('\tk8 = %.11f\n',k(8))8 N5 j# ?$ a" Q! s! o1 q
fprintf('\tk9 = %.11f\n',k(9))3 z q! F1 W; b% f
fprintf('\tk10 = %.11f\n',k(10))
, d8 z& P* z/ nfprintf(' The sum of the squares is: %.1e\n\n',resnorm)1 P& w( B* d+ B, a3 k4 r; p
k_fmls = k;% ~6 q2 o, S8 j8 |9 E5 _3 e
output8 M! N$ ~- Q/ h/ z
tspan = [0 15 30 45 60 90 120 180 240 300 360];
# M. N6 G/ j( ?7 b t3 E, F7 h[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
- k$ v. t, \; S; wfigure;3 B' G6 p5 p% ]! e# o) R* N9 n. a
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
9 |* I; U# H2 s8 Y8 |figure;plot(t,x(:,2:5));
7 O' m) {% b" T& dp=x(:,1:5)/ E9 y: P% F# V% m# A: I
hold on
5 H% O9 t; c0 ^. Y6 i% uplot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')* E% h4 V, B, k
) H1 D9 }+ [& O; j1 y
* x% _# I6 l$ _1 N4 C, `( j- u
6 Q" G" D# J5 X5 Q' ifunction f = ObjFunc7LNL(k,x0,yexp)
/ u! I. n9 ~4 ltspan = [0 15 30 45 60 90 120 180 240 300 360]; g: C& z8 k. N( R, q. N
[t, x] = ode45(@KineticEqs,tspan,x0,[],k);
5 b+ ^! ?) @. |y(:,2) = x(:,1);
; r3 B7 r( ^% T% _/ b k! t7 ^" W1 my(:,3:6) = x(:,2:5);
* k9 x4 S/ e1 b' p; _f1 = y(:,2) - yexp(:,2);
: X$ e. {& A% uf2 = y(:,3) - yexp(:,3);" {4 N: Q$ W- k8 E; @. a. m; w3 H8 O
f3 = y(:,4) - yexp(:,4);
- B0 c- V8 u5 t, k8 @f4 = y(:,5) - yexp(:,5);2 p# J* b0 k' [' ]
f5 = y(:,6) - yexp(:,6);/ U9 ~9 X4 E% M) K' ~/ u1 i
f = [f1; f2; f3; f4; f5];2 ]; d" |; ]# |6 p
6 i5 Z: z/ i* d/ S* w2 J% h6 ^1 o
6 N/ p' k3 f: z* @; s( V
; M( Z2 M( j; y% w6 L; Nfunction f = ObjFunc7Fmincon(k,x0,yexp)
$ H9 i2 L+ H) d( }- p' Y" u5 ktspan = [0 15 30 45 60 90 120 180 240 300 360];
8 \) l" p& e% ]; W ~) ~[t x] = ode45(@KineticEqs,tspan,x0,[],k);
' r7 g1 }( U, ^2 d5 S2 }y(:,2) = x(:,1);
& L M- U1 _ }) l5 b7 Ky(:,3:6) = x(:,2:5);1 G7 X' `! I& ~8 I* H0 `+ d0 j
f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
0 r) I; E$ G+ ^/ o/ p! M2 n + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...) o8 ]: D- |& v: o
+ sum((y(:,6)-yexp(:,6)).^2) ;9 x- ?4 R! c" E7 i
" z! D9 |8 c* W0 T1 o% S* [) y
$ R) F, M% b! f% e2 P: |
1 v, N% l3 `3 F: g6 l( \5 j- \9 o. X5 e& x
function dxdt = KineticEqs(t,x,k)
3 \$ P2 `# n' |dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
- `/ a$ a8 M, P2 q% |% x- fdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
3 ~8 Y* h' }- zdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);5 L3 r8 G, L0 T5 j( G* x
dLadt = k(7)*x(5);
, Z1 U" }+ H5 i9 }1 QdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
- R3 \* n) P: r. |/ B3 gdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
" K4 J0 M8 N1 y% b8 u# Y
; H( r. S: |! f8 |; f: z! P2 a8 Y: f% u# P
|
zan
|