- 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# L3 G6 ]9 N. p9 B6 }& j
% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4. `7 X6 f7 I/ q* V8 a: e. ?
% k6->k6 k7->k7
3 G; W% @: h2 i2 d% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
- Z, l! F2 ?. H k* _% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);1 r- N5 z0 @1 t3 _
% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);) Y( i5 M4 e4 \! X9 _: a" Z* E
% dLadt = k(7)*C(Hmf);
# b/ ]/ R U. S( {* `$ E' {9 U%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);
$ p3 E" k/ Q# V+ Z2 _, n1 eclear all% L9 ]7 o) y2 a2 W8 X
clc; @) ~/ U. h% k! c( _: ]' P! j6 P
format long+ }! ?4 ` a% b" W# H4 }7 f
% t/min Glc Fru Fa La HMF/ mol/L 4 ?- g2 k+ ]/ d- |
Kinetics=[0 0.25 0 0 0 0& x8 ]2 N: ^+ `" `
15 0.2319 0.01257 0.0048 0 2.50E-04
X# {0 o, F' }% G+ Q: |) M 30 0.19345 0.027 0.00868 0 7.00E-04& L# k* v& x+ S' j) h2 `
45 0.15105 0.06975 0.02473 0 0.0033$ Q% F! y) ]; L* v ^# Y
60 0.13763 0.07397 0.02615 0 0.00428
6 G# t: Q: c5 F/ f 90 0.08115 0.07877 0.07485 0 0.01405
$ @+ ]% \% w' j! s9 @8 e m* F3 @ 120 0.0656 0.07397 0.07885 0.00573 0.02143
+ Z I8 F' b/ _; c/ d8 Z 180 0.04488 0.0682 0.07135 0.0091 0.03623; u& \/ a9 S5 y+ ~% C( Y
240 0.03653 0.06488 0.08945 0.01828 0.05452
7 N6 T2 N/ Y- |! Y 300 0.02738 0.05448 0.09098 0.0227 0.0597
, ]+ J U) b3 E8 |5 p, _ 360 0.01855 0.04125 0.09363 0.0239 0.06495];% y* W" w6 o2 H ]" A8 \7 x
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* O: r( b' \" n w/ `6 l
lb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限
6 K% \% x4 H' g0 Jub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限2 d: H# Y% y/ D" D/ Q0 k9 w. _
x0 = [0.25 0 0 0 0];
2 p x E& l6 L% oyexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]
8 C6 @5 k) S' D' f; d& P% warning off
+ }* ?, F# N7 w* d8 W L! g% 使用函数 ()进行参数估计
/ e' b4 V% A% ?. S4 w" w. ][k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);6 b5 Y% q7 ~& X+ O
fprintf('\n使用函数fmincon()估计得到的参数值为:\n')# M# ~, z$ x6 q, |) j9 p
fprintf('\tk1 = %.11f\n',k(1))( X- } ?3 \# A- ?
fprintf('\tk2 = %.11f\n',k(2))* N$ a+ Q- `! O/ k
fprintf('\tk3 = %.11f\n',k(3))8 Q( w$ G5 L$ M7 W# c3 ^8 @
fprintf('\tk4 = %.11f\n',k(4))% B* j3 I3 V4 \ w
fprintf('\tk5 = %.11f\n',k(5))" k& a0 I" u/ k0 ~
fprintf('\tk6 = %.11f\n',k(6))
0 z/ B! W( z& O$ t& e7 wfprintf('\tk7 = %.11f\n',k(7))
# G7 u# A) X0 v1 ^fprintf('\tk8 = %.11f\n',k(8))
. P- B+ f3 r( Dfprintf('\tk9 = %.11f\n',k(9))' l! W. E8 `# F& d5 W
fprintf('\tk10 = %.11f\n',k(10))
5 A' d* A6 Q* ^ s+ j3 ^fprintf(' The sum of the squares is: %.1e\n\n',fval)
9 H6 }: V }( f4 J+ e2 vk_fm= k;
$ C' S a' z( h- O6 ~/ _% warning off x2 O+ d& Q* P' h n5 R6 {" N
% 使用函数lsqnonlin()进行参数估计! g2 C1 ^# W2 q3 p. J5 r2 `
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...7 e* {' J' {+ w; T' Q
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
7 J" {; m, O3 `3 Y4 K) r# M. J* Kci = nlparci(k,residual,jacobian);& ?$ ]$ y* Z7 i* K8 N( y+ W4 n. M9 `
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
4 `& Q: T" _! z+ Kfprintf('\tk1 = %.11f\n',k(1))
* O6 s1 ~: f: wfprintf('\tk2 = %.11f\n',k(2))
! E# C! Z. M. O; zfprintf('\tk3 = %.11f\n',k(3))' @: N7 F4 S1 o) W0 b0 l
fprintf('\tk4 = %.11f\n',k(4))5 ?+ g1 N/ ]6 v! Y& U, |
fprintf('\tk5 = %.11f\n',k(5))
* F: @! T6 a5 U. c% v! [fprintf('\tk6 = %.11f\n',k(6))
: S# F9 J. t* I0 j6 o; b5 zfprintf('\tk7 = %.11f\n',k(7))
. a) A: h( T; a S8 U8 `5 Nfprintf('\tk8 = %.11f\n',k(8))
, U1 C k. S- K" g L7 ~fprintf('\tk9 = %.11f\n',k(9))
3 P9 P: R0 |" f. x; sfprintf('\tk10 = %.11f\n',k(10))
" i Y6 L0 d# ]' E# ofprintf(' The sum of the squares is: %.1e\n\n',resnorm)) ?7 J$ q6 ]% j3 s
k_ls = k;( f6 y5 m F n
output
% f: U- F9 S; mwarning off( d) R4 A& |1 U2 F& Z
% 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
- A: G2 j0 d. \, e$ v. x9 bk0 = k_fm;
* v9 K4 G* a8 c. _[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...9 T2 G- P$ s: w6 f) d0 E5 {
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
) ?0 D- B& Q0 a- B+ qci = nlparci(k,residual,jacobian);* u) w* V+ C6 `
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')- P5 X2 o6 j+ a5 Y9 e- X
fprintf('\tk1 = %.11f\n',k(1))1 @, g, n. o3 t0 b
fprintf('\tk2 = %.11f\n',k(2))
8 w! q7 g1 F6 S. kfprintf('\tk3 = %.11f\n',k(3))5 V5 e& X1 f- W8 x7 o+ A, J* W% }
fprintf('\tk4 = %.11f\n',k(4))
, O: [: B' A/ x9 k/ Yfprintf('\tk5 = %.11f\n',k(5))6 u+ z# D2 w( j5 r$ x7 I
fprintf('\tk6 = %.11f\n',k(6))* d4 m7 h+ A- u% U
fprintf('\tk7 = %.11f\n',k(7)): B! y1 b9 b3 Z' V
fprintf('\tk8 = %.11f\n',k(8)). l+ t; B0 o S6 J
fprintf('\tk9 = %.11f\n',k(9))& X6 c" H, m* B+ z( f
fprintf('\tk10 = %.11f\n',k(10))
9 H4 t; a8 l3 q( z+ o1 P3 ofprintf(' The sum of the squares is: %.1e\n\n',resnorm)
8 O& D/ r8 i& q4 M; U5 Bk_fmls = k;/ U6 B0 }0 Y: l5 { G+ R
output
2 ~9 O( I6 h# P# r5 [. ?" stspan = [0 15 30 45 60 90 120 180 240 300 360];
9 D7 L- o$ p$ u% [6 p3 }$ H5 _& J# O[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
3 ?* E! V2 Y5 f7 N+ s! ~) Nfigure;
8 M( C7 c) O- |3 O" G8 }! ~plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
+ A' c) R- V0 d8 @+ @figure;plot(t,x(:,2:5));! J# @8 {6 O2 A; x; A
p=x(:,1:5)
- I2 C( H- M1 W6 {6 }" x3 O! hhold on- t5 m; I7 E; @$ J. N. N; b
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
8 _4 O& N( f- v* u
+ ]5 U7 L% `5 l" c) z' u
$ S, C* f3 ^) _2 M5 A/ ]& Y! U1 R1 D) a) [
function f = ObjFunc7LNL(k,x0,yexp)
& H1 a$ E9 I u z8 Z8 M; z6 Ptspan = [0 15 30 45 60 90 120 180 240 300 360];
8 ]( n2 W- Y, p, I# G" U- @7 |# t& Q[t, x] = ode45(@KineticEqs,tspan,x0,[],k);
4 ~& @* V" B! B1 s3 a9 g8 U4 ?. Uy(:,2) = x(:,1);
0 Q& ]% d( h5 p) T$ `8 Oy(:,3:6) = x(:,2:5);4 ]4 p1 P. P2 P2 f3 f
f1 = y(:,2) - yexp(:,2);' D4 H: A. Q* B- r3 q7 D
f2 = y(:,3) - yexp(:,3);
) Q* A! E. ^' d% _( ~: J# k4 E1 If3 = y(:,4) - yexp(:,4);
5 H# Y( M d" v5 a: Of4 = y(:,5) - yexp(:,5);
/ W* A$ ]" z8 ]) b- ~f5 = y(:,6) - yexp(:,6);
6 b3 f1 B" ^6 G' i; F- i+ af = [f1; f2; f3; f4; f5];
0 H {4 B& N% {& y# z3 ~! i- E7 p6 z1 T' V* d" f1 X8 N
+ M a) z. Y6 u; Z$ L) d- e1 _. z! D( e ?' |2 f5 T
function f = ObjFunc7Fmincon(k,x0,yexp), m& ?) b" b3 Q' p. o3 C
tspan = [0 15 30 45 60 90 120 180 240 300 360];
6 C9 {# W8 N9 J# X' g6 K[t x] = ode45(@KineticEqs,tspan,x0,[],k);
3 g3 ?: l1 m S" d$ m" @( |y(:,2) = x(:,1);
: N2 i, K" X5 Ky(:,3:6) = x(:,2:5);1 m {0 N2 s5 Q: x o# X
f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
- Z! K; T& X0 e/ U, W" q + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...
' w8 \. x6 _; x) k1 ] d + sum((y(:,6)-yexp(:,6)).^2) ;
; p. C) @4 h7 L/ u9 j3 n
3 J' g, ^/ e5 t1 }# C6 d7 j6 x
$ ~; P2 v1 [4 h5 T: O
7 f4 O9 R3 B1 e, w) N, e% g" t9 l
5 q( o: p& P9 o8 rfunction dxdt = KineticEqs(t,x,k)6 a+ ~7 @- W, l" ?! u
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
) _/ U2 j( x l+ O9 K' x/ |# BdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
. i& L; b( C$ TdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
1 S" b* B8 e: V9 s( D! rdLadt = k(7)*x(5);
- a v) z. R/ WdHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
5 d5 b: g! v' B& x7 O5 sdxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
& P) d. U, N1 T
1 Z+ i! y |: b! }' A2 Q/ |9 C0 ]+ Z2 o. }
|
zan
|