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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 parafit5 {1 p, Q: m7 w! t4 M7 B) k
% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4) P) g Y) n9 ?
% k6->k6 k7->k7/ j( \6 H0 y1 s
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);1 w9 i" m* ]- F. A, B# _# i
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
1 N, b- i, w/ ?3 _) \8 S* l+ s% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);) h# D& S6 t1 A3 M+ ^* Y" P
% dLadt = k(7)*C(Hmf);. k; A$ I- U i+ o$ V& Y u
%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);
" _# a' A7 d' k" l9 rclear all% _% |4 V3 }9 q' W
clc
) c& z$ }# `+ P; K5 u; t$ Qformat long
' A( i6 S: x5 [1 L5 j) a% M% t/min Glc Fru Fa La HMF/ mol/L
" ^+ B8 K, i6 T2 [) U" } Kinetics=[0 0.25 0 0 0 0
0 V2 r7 m' D1 B 15 0.2319 0.01257 0.0048 0 2.50E-04
- A$ \& W( i3 y) i5 y* v 30 0.19345 0.027 0.00868 0 7.00E-04
) I" [% T# S0 F 45 0.15105 0.06975 0.02473 0 0.0033
) G$ T3 ?2 j# m 60 0.13763 0.07397 0.02615 0 0.00428
. L g. _& ~" }! H8 W4 p x 90 0.08115 0.07877 0.07485 0 0.01405
5 f' a* g3 B) v4 o* |3 L 120 0.0656 0.07397 0.07885 0.00573 0.02143 F( `* {0 k3 @- a' |0 y9 ^6 W
180 0.04488 0.0682 0.07135 0.0091 0.03623# @1 |! J2 y2 {: D1 {0 _
240 0.03653 0.06488 0.08945 0.01828 0.05452
/ B+ B+ n/ S# M, @' P 300 0.02738 0.05448 0.09098 0.0227 0.0597
, Q+ u0 b4 E2 d& X" a/ r 360 0.01855 0.04125 0.09363 0.0239 0.06495];) b* E& r7 s1 ]$ @! F$ b
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$ |* U% _9 l1 l( @; {
lb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限! J% v8 D( Y- F! J( l2 x; t$ v/ x4 h
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限
# X) N/ u. d4 a- P' Px0 = [0.25 0 0 0 0];
) ?9 U% [7 H+ R2 ~" \yexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]
5 x1 G: s b; ]+ w3 @% warning off
9 X& f1 G3 q7 o% 使用函数 ()进行参数估计4 q9 S. Y) ?$ e* e: ` m
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);# ^; f* H, }& T6 p4 K- H
fprintf('\n使用函数fmincon()估计得到的参数值为:\n')# ~3 B# i% {6 v) m8 h7 U8 G+ Q2 c% V. a
fprintf('\tk1 = %.11f\n',k(1)) Y M: l7 k4 L8 W8 h
fprintf('\tk2 = %.11f\n',k(2))( o, E* v' [" D! j
fprintf('\tk3 = %.11f\n',k(3))5 s8 ^9 y" w4 V$ O' ^8 Y S
fprintf('\tk4 = %.11f\n',k(4))
7 s, i* y- K0 `) r6 p( T) r* D2 \fprintf('\tk5 = %.11f\n',k(5))% U! a& ]6 o- s6 b" F5 a/ X4 }% i
fprintf('\tk6 = %.11f\n',k(6))- f4 a! q: C2 t4 I3 y
fprintf('\tk7 = %.11f\n',k(7))7 G; X+ e, T {; f% t8 {& b
fprintf('\tk8 = %.11f\n',k(8))
' \- S2 v V1 T; P8 ]" R8 Jfprintf('\tk9 = %.11f\n',k(9))
7 I- I% [! T! Y6 d% b }fprintf('\tk10 = %.11f\n',k(10))! S* M& `! i- i/ Y
fprintf(' The sum of the squares is: %.1e\n\n',fval)9 e/ P7 a# m) l% C7 o' Z E% B+ k
k_fm= k;
$ f' t8 r0 U3 x2 |" ^% warning off' o$ x* \; ?# ?
% 使用函数lsqnonlin()进行参数估计2 \/ Y U. `- i; T2 n
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...# Q+ t+ l1 `. e3 b6 p
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); $ s8 T6 i8 k# t# U
ci = nlparci(k,residual,jacobian);
; M+ e& H/ B, Q9 b8 H+ ^fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
' N1 |) G" }- W+ x5 K4 h9 [4 _( _fprintf('\tk1 = %.11f\n',k(1))! K8 B: j% Y, h3 b& U; q; c7 m
fprintf('\tk2 = %.11f\n',k(2))# P, \1 |1 k5 V$ ^; S7 d% r
fprintf('\tk3 = %.11f\n',k(3))
6 b' X& ~; Y; u- z0 Dfprintf('\tk4 = %.11f\n',k(4))7 u! X" D) X F0 ~$ I% ] j; n* g5 j
fprintf('\tk5 = %.11f\n',k(5))
! N& C2 G* Q) T7 U. `0 lfprintf('\tk6 = %.11f\n',k(6))4 v( Z5 Z. L. f
fprintf('\tk7 = %.11f\n',k(7))
4 s- N& P3 W! b' |fprintf('\tk8 = %.11f\n',k(8))
$ { l' u+ o5 Q- |* Dfprintf('\tk9 = %.11f\n',k(9))' V" P( |; {% D$ V
fprintf('\tk10 = %.11f\n',k(10))
) @3 v' C# H z2 Wfprintf(' The sum of the squares is: %.1e\n\n',resnorm)
+ u/ f3 G c2 d1 w% D4 Kk_ls = k;
& ^7 }$ }+ {6 |7 U3 Q5 Soutput
# l+ ?. i$ h# Rwarning off/ w5 x) X& r( K) w
% 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- d7 x( K( w( P: O8 x% B& E' O% ?
k0 = k_fm;" A0 j$ `1 ~# w+ k1 m5 d6 a
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...4 G f+ e9 l O& e) [8 A% B; E
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); $ s, _; j; c8 q% q
ci = nlparci(k,residual,jacobian);2 T! Q; {( u! |* L2 |7 J) k
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'); R4 `. A5 T+ x
fprintf('\tk1 = %.11f\n',k(1))- O% W5 E5 g! P8 K8 M# P
fprintf('\tk2 = %.11f\n',k(2))
7 z, l) ^/ I5 V T9 ~! Z/ Jfprintf('\tk3 = %.11f\n',k(3))
) i! E i% {) d- a: ~' A* nfprintf('\tk4 = %.11f\n',k(4))
0 |3 K* g; H) n: n$ E$ zfprintf('\tk5 = %.11f\n',k(5))) M( H% E- O$ z1 d+ Y2 q4 I
fprintf('\tk6 = %.11f\n',k(6))
: L) K) U* q& l5 l& e5 ^3 R( d9 Q$ \fprintf('\tk7 = %.11f\n',k(7))
; i* n/ A9 G7 Gfprintf('\tk8 = %.11f\n',k(8))
- p/ U/ G* R6 a3 {9 b; V8 i8 y2 Kfprintf('\tk9 = %.11f\n',k(9))- ?7 p) u8 m% G `! L" s8 d
fprintf('\tk10 = %.11f\n',k(10))
) n" a: L! ?# @( \" G5 g* l$ F* y7 efprintf(' The sum of the squares is: %.1e\n\n',resnorm). r- a" L' C2 O: [( Q: x
k_fmls = k;
3 g2 O: {$ H' C9 U7 w5 Toutput
0 S6 y7 ?; g# xtspan = [0 15 30 45 60 90 120 180 240 300 360];
9 u/ \* O& F) K- f[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
0 N5 [& ]+ F k Y4 m0 ifigure;% O k# s, t* ]/ k: ^0 D
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')+ E. f n7 U' ^8 I
figure;plot(t,x(:,2:5));
: Z% @# {' c+ C/ J4 [6 \ Dp=x(:,1:5)
}0 V1 @+ q2 K$ ?% }# fhold on
* }: t7 c/ k" j& N! \8 V' \plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')6 W6 B8 G% L4 [5 |/ C
% ~) X0 z+ J9 i/ j
( E6 a/ u1 K) |' j
8 M: N% U4 v5 d: q2 k$ o/ o8 Wfunction f = ObjFunc7LNL(k,x0,yexp)
6 j* |* u; N4 v! s5 g' p6 ~2 X! g' Itspan = [0 15 30 45 60 90 120 180 240 300 360];
4 t4 p8 ]! s, _5 }8 S! @[t, x] = ode45(@KineticEqs,tspan,x0,[],k); 6 _9 T4 X' n. l, L ], ?1 h: ?$ j8 k
y(:,2) = x(:,1); P( p- C( H& z% @! Z
y(:,3:6) = x(:,2:5);
1 r3 n/ ]0 i+ Jf1 = y(:,2) - yexp(:,2);+ Z# C# |8 [7 m2 F! ` e, Q
f2 = y(:,3) - yexp(:,3);8 g5 I% e& X, a( x1 o
f3 = y(:,4) - yexp(:,4);
1 A- j7 N, f) q8 ] Q5 O- b9 pf4 = y(:,5) - yexp(:,5);
3 `& j6 ?0 H# B& a; Z/ @1 s) D8 af5 = y(:,6) - yexp(:,6);
* g$ ~ C7 \5 |" u) O) Jf = [f1; f2; f3; f4; f5];
$ \1 s/ y* `7 w# C" N/ a) j- u9 q$ }4 K( b; m
, Z1 e+ u; r8 d' a& u
2 B! U9 l9 E& X/ Qfunction f = ObjFunc7Fmincon(k,x0,yexp)
) f2 I" U0 R* z2 Ktspan = [0 15 30 45 60 90 120 180 240 300 360];/ f0 ^( p& Y ^; W7 C2 [" U
[t x] = ode45(@KineticEqs,tspan,x0,[],k);
6 L0 C6 t& k. Y( o9 a4 q8 A: zy(:,2) = x(:,1);
* a% ^8 y2 C( |& Ny(:,3:6) = x(:,2:5);; Z& s+ N4 h( ~: Y
f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
+ x" z" X0 y8 X- @ + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...9 Y4 }( Q2 B1 b) z* O
+ sum((y(:,6)-yexp(:,6)).^2) ;+ g' P' X9 t* }
; e+ x) Z" b- r! d# K" Y
9 v& T- S" f+ W, {0 }# p5 y" v! Z* g; h; x
2 J/ v0 W, c5 y1 F' x! j
function dxdt = KineticEqs(t,x,k)( Z5 m3 v4 v+ b; O
dGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
# N7 H/ _( q( E! xdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
2 q8 f9 f# t! R' r! Y. sdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);. M7 d9 ]/ H0 ?: q
dLadt = k(7)*x(5);+ }7 H$ y" [+ A6 @+ j$ J
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);4 x8 h8 J7 d) g9 E3 O
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
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& c2 N2 M# g! n1 J9 r; s
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