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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. R$ V* [+ n& G+ G4 f+ M, P
% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
2 p& W7 f- t) @* Y% k6->k6 k7->k7. C; @& e8 l) Z
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);) A0 e( e/ O4 t$ ^" x. R
% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
" L% Z( U+ j' o8 t) c; ?% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);3 f2 t! S8 g2 X
% dLadt = k(7)*C(Hmf); S! z" \' O% Z8 I% G
%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);
6 @9 K8 J' p) yclear all; b$ E, S+ ?* [) K/ u
clc5 `( i p7 b$ `# u0 t
format long- w* I1 Y4 a- \: U& D8 |) A; L+ a
% t/min Glc Fru Fa La HMF/ mol/L * O$ y. N8 j9 h# |2 i
Kinetics=[0 0.25 0 0 0 0. D# U# ^5 `: W, l3 A, l+ }
15 0.2319 0.01257 0.0048 0 2.50E-04$ z( r4 E# L6 \$ i
30 0.19345 0.027 0.00868 0 7.00E-047 b6 H9 e9 x2 a, g3 L
45 0.15105 0.06975 0.02473 0 0.0033
" r6 C" t5 q" q 60 0.13763 0.07397 0.02615 0 0.00428: B$ U5 k) U- A5 B
90 0.08115 0.07877 0.07485 0 0.01405
$ X' }- ~% G# @$ Y# v! a 120 0.0656 0.07397 0.07885 0.00573 0.021435 p( \$ A! i c" _
180 0.04488 0.0682 0.07135 0.0091 0.03623' S; O. |2 V, ]8 b
240 0.03653 0.06488 0.08945 0.01828 0.054520 T' K- t8 H+ L+ A
300 0.02738 0.05448 0.09098 0.0227 0.0597
# ~* k' v1 A# X4 h( v% K# v 360 0.01855 0.04125 0.09363 0.0239 0.06495];
3 p) @, _9 _" s7 K& ak0 = [0.0000000005 0.0000000005 0.0000000005 0.00000000005 0.00005 0.0134 0.00564 0.00001 0.00001 0.00001]; % 参数初值) n% h+ R/ z2 u7 ~
lb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限5 x2 H% t; Q+ c! k1 s
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限
: y% E- S9 D5 g, H% [! v" x) qx0 = [0.25 0 0 0 0];5 X( K* f/ H/ y3 R
yexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]
4 }" |" B D& t! D0 i" Q# I5 {8 i% warning off* W& N: z/ ?$ h$ z. ^9 s% `/ |
% 使用函数 ()进行参数估计% s2 b" r; @0 m" J0 e2 {% w
[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);5 f/ x4 \ a& {, {% S
fprintf('\n使用函数fmincon()估计得到的参数值为:\n')+ ]* q8 i9 P* d
fprintf('\tk1 = %.11f\n',k(1)) S2 m2 F$ ~, R8 m
fprintf('\tk2 = %.11f\n',k(2))
- _- o2 e) g' F z. ~4 S2 P8 rfprintf('\tk3 = %.11f\n',k(3))
5 p* b. g: l* \% v) gfprintf('\tk4 = %.11f\n',k(4))
: p) ~" T) d; H* L0 Pfprintf('\tk5 = %.11f\n',k(5))7 y$ L. G( J9 U/ R* I, ]' b* X: a
fprintf('\tk6 = %.11f\n',k(6))9 P7 Z4 ]5 N& {9 \8 s/ Q# d
fprintf('\tk7 = %.11f\n',k(7))7 V! G/ D2 s! z. W/ e
fprintf('\tk8 = %.11f\n',k(8)): j/ ~7 d) E1 A& N5 G1 W
fprintf('\tk9 = %.11f\n',k(9))% u( c- G) I& O* Z2 \4 M0 `
fprintf('\tk10 = %.11f\n',k(10))& j* N9 F9 o: G' M2 p& I9 W7 d
fprintf(' The sum of the squares is: %.1e\n\n',fval)
8 B9 d* e c9 M* a7 G+ Ek_fm= k;" p% y" l" V6 j" y5 W- B0 x3 p8 A4 T
% warning off6 d/ L' @7 ]6 h2 |7 @
% 使用函数lsqnonlin()进行参数估计
; y8 `: \; a, Q+ K7 x[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...6 ` W! ]. M: J1 q* |$ J# l. L
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
- Y& }2 H( d: P6 p; [" \ci = nlparci(k,residual,jacobian);8 E2 W* H1 I% a8 z) |
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
7 m2 X! `, r+ [8 | ]fprintf('\tk1 = %.11f\n',k(1))
! _! M5 q" b6 Rfprintf('\tk2 = %.11f\n',k(2))
2 ?) `' g) ~ _- m. `fprintf('\tk3 = %.11f\n',k(3))
0 x6 h% V) U5 E4 M0 Z( [1 q$ P- ]% S' Lfprintf('\tk4 = %.11f\n',k(4))
8 M" f/ P: l( Vfprintf('\tk5 = %.11f\n',k(5))/ M1 L* G9 S. o3 h9 d5 T
fprintf('\tk6 = %.11f\n',k(6))& x# Y0 z- m' T0 \ g
fprintf('\tk7 = %.11f\n',k(7))
, I' ]. s+ J/ K6 G) @$ w0 Tfprintf('\tk8 = %.11f\n',k(8))
( |( ?7 a3 f. v4 g; e0 g* I3 X4 C; sfprintf('\tk9 = %.11f\n',k(9))$ p9 d+ b- B) v6 u
fprintf('\tk10 = %.11f\n',k(10))
$ n4 M6 y! S& s' jfprintf(' The sum of the squares is: %.1e\n\n',resnorm)1 \! I- z( h/ o9 i# S
k_ls = k;* g+ U1 U1 b5 @! p% h/ }+ t
output
- f, A- A$ b( l; }& ^3 _warning off
/ }9 X; M, `* v0 u) U% 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3 x. Z* j. X1 o8 `" a" l! E: v
k0 = k_fm;
5 m+ ^+ {0 Z; Q$ I1 M; g0 F[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...7 Z* S' z3 I+ f# _
lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp); 1 F5 h1 c- C- [0 v: S$ u
ci = nlparci(k,residual,jacobian);
) x) E* n* I0 d' vfprintf('\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')
$ p4 e$ x' {9 w A2 Ffprintf('\tk1 = %.11f\n',k(1))6 B5 q' K$ c0 i6 [4 O
fprintf('\tk2 = %.11f\n',k(2))
3 d+ u. Y+ d# n5 {$ ]7 A( bfprintf('\tk3 = %.11f\n',k(3))8 Z, q8 \( |0 m5 T7 Y# H+ W/ R& W T6 D
fprintf('\tk4 = %.11f\n',k(4)). @) d0 d( b6 ]/ ^9 c5 \
fprintf('\tk5 = %.11f\n',k(5))0 \" w6 ?) F& c9 a
fprintf('\tk6 = %.11f\n',k(6)); x+ a. O9 B; {" k
fprintf('\tk7 = %.11f\n',k(7))8 ^' D4 R- |+ H! \( Y4 l
fprintf('\tk8 = %.11f\n',k(8))
0 l# }! O7 n- F$ Z" v" lfprintf('\tk9 = %.11f\n',k(9)), g$ Q+ `/ O/ I( [& I( h% h
fprintf('\tk10 = %.11f\n',k(10))
. T$ n9 H: V7 ~fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
' Q7 v. B. H, t Q( y& [k_fmls = k;
( \ A0 U8 Y* H/ ?, p! l% _output9 d% {' {- I; ^& Y
tspan = [0 15 30 45 60 90 120 180 240 300 360];
% v; Y" c* S/ S6 r9 I7 K/ J[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls);
: G, p! z! I6 t/ d6 Xfigure;/ ?) n8 O3 V. o/ @( f0 y
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')
8 \* ^6 ^. [5 O* qfigure;plot(t,x(:,2:5));' q! B; V, C6 k. Z
p=x(:,1:5)6 J' _3 o8 q% l/ Y% z8 i
hold on
7 H! K" a5 a9 O3 m8 _plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')% |+ J; `- H5 B
* Q3 E7 A" [ E" k' u/ A" n/ {: }! [) V% B
# I, u6 Q! h/ i5 g, O7 y2 [& _8 v
function f = ObjFunc7LNL(k,x0,yexp)* e Q5 g: `2 G: s v* y3 p f
tspan = [0 15 30 45 60 90 120 180 240 300 360];' _2 d; `0 Z+ w ^; a
[t, x] = ode45(@KineticEqs,tspan,x0,[],k); * K9 l9 y4 K5 L& i
y(:,2) = x(:,1);
0 _1 I( `. u# R5 A7 {' o$ ^y(:,3:6) = x(:,2:5);& D" x. M) a2 ]' T1 s7 l2 e
f1 = y(:,2) - yexp(:,2);/ _! c4 e9 H& c$ S c# m
f2 = y(:,3) - yexp(:,3);
% S- I" \9 V4 v, ^f3 = y(:,4) - yexp(:,4);9 u& s' W# z2 \$ g/ g1 U6 w B
f4 = y(:,5) - yexp(:,5); f& z$ a8 f: P5 W% @
f5 = y(:,6) - yexp(:,6);7 y% v" ?0 N# s/ | \
f = [f1; f2; f3; f4; f5];( ]3 a; A0 C+ b; O
6 Z2 s3 f0 u- X0 C' j. @. P3 O
9 v' G! \) C/ y- G: o" w5 {: v. `0 }- R8 h2 d0 h
function f = ObjFunc7Fmincon(k,x0,yexp)
: X- o/ `& n E7 @tspan = [0 15 30 45 60 90 120 180 240 300 360];8 P% r: U$ J6 q$ [
[t x] = ode45(@KineticEqs,tspan,x0,[],k);
1 r$ T( L& D' {y(:,2) = x(:,1);
6 w' a: O; S' ty(:,3:6) = x(:,2:5);
0 v0 A6 c1 g. U% G3 {' B& @f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
( c/ q2 T$ N/ B1 p3 h+ u$ a- G6 G + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...
4 Z& x( m9 L1 K7 C7 k + sum((y(:,6)-yexp(:,6)).^2) ;9 J/ M# G. Q" q3 t/ B: A7 T% y2 u
* p0 u" M0 q$ e5 c6 n& i7 O
* R6 L% M- _' h# Q3 i
$ D5 H- R8 z& Z4 S, K% J5 G
! \$ G! t! I4 S. Cfunction dxdt = KineticEqs(t,x,k)
! A# K9 l6 s) K1 t# f+ p. DdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);
- y7 v6 {" {1 u* O# I; I1 v; e& CdFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);' [; k1 \6 E6 F' Y+ ?* w
dFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
* s+ h# E7 D$ b L4 q% ^dLadt = k(7)*x(5);. v" s8 N( d# U; n
dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);8 ^# X; V( m9 n
dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];$ u/ Q$ v- W, R: X1 n p: h
1 E: E' A$ \; _- a
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