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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
; N% b" `% o! _2 ` H* v% k1->k-1,k2->k1,k3->k2,k4->k3,k5->k4
; T4 z5 M9 `7 G% k6->k6 k7->k77 P$ d1 Y1 P! S2 t! a
% dGlcdt = k-1*C(Fru)-(k1+k2)*C(Glc);
9 `) B. k! w# ], H3 o% dFrudt = k1*C(Glc)-(k-1+k3+k4)C(Fru);
. O. A$ Z6 Z1 X5 f% dFadt = k(2)*C(Glc)+k4*C(Fru)+(k6+k7)*C(Hmf);; _3 f" Q2 C0 X( [! _2 T1 r
% dLadt = k(7)*C(Hmf);
/ g7 L; P1 a P0 E0 N H9 G%dHmfdt = k(3)*C(Fru)-(k6+k7)*C(Hmf);4 H7 M6 N4 o3 |& C+ X2 L0 [
clear all
/ Z F: `* p' [( g2 Tclc/ C# d9 v( u0 i( ]( f9 z z0 R
format long9 k6 P( q, |+ Y) S7 D$ x
% t/min Glc Fru Fa La HMF/ mol/L 9 {/ n) K" |; p: x2 }
Kinetics=[0 0.25 0 0 0 0% h4 {$ ^* C0 v
15 0.2319 0.01257 0.0048 0 2.50E-046 l3 J" t" f' L' n7 Q
30 0.19345 0.027 0.00868 0 7.00E-04
, t4 r/ W% M$ s7 y 45 0.15105 0.06975 0.02473 0 0.0033
# y# e. w: L; S, M2 [ 60 0.13763 0.07397 0.02615 0 0.00428/ M" B& X5 p1 l. l
90 0.08115 0.07877 0.07485 0 0.01405
. k6 G: ?. I8 Y2 X _7 U 120 0.0656 0.07397 0.07885 0.00573 0.021432 O; q2 Q& n( p1 a+ P( f) U
180 0.04488 0.0682 0.07135 0.0091 0.03623. n: F( J/ R! D5 N/ D, \
240 0.03653 0.06488 0.08945 0.01828 0.05452+ |+ R" s( D0 z+ D+ B! I) L# P- h
300 0.02738 0.05448 0.09098 0.0227 0.0597
/ W$ g( S% y# M$ {/ q, O 360 0.01855 0.04125 0.09363 0.0239 0.06495];0 t9 i' `9 ^5 I5 R5 W$ f; q
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6 i- l ?' Y6 w4 _* R& I0 {9 N3 A: y2 }2 J
lb = [0 0 0 0 0 0 0 0 0 0]; % 参数下限) Z+ v/ x. b7 b+ D& G0 D
ub = [1 1 1 1 1 1 1 1 1 1]; % 参数上限( {8 L3 _; y! T5 i( i
x0 = [0.25 0 0 0 0];
" C8 f' _/ {) A' ]0 }# y* Cyexp = Kinetics; % yexp: 实验数据[x1 x4 x5 x6]0 E9 D, ^' @2 u3 s& w* ? a7 r
% warning off
9 }, Z1 f" o( ^1 T- x! f% 使用函数 ()进行参数估计
. h# Y3 ~/ n! S3 D[k,fval,flag] = fmincon(@ObjFunc7Fmincon,k0,[],[],[],[],lb,ub,[],[],x0,yexp);3 a' v5 H" N8 M& ]0 z% I" p
fprintf('\n使用函数fmincon()估计得到的参数值为:\n')
0 Q. r1 a g3 q' a' Afprintf('\tk1 = %.11f\n',k(1))
2 g" m4 b0 r/ t' Cfprintf('\tk2 = %.11f\n',k(2))
$ ~! G. l$ D- Cfprintf('\tk3 = %.11f\n',k(3))0 K0 a: {2 t- p- ]& E) D1 O: ~) i
fprintf('\tk4 = %.11f\n',k(4))
, A5 }8 a" [" h1 Wfprintf('\tk5 = %.11f\n',k(5))
$ k6 ^, a6 ^) E: wfprintf('\tk6 = %.11f\n',k(6))- @1 N, }# `& ]
fprintf('\tk7 = %.11f\n',k(7))
/ T. Y1 \5 _( g$ `fprintf('\tk8 = %.11f\n',k(8))
7 i$ ^' i( s2 _- l1 `) @fprintf('\tk9 = %.11f\n',k(9)), i$ O; v! c, _5 L8 A2 K& b4 v
fprintf('\tk10 = %.11f\n',k(10))4 y. A7 \- ~7 F9 a
fprintf(' The sum of the squares is: %.1e\n\n',fval) X7 A6 \* K* r
k_fm= k;# p3 m# ?. c, H+ j( t9 H4 Y! h; H
% warning off
; I1 T1 R$ c- [% 使用函数lsqnonlin()进行参数估计8 l, n/ X. s$ m6 l3 u
[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
4 }$ ]( O- C+ n J9 X$ A4 {& b) A lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
) r- Z" h* D- r$ Z" q+ tci = nlparci(k,residual,jacobian);& }$ s6 O2 u* G! x/ b
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
+ J) u8 l* H- o, ffprintf('\tk1 = %.11f\n',k(1))
% @+ J# f& P* ~& Efprintf('\tk2 = %.11f\n',k(2))' x3 y* n2 a! p
fprintf('\tk3 = %.11f\n',k(3))
" ~* n$ z1 \% Q: ]: ?fprintf('\tk4 = %.11f\n',k(4))5 @. y8 f: C; a. o$ l0 j
fprintf('\tk5 = %.11f\n',k(5)); E; t3 ] f# L- n% B
fprintf('\tk6 = %.11f\n',k(6))% I y. [4 V' N( F
fprintf('\tk7 = %.11f\n',k(7))2 ]5 n r! P: |, f4 w. z& Y) v0 m
fprintf('\tk8 = %.11f\n',k(8))1 B a# s; m* L, D( P9 i
fprintf('\tk9 = %.11f\n',k(9))/ h5 P: n, v- Y' z6 J
fprintf('\tk10 = %.11f\n',k(10)), p- J9 [! j# _6 S. o4 z% D
fprintf(' The sum of the squares is: %.1e\n\n',resnorm)
- h$ t& d6 I/ k, _: r: u9 A6 d9 dk_ls = k;
7 x* n& e0 ^# e4 Z( G Zoutput' K x( r* t1 ?: t7 W
warning off+ ^8 r6 [, {, L
% 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
6 Y0 J( c+ G+ t9 ?5 u$ Ok0 = k_fm;
# ]/ E6 e* g6 M" i6 p[k,resnorm,residual,exitflag,output,lambda,jacobian] = ...
; W- _3 _2 Y8 [3 e lsqnonlin(@ObjFunc7LNL,k0,lb,ub,[],x0,yexp);
D1 v4 _4 |& E( C3 _+ G% V6 g# Fci = nlparci(k,residual,jacobian);* k/ G5 E# v" X& t& E9 q1 s
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'). p1 V4 }+ C6 C) [( m2 |! F9 s' N3 R
fprintf('\tk1 = %.11f\n',k(1))
, l4 g' J3 f/ W* C" |# g# ofprintf('\tk2 = %.11f\n',k(2)); A) C. W' F3 d5 [: c
fprintf('\tk3 = %.11f\n',k(3))
$ ]+ M \* H+ Q9 a1 m7 k! Tfprintf('\tk4 = %.11f\n',k(4)) l) c& `; G7 ~3 p) j" M8 V' P
fprintf('\tk5 = %.11f\n',k(5))- F6 P+ S$ ^/ F0 F" |+ N9 I* ?
fprintf('\tk6 = %.11f\n',k(6))0 z6 `2 n' `& ~* e0 ^- b8 E
fprintf('\tk7 = %.11f\n',k(7))
1 U/ |- M0 j, i, s' C& gfprintf('\tk8 = %.11f\n',k(8))3 E, W% {/ f7 w
fprintf('\tk9 = %.11f\n',k(9))
5 n6 a/ u! M! k, u% Zfprintf('\tk10 = %.11f\n',k(10))7 X! }: [, p: v/ e: y; {( n1 f# V% {
fprintf(' The sum of the squares is: %.1e\n\n',resnorm), j! a! S" \* }- w6 q
k_fmls = k;
A# q( F/ u2 p, doutput
6 p# \# ~8 L) {7 W. c# X9 t" V- ntspan = [0 15 30 45 60 90 120 180 240 300 360];
$ [* o' X6 G9 x! k6 ~[t x] = ode45(@KineticEqs,tspan,x0,[],k_fmls); + [2 ~- B) p! B+ [
figure;* I! \( V o1 V+ \8 r; Z; q0 |
plot(t,x(:,1),t,yexp(:,2),'*');legend('Glc-pr','Glc-real')" P7 l9 o; k4 a" W
figure;plot(t,x(:,2:5));
2 z, b" q8 N7 ap=x(:,1:5)
, _, U8 S7 a) i% i% \# o6 {6 bhold on/ r K* ?/ }7 Z4 g: P2 J5 Z3 Z
plot(t,yexp(:,3:6),'o');legend('Fru-pr','Fa-pr','La-pr','HMF-pr','Fru-real','Fa-real','La-real','HMF-real')
' @8 O: k$ a5 P8 D8 v; l& X
, S4 ]0 j1 _7 ]: G% E$ @" U" Y# R$ F6 b3 t& N
: E" Q; m f% P( yfunction f = ObjFunc7LNL(k,x0,yexp)) @, N& ~2 l- f# Z2 R
tspan = [0 15 30 45 60 90 120 180 240 300 360];
" l7 X$ v+ {& r! W/ }( R, j[t, x] = ode45(@KineticEqs,tspan,x0,[],k); 7 X/ ?3 M8 U1 M2 J8 M
y(:,2) = x(:,1);
; N. \2 T2 c* z ^y(:,3:6) = x(:,2:5);
/ a" E! w* c" d3 d; d2 U; c3 xf1 = y(:,2) - yexp(:,2);: j5 U! `( [, F& P( t4 a6 `7 S
f2 = y(:,3) - yexp(:,3);
1 w7 w. n- k; E9 {: df3 = y(:,4) - yexp(:,4);* Z% a, ~- g. Z9 Q& h6 _) y
f4 = y(:,5) - yexp(:,5);, M/ [" Z- U1 u- _! F; Z8 d6 U
f5 = y(:,6) - yexp(:,6);3 o# u4 H4 r! x- [5 E5 U5 T8 U& q
f = [f1; f2; f3; f4; f5];
9 s( e7 F/ n, Y$ G2 f
2 w p. t1 W. T f4 t
. Q% X _( K Q6 Z: q- P$ Q- k( c3 ?9 l9 ^* n
function f = ObjFunc7Fmincon(k,x0,yexp)( i5 G9 y6 b) y$ A
tspan = [0 15 30 45 60 90 120 180 240 300 360];; H- ^- D% z' l$ T
[t x] = ode45(@KineticEqs,tspan,x0,[],k); 7 Z( h7 n: U! u; s" o7 Z+ O
y(:,2) = x(:,1);" G( v" h; @! L* V3 R$ G
y(:,3:6) = x(:,2:5);1 }/ o+ i. _, \7 G" S
f = sum((y(:,2)-yexp(:,2)).^2) + sum((y(:,3)-yexp(:,3)).^2) ...
% w# L" q7 v& P0 d4 T + sum((y(:,4)-yexp(:,4)).^2) + sum((y(:,5)-yexp(:,5)).^2) ...( R9 G8 x- j; L6 J! _4 p/ {
+ sum((y(:,6)-yexp(:,6)).^2) ;
' d( a4 V4 f* U4 E8 S4 b( t3 o3 }
( C8 G9 a% V- h, I# m& k9 g7 t. D& X. H
( F- p2 p, B2 M' E6 v
% X0 `8 \: I5 f# H* L" L
function dxdt = KineticEqs(t,x,k)
& U- {7 S' R% ^' XdGldt = k(1)*x(2)-(k(2)+k(3)+k(8))*x(1);9 H& y5 {; b3 z; n1 s7 y
dFrdt = k(2)*x(1)-(k(1)+k(4)+k(5)+k(9))*x(2);
& g5 [9 T+ M7 B% LdFadt = k(3)*x(1)+k(5)*x(2)+(k(6)+k(7))*x(5);
) `4 }8 K' N& jdLadt = k(7)*x(5);
7 w) z0 W; o7 [dHmdt = k(4)*x(2)-(k(6)+k(7)+k(10))*x(5);
# g* j2 `6 [0 Q$ p5 D( _dxdt = [dGldt; dFrdt; dFadt; dLadt; dHmdt];
) w5 ]3 K, i9 E6 ?& W- ?* n' ]' a5 W3 w0 B
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