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[交流] 使用lsqnonlin函数优化动力学参数，总是得不到合理的结果

大家好:
      我最近在使用matlab回归动力学参数，首先是使用4阶龙哥库塔算法进行积分，之后使用lsqnonlin进行非线性最小二乘拟合，运行已经写好的m文件，总是得不到合理的结果，不知道是不是自己程序编写有问题，请大神指导，谢谢。
下面粘贴上自己的m文件：
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function zqq100
% 动力学ODE方程模型的参数估计
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
clc
kz0 = [1.73  -3  4.3  3.4  29.4  26.46  22.8  29.4];       % 参数初值
lb  = [];                                                 % 参数下限
ub  = [];                                                 % 参数上限
x0  = [72516.987800 7922.540990 2213.519110 2440.339360];
KineticsData;
yexp = ExpData(:,2:5);                   % yexp: 实验数据[x1 x2 x3 x4]

%再参数化
a = 0; b = 0.022146; d=0.000022146;
tt=a:d:b;
z = func(tt);
Tintegral = quadl(@func,a,b);             %  实际上应该是(1000/T)integral
Taverage  = Tintegral/(b-a) ;             %  实际上应该是(1000/T)average

% 优化参数设置
options=optimset ('Display','iter','TolX',1e-25,'TolFun',1e-25,'LargeScale','off','MaxIter',2,'MaxFunEvals',inf);

% 使用函数lsqnonlin()进行参数估计
[kz,resnorm,residual,exitflag,output,lambda,jacobian] = ...
lsqnonlin(@ObjFunc4LNL,kz0,lb,ub,options,x0,yexp,Taverage);
ci = nlparci(kz,residual,jacobian);

%把回归参数转化为自己需要的参数
k01 = exp(kz(1)+kz(5)*Taverage);
ke1 = exp(ci(1,2)-kz(1)+(ci(5,2)-kz(5))*Taverage);
Ea1 = kz(5)*1000*8.314;
Ee1 = (ci(5,2)-kz(5))*1000*8.314;

k02 = exp(kz(2)+kz(6)*Taverage);
ke2 = exp(ci(2,2)-kz(2)+(ci(6,2)-kz(6))*Taverage);
Ea2 = kz(6)*1000*8.314;
Ee2 = (ci(6,2)-kz(6))*1000*8.314;

k03 = exp(kz(3)+kz(7)*Taverage);
ke3 = exp(ci(3,2)-kz(3)+(ci(7,2)-kz(7))*Taverage);
Ea3 = kz(7)*1000*8.314;
Ee3 = (ci(7,2)-kz(7))*1000*8.314;

k04 = exp(kz(4)+kz(8)*Taverage);
ke4 = exp(ci(4,2)-kz(4)+(ci(8,2)-kz(8))*Taverage);
Ea4 = kz(8)*1000*8.314;
Ee4 = (ci(8,2)-kz(8))*1000*8.314;
% ------------------------------------------------------------------
% 输出结果
fprintf('\n\n使用函数lsqnonlin()估计得到的参数值为:\n')
fprintf('\tk01 = %.4f ± %.4f\n',k01,ke1)
fprintf('\tk02 = %.4f ± %.4f\n',Ea1,Ee1)
fprintf('\tk03 = %.4f ± %.4f\n',k02,ke2)
fprintf('\tk04 = %.4f ± %.4f\n',Ea2,Ee2)
fprintf('\tEa1 = %.4f ± %.4f\n',k03,ke3)
fprintf('\tEa2 = %.4f ± %.4f\n',Ea3,Ee3)
fprintf('\tEa3 = %.4f ± %.4f\n',k04,ke4)
fprintf('\tEa4 = %.4f ± %.4f\n',Ea4,Ee4)
fprintf('  The sum of the squares is: %.1e\n\n',resnorm)

% ------------------------------------------------------------------
function f = ObjFunc4LNL(kz,x0,yexp,Taverage)
tspan = [0.000000 0.006021 0.009538 0.012340 0.014647 0.016594 0.018268 0.019730 0.020395 0.021021 0.021613 0.022146];
[t x] = ode45(@KineticEqs,tspan,x0,[],kz,Taverage);
y(:,1:4)=x(:,1:4);
f1 = y(:,1) - yexp(:,1);
f2 = y(:,2) - yexp(:,2);
f3 = y(:,3) - yexp(:,3);
f4 = y(:,4) - yexp(:,4);
f = [f1; f2; f3; f4];

% ------------------------------------------------------------------
function dxdt = KineticEqs(t,x,kz,Taverage)

T = 2E+09*t.^4 - 8E+07*t.^3 + 1E+06*t.^2 + 1593.6*t + 823.94;
D = 1000./T-Taverage;

k(1)=exp(kz(1)-kz(5)*D);
k(2)=exp(kz(2)-kz(6)*D);
k(3)=exp(kz(3)-kz(7)*D);
k(4)=exp(kz(4)-kz(8)*D);

dxdt =  ...
[ ( - k(1)*x(1) )
( - k(1)*x(1) - k(3)*x(3) + k(2)*x(2) )
( - k(1)*x(1) + k(3)*x(3) + k(4)*x(3) )
( - k(2)*x(2) - k(3)*x(3) - k(4)*x(3) )
];
% ------------------------------------------------------------------
function z = func(tt)
z =1000./( 2E+09*tt.^4 - 8E+07*tt.^3 + 1E+06*tt.^2 + 1593.6*tt + 823.94);

数据文件
% 动力学数据:
%    t       y1       y2       y3       y4
ExpData = ...
[ 0.000000 72516.987800 7922.540990       2213.519110    2440.339360
0.006021 42499.607900 22206.384100 3306.398400    3606.838600
0.009538 29000.355000 29930.619400 3600.077060    3836.127990
0.012340 20185.280200 35570.546400 3528.468400    3684.127360
0.014647 14159.635500 39715.404600 3262.616960    3307.931340
0.016594 9923.223120       42747.821100 2919.806950    2824.661990
0.018268 6889.657400       44873.256100 2561.423650    2313.346410
0.019730 4712.646380       46269.306400 2219.932610    1823.752130
0.020395 3871.540620       46727.452000 2061.574630    1592.788930
0.021021 3166.514550       47033.087200 1914.970250    1369.417740
0.021613 2580.686780       47184.935100 1784.008050    1149.425230
0.022146 2121.809490       47180.789300 1679.141140    937.562404
]

[ Last edited by zhangqq72270 on 2013-8-14 at 10:15 ]

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