Активный эксперимент идентификации нелинейной системы. Оптимальный D-план экспериментов для получения модели исследуемой системы с заданной точностью при различных условиях, страница 3

Neks = 1; % 1 10        % количество экспериментов

Ntest = 100; % 100 1000 10000

delta_linear = 0;

delta_interaction = 0;

delta_purequadratic = 0;

delta_quadratic = 0;

eps_linear = 0;

eps_interaction = 0;

eps_purequadratic = 0;

eps_quadratic = 0;

X1=[1 2];

X2=[2 3];

X3=[3 4];

X4=[4 5];

X5=[5 6];

for k = 1: Neks

for i = 1: Ntest

x1=X1(1)+(X1(2)-X1(1))*rand(1,1);

x2=X2(1)+(X2(2)-X2(1))*rand(1,1);

x3=X3(1)+(X3(2)-X3(1))*rand(1,1);

x4=X4(1)+(X4(2)-X4(1))*rand(1,1); 

x5=X5(1)+(X5(2)-X5(1))*rand(1,1);

beta = beta_linear;

y_linear = beta(1) + beta(2)*x1 + beta(3)*x2 + beta(4)*x3+beta(5)*x4+beta(6)*x5;

beta = beta_interaction;

y_interaction = beta(1) + beta(2)*x1 + beta(3)*x2 + beta(4)*x3+beta(5)*x4+beta(6)*x5...

+beta(7)*x1*x2+beta(8)*x1*x3+beta(9)*x1*x4+beta(10)*x1*x5+beta(11)*x2*x3...

+beta(12)*x2*x4 +beta(13)*x2*x5+beta(14)*x3*x4+beta(15)*x3*x5+beta(16)*x4*x5;   

beta = beta_quadratic;

y_quadratic = beta(1) + beta(2)*x1 + beta(3)*x2 + beta(4)*x3+beta(5)*x4+beta(6)*x5...

+beta(7)*x1*x2+beta(8)*x1*x3+beta(9)*x1*x4+beta(10)*x1*x5+beta(11)*x2*x3...

+beta(12)*x2*x4 +beta(13)*x2*x5+beta(14)*x3*x4+beta(15)*x3*x5+beta(16)*x4*x5...

+beta(17)*x1*x1+beta(18)*x2*x2+beta(19)*x3*x3+beta(20)*x4*x4+beta(21)*x5*x5;

beta = beta_purequadratic;

y_purequadratic = beta(1) + beta(2)*x1 + beta(3)*x2 + beta(4)*x3+beta(5)*x4+beta(6)*x5...

+beta(7)*x1*x1+beta(8)*x2*x2+beta(9)*x3*x3+beta(10)*x4*x4+beta(11)*x5*x5;    

yt = ((x2.^3).*x3)+x1+(x5.^x4);

delta_linear(i)= abs((y_linear-yt)/yt);

delta_interaction(i)= abs((y_interaction-yt)/yt);

delta_quadratic(i)= abs((y_quadratic-yt)/yt);

delta_purequadratic(i)= abs((y_purequadratic-yt)/yt);   

end

eps_linear(k) = mean(delta_linear);

eps_interaction(k) = mean(delta_interaction);

eps_quadratic(k) = mean(delta_quadratic);

eps_purequadratic(k) = mean(delta_purequadratic);

end

eps_mean_linear = mean(eps_linear)

eps_mean_interaction = mean(eps_interaction)

eps_mean_quadratic = mean(eps_quadratic)

eps_mean_purequadratic = mean(eps_purequadratic)

x = [ 100; 1000; 10000];

y1 = [0.3802 ;0.3866; 0.3884];

y2 = [0.3986;0.3884;0.3874];

y3 = [0.2955;0.2993;0.2968 ];

y4 = [0.2969;0.2948;0.2955];

y5 = [0.1096;0.1087;0.1073 ];

y6 = [ 0.1080;0.1060;0.1065 ];

y7 = [0.3506;0.2680;0.2623];

y8 = [ 0.2696;0.2650;0.2623];

plot(x,y1,'b');

hold on

plot(x,y2,'b--');

hold on

plot(x,y3,'g');

hold on

plot(x,y4,'g--');

hold on

plot(x,y5,'r');

hold on

plot(x,y6,'r--');

hold on

plot(x,y7,'k');

hold on

plot(x,y8,'k--');