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rbto_mc_L.m
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rbto_mc_L.m
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%%% use Monte Carlo
function rbto_mc_L(nelx, nely, penal, x, dismax, dof, a,b)
rng(0);
nKL = 2;
nu = 0.3;
k = [ 1/2-nu/6 1/8+nu/8 -1/4-nu/12 -1/8+3*nu/8 ...
-1/4+nu/12 -1/8-nu/8 nu/6 1/8-3*nu/8];
KE = 1/(1-nu^2)*[ k(1) k(2) k(3) k(4) k(5) k(6) k(7) k(8)
k(2) k(1) k(8) k(7) k(6) k(5) k(4) k(3)
k(3) k(8) k(1) k(6) k(7) k(4) k(5) k(2)
k(4) k(7) k(6) k(1) k(8) k(3) k(2) k(5)
k(5) k(6) k(7) k(8) k(1) k(2) k(3) k(4)
k(6) k(5) k(4) k(3) k(2) k(1) k(8) k(7)
k(7) k(4) k(5) k(2) k(3) k(8) k(1) k(6)
k(8) k(3) k(2) k(5) k(4) k(7) k(6) k(1)];
numSamples = 100000/2;
u(1:numSamples) = 0;
[eigV, eigF] = KL(nelx, nely, nKL);
roots = [sqrt(3 + sqrt(6))...
-sqrt(3 + sqrt(6))...
sqrt(3 - sqrt(6))...
-sqrt(3 - sqrt(6))];
colPoints = [ 0 0;...
roots(1) 0;...
0 roots(1);...
roots(2) 0;...
0 roots(2);...
roots(3) 0;...
0 roots(3);...
roots(4) 0;...
0 roots(4);...
roots(3) roots(3);...
roots(4) roots(4);...
roots(3) roots(4);...
roots(4) roots(3);...
roots(1) roots(3);...
roots(1) roots(4);...
roots(3) roots(1);...
roots(4) roots(1);...
roots(2) roots(3);...
roots(3) roots(2);...
roots(2) roots(4);...
roots(4) roots(2);...
roots(1) roots(2);...
roots(2) roots(1)];
data = randn(numSamples,nKL);
% data = rand(numSamples,nKL);
% for i = 1:nKL
% index = randperm(numSamples);
% prob = (index'-data(:,i))/numSamples;
% data(:,i) = sqrt(2)*erfinv(2*prob-1);
% end
tic
parfor i = 1:numSamples
Z = sqrt(eigV) .* data(i, :)';
E(1:nely, 1:nelx) = 0;
for j = 1:nKL
E = E + Z(j) * squeeze(eigF(j, :, :));
end
E = a + (b - a) * normcdf(E);
[U] = FEL(nelx, nely, x, penal, KE, E, dof);
u(i) = U(dof);
end
toc
disp('Prob: ');
prob = sum(abs(u) - dismax >= 0)/numSamples
% disp('1 - Prob: ');
% 1 - sum(dismax - abs(u) <= 0)/numSamples
disp('mean: '); mcsu = mean(u)
disp('std: '); mcsstd = std(u)
s = length(colPoints);
v(1:s) = 0;
for i = 1:s
Z = sqrt(eigV) .* colPoints(i, :)';
E(1:nely, 1:nelx) = 0;
for j = 1:nKL
E = E + Z(j) * squeeze(eigF(j, :, :));
end
E = a + (b - a) * normcdf(E);
[U] = FEL(nelx, nely, x, penal, KE, E, dof);
v(i) = U(dof);
end
numVar = 10;
N(1:s, 1:numVar) = 0;
for i = 1:s
N(i, 1) = 1;
N(i, 2) = colPoints(i, 1);
N(i, 3) = colPoints(i, 2);
N(i, 4) = colPoints(i, 1) ^ 2 - 1;
N(i, 5) = colPoints(i, 2) ^ 2 - 1;
N(i, 6) = colPoints(i, 1) * colPoints(i, 2);
N(i, 7) = colPoints(i, 1) ^ 3 - 3 * colPoints(i, 1);
N(i, 8) = colPoints(i, 2) ^ 3 - 3 * colPoints(i, 2);
N(i, 9) = colPoints(i, 1) * colPoints(i, 2) ^ 2 - colPoints(i, 1);
N(i, 10) = colPoints(i, 2) * colPoints(i, 1) ^ 2 - colPoints(i, 2);
end
a = N'*N \ N' * v';
disp1(1:numSamples) = 0;
tic
for i = 1:numSamples
x = data(i, :);
disp1(i) = a(1) + a(2) * x(1) + a(3) * x(2) + ...
a(4) * (x(1) ^ 2 - 1) + a(5) * (x(2) ^ 2 - 1) + ...
a(6) * x(1) * x(2) + ...
a(7) * (x(1) ^ 3 - 3 * x(1)) + a(8) * (x(2) ^ 3 - 3 * x(2)) + ...
a(9) * (x(1) * (x(2) ^ 2) - x(1)) + a(10) * ((x(1) ^ 2) * x(2) - x(2));
end
toc
mdis = mean(disp1)
stddis = std(disp1)
fileID = fopen('data.txt','a+');
fprintf(fileID,'\nprob: %4.7f',prob);
fprintf(fileID,'\nMCS mean: %4.7f',mcsu);
fprintf(fileID,'\nMCS std: %4.7f',mcsstd);
fprintf(fileID,'\nSRSM mean: %4.7f',mdis);
fprintf(fileID,'\nSRSM std: %4.7f',stddis);
fprintf(fileID,'\n\n');
fclose(fileID);
%colormap(gray); imagesc(-x); axis equal; axis tight; axis off; pause(1e-6);
[f1,x1] = ecdf(u);
[f2,x2] = ecdf(disp1);
figure
hold on
r = length(x1)-10:length(x1);
plot(x1(r),f1(r),'-ob')
plot(x2(r),f2(r),'--r*')
legend('MCS','SRSM','Location','best')
xlabel('Displacement')
ylabel('Cumulative probability')
box on
hold off
figure
hold on
plot(x1,f1,'-b')
plot(x2,f2,'--r')
legend('MCS','SRSM','Location','best')
xlabel('Displacement')
ylabel('Cumulative probability')
box on
hold off
end