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multiplecheese_irrsm_typeii.m
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% IMLICIT-RESPONSE RESIDUAL SPACE MAPPING ALGORITHM-T2
% MULTIPLE-CHEESE CUTTER ILLUSTRATION
%% House keeping
clc; close all;
clearvars;
co = [4 2]; fo =[4 4];
% ic = 2;
for ic = 1:length(co)
%% Inits
% desired fine model volume response
Raim = 10;
% candidate designable parameters
% initial guess; length and width
% n.b: if c ~= f then there is a misalignment
% to get the root solution, first calculate without misalignment, c == f
% then calculate with misalignment.
l=1; c = co(ic); w_c = 1;
l_c = moptm_coarse(Raim,[l, c, w_c]);
%
l_f = l_c; f1=fo(ic); f2=fo(ic); w_f=1; w_f1=1; w_f2=1;
%% Initial
% coarse model
R_c = Rcoarse([l_c,c, w_c]);
% fine model
R_f = Rfine([l_f, f1, f2, w_f, w_f1, w_f2]);
% aim
Raim = [Raim Raim Raim];
% display
fprintf('\nIteration.%g\n', 0)
fprintf('l:%g\n', l_c)
fprintf('w:%g\n', w_c)
fprintf('R_c: %g\n',R_c')
fprintf('R_f: %g\n',R_f')
fprintf('Fine aim: %g\n',Raim')
id = 1;
itTab = []; % store parameters per iteration
chck = norm(Raim - R_f); % [] store norm error
itTab = [itTab; [0 0 0 0 0 l_c w_c R_c 0 0 0 R_f (chck(id)*100/(sum(Raim)/3))]];
optl = Inf;
Rf = R_f; % [] store fine model response
%% SM Iteration
while chck > 1e-3
%% Parameter Extraction -> width
% rng default % For reproducibility
fun_x = @(x)norm( R_f - (Rcoarse([l_c, c, w_c+x]) )); % cost function
% options = optimoptions(@fminunc, 'Algorithm', 'quasi-newton')
% options = optimoptions(@simulannealbnd, 'HybridFcn', 'fminunc')
% options = optimoptions(@particleswarm, 'SwarmSize',64,'HybridFcn', @fminsearch)
% fminsearch - derivative free- simplex method.
% options = optimoptions('fminimax','AbsoluteMaxObjectiveCount',3);
x = fminsearch(fun_x,w_c); % alternative:fminsearch, or fminunc, but slower convergence
%
w_c = w_c+x;
%% Residual enhanced Surrogate
% coarse model
R_c = Rcoarse([l_c, c, w_c]);
% calculate residual
dR = R_f - R_c;
% new surrogate with residual
% R_s = (Rcoarse([l_c + l, c, w_c])+ dR);
R_s = Rsurrogate([l_c,c,w_c],dR);
% display
fprintf('\nIteration.%g\n', id)
fprintf('q1: %g\n',x)
fprintf('l:%g\n', l_c)
fprintf('w:%g\n', w_c)
fprintf('R_s: %g\n',R_s')
fprintf('R_c: %g\n',R_c')
fprintf('R_f: %g\n',R_f')
fprintf('Fine aim: %g\n',Raim')
% itTab = [itTab; [id x dR l_c w_c R_s R_c R_f (chck(id)*100/(norm(Raim)))]];
%% Optmise Surrogate, Prediction -> length
[l_c, lopt] = optim_sug(Raim,[l_c,c,w_c],dR);
l_f = l_c;
%% Fine Model Verification
% coarse model
R_c = Rcoarse([l_c, c, w_c]);
% fine model
R_f = Rfine([l_f, f1, f2, w_f, w_f1, w_f2]);
Rf = [Rf; R_f];
% display
fprintf('\nIteration.%g\n', id)
fprintf('q1: %g\n',x)
fprintf('l:%g\n', l_c)
fprintf('w:%g\n', w_c)
fprintf('R_s: %g\n',R_s')
fprintf('R_c: %g\n',R_c')
fprintf('R_f: %g\n',R_f')
fprintf('Fine aim: %g\n',Raim')
% dR = R_f - R_c
%% Termination Condition
% calculate error-accuracy
chck = [chck; norm(Raim - R_f)]; %#ok<*AGROW>
% store parameters
itTab = [itTab; [id x dR l_c w_c R_s R_c R_f (chck(id)*100/(norm(Raim)))]];
% terminate iteration if a limit attractor reached.
if (id >= 2)
if abs(chck(id) - chck(id-1)) <= 1e-4
break;
end
end
id = id + 1;
end
% store the root fine model solution
if ic == 1
chck_opt = chck;
l_opt = l_f;
else
% display
formatSpec = 'Fine Model Parameters are: %g, %g, %g (units)\n';
fprintf(formatSpec,[l_f; w_f; 1])
formatSpec = 'Fine Model Cheese Volume are: %g, %g, %g (cubic units)\n';
fprintf(formatSpec,R_f')
end
end
%% Visualization
figure(1);
% subplot 1
subplot(211)
plot(1:numel(chck),chck,'-.sr','MarkerSize',5,'LineWidth',0.75)
grid on;
xlabel('Iteration','Interpreter','latex')
ylabel('$$Norm-2 Error$$',...
'FontSize',10,'Interpreter','latex')
title('Multiple Cheese Cutter: Implicit Response Residual Space Mapping Optimization-2',...
'FontSize',10,'Interpreter','latex')
axis([1,inf,min(chck)-0.01,inf])
%
subplot(212)
for ix = 1:id
l_err(ix) = norm(l_opt - itTab(ix,6));%#ok<SAGROW>
end
plot(l_err,'-.','Marker','.','MarkerSize',20,'LineWidth',0.25)
grid on;
xlabel('Iteration','Interpreter','latex')
ylabel('Error, $$||l_{f}-{l_{f}}^{\ast}||$$',...
'FontSize',10,'Interpreter','latex')
title('Multiple Cheese Cutter: Fine-Model Response',...
'FontSize',10,'Interpreter','latex')
axis([1,inf,min(l_err)-0.01,inf])