comgui('close all clear');

% Demonstration of the test/analysis correlation capabilities of the SDT
% for the case of the GARTEUR SM-AG-19 Testbed.
%
% The test results used in this demo were kindly provided by one of the 11
% participants of the GARTEUR SM-AG-19 action group.
%
% The documentation associated to this demo is accessible using doc('sdt/pre')


% initialize by loading results of the GARTFE and GARTTE demos
femesh('reset');
load sdt_gart FEnode FEelt mdof md0 f0 sdof IIpo IIres pl il
fecom(';guione;view3;sub 1 1');femesh plotelt; cf=feplot;
model=struct('Node',FEnode,'Elt',FEelt,'DOF',mdof,'pl',pl,'il',il);

%-----------------------------------------------------------------
%
% This restarts correlation as detailed in GARTTE

sens=fe_sens('model',model);
sens.tdof=sdof;
sens=fe_sens('arigid',sens);

% Comparisons of frequency and MAC, start by finding analysis modes that
% best match each test result and compare

figure(1);clf;
subplot(211);
ii_mac(IIres.',md0,'sens',sens,'labela','Test','labelb','FEM','mac pair plot')
subplot(212);ii_mac(1,'fa',IIpo,'fb',f0,'mac error');


demosdt('pause');%------------------------------------------------

% In many cases, one wants to predict the response at non measured nodes
% using expansion methods

% For example, a modal expansion on the basis of the first 14 modes

mdex1 = fe_exp(IIres.',sens,md0(:,1:14));

out=ii_mac(1,'macpair'); ind=out.indb;

cf.def(1)={mdex1,mdof,IIpo};
cf.def(2)={md0(:,ind),mdof,f0(ind)};
fecom(';sub1 1;sel1egid>0;show2def;ScaleMatch;ch+3');

% You might want to take the time to see the influence of changing the number
% of modes selected for the expansion (its an interesting problem).

demosdt('pause');%------------------------------------------------

% For more robustness you will prefer a static expansion

[m,k,mdof] = fe_mk(model,'options',[0 1]);

mdex2 = fe_exp(IIres.',0,sens,m,k,mdof);
cf.def(1)={mdex2,mdof,IIpo(:,1)};


demosdt('pause');%------------------------------------------------

% but the best results will be obtained using a dynamic expansion combining
% static and modal expansion. This dynamic expansion can be performed on a
% reduced basis as shown below (this makes its numerical cost acceptable even
% for very large models).
%
% Assuming that your DOFs are already renumbered (automatic above 1000 DOF, see
% fe_mk) a typical call for Reduced Basis Dynamic Expansion (RBDE) would be

[md0,f0,kd] = fe_eig(m,k,[6 30 1e2]); f0=f0/2/pi;
T = fe_norm([kd \ ((sens.cta)') md0],m,k);
mdex3 = fe_exp(IIres.',IIpo(:,1)*2*pi,sens,m,k,mdof,T);
cf.def(1)={mdex3,mdof,IIpo(:,1)};
fecom(';sel1egid>0;show2def');

% You could also compute Minimum Dynamic Residual Expansion (MDRE) with
%
% T = fe_norm(T,m,k); % needed to prevent numerical conditionning problems
%  mdex3 = fe_exp(IIres.',IIpo(:,1)*2*pi,sens,m,k,mdof,T,'mdre');
%
% and MDRE with measurement error (MDRE-WE) using 
%
% opt=struct('type','mdrewe','gamma',1,'MeasErr',.1);
% [mdex3,opt,mdexT,err] = fe_exp(IIres.',IIpo(:,1)*2*pi,sens,m,k,mdof,T,opt);

demosdt('pause');%------------------------------------------------

% To illustrate the influence of the expansion method on the quality of the
% correlation you can take a look at the mass wheighted MAC
% (normalized mass cross-orthogonality criterion) for the 3 expansion methods

aa = ii_mac(1,'mac pair'); i1=aa.indb;
a1=ii_mac(md0(:,i1),mdex1,m);a2=ii_mac(md0(:,i1),mdex2,m);
a3=ii_mac(md0(:,i1),mdex3,m);
aa = [[1:size(IIpo,1)]' IIpo(:,1) f0(i1) (IIpo(:,1)./f0(i1)-1)*100 ...
      diag(aa.data) diag(a1.data) diag(a2.data) diag(a3.data)];
fprintf(1,' # :  Test   FE    (Delta F , MAC, M-MAC for MOD,  STA,  RBD)\n');fprintf(1,'%2i : %6.2f %6.2f (%6.1f %%, %4.2f,  %11.2f, %4.2f, %4.2f)\n',aa')

%-----------------------------------------------------------------
eval(demosdt('echooff'))

%       Etienne Balmes  28/07/95, 22/03/01
%       Copyright (c) 1990-2003 by SDTools, All Rights Reserved
%       $Revision: 1.5 $  $Date: 2006/02/23 07:47:08 $