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Topic: CLOSELOOP FEEDBACK TIMESERIES DESIGN EXAMPLE
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Greg Heath

Posts: 5,871
Registered: 12/7/04
CLOSELOOP FEEDBACK TIMESERIES DESIGN EXAMPLE
Posted: Apr 2, 2013 4:07 AM
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% 1234567890123456789012345678901234567890123456789012345
% This design uses as many defaults as possible. In general,
% 1. The input delay vector, ID, should be chosen from the significant
% T/X cross-correlation lags of the training set . For regression, include
% ID = 0. For prediction, ID > 0. The default value is ID = [ 1:2 ] (prediction)
% 2. The output feedback delay vector FD > 0 should be chosen from
% the significant autocorrelation lags of the training targets. The default
% value is FD = [ 1:2 ]
% 3. The number of hidden nodes, H, should be obtained by trial and
% error. The optimum value is the smallest one that achieves the
% specified error goal. When searching for Hopt, start with the range
% 0<= H <= Hub that results in the number of unknown weights, Nw,
% being less than the number of training equations, Ntrneq. The default
% value is H = 10. If H > Hub, Nw > Ntrneq, and the net is OVERFIT.
% There are several mitigation methods to prevent the overfit net from
% being OVERTRAINED and memorizing the training data so closely
% that the net performs poorly on nontraining data. The default method
% is "Validation set stopping" where the error of a nontraining validation
% set is monitored. Training is stopped if the validation error reaches a
% minimum before the training set error reaches the specified goal.
% 4. Closeloop training with feedack delays can be very time consuming.
% As an alternative, an openloop design is obtained first by replacing the
% feedback connection with an extra input that contains target values.
% When the openloop design is satisfactory, the extra input is connected
% to the output to form the closeloop configuration. If the closeloop
% configuration does not perform as well as the openloop configuration,
% it can be trained further. Initializing the closeloop configuration with the
% openloop design saves a considerable amount of time; especially when
% a search for Hopt is needed.
% 5. There are 8 timeseries data sets that are available for experimentation
% via the command help nndatasets. You can also linearly combine data
% sets if you need more fun.

clear all, close all, clc
tic
[ X, T ] = simplenarx_dataset;
[I N ] = size(X)
[O N ] = size(T)
Ntrn = N-2*round(0.15*N) % default 0.7/0.15/0.15 trn/val/tst ratios
trnind = 1:Ntrn;
Ttrn = T(trnind);
Ntrneq = prod(size(Ttrn))

%ID = 1:2 %default for Prediction
ID = 0:2 % Regression
FD = 1:2 % default
NID = length(ID)
NFD = length(FD)
LDB = max([ID,FD]) % Length of the delay buffer
Hub = -1 + ceil( (Ntrneq-O) / (NID*I + NFD*O+1))
H =5 % <= Hub (default is H = 10)
Nw = (NID*I+NFD*O)*H +(H+1)*O

%THE OPENLOOP DESIGN AND PERFORMANCE

net = narxnet(ID,FD,H);
net.divideFcn = 'divideblock'; % Overrides the default 'dividerand'
[ Xs Xi Ai Ts] = preparets( net, X, {},T );
[net tr Ys Es Xf Af ] = train(net,Xs,Ts,Xi,Ai);
view(net)
whos Xs Ts Xi Ai Ys Es Xf Af
ts = cell2mat(Ts);
ys = cell2mat(Ys);
figure(1)
hold on
plot(ts, 'k--')
plot(ys,'b')

%% THE CLOSELOOP DESIGN AND PERFORMANCE

netc = closeloop(net);
view(netc)
[ Xsc Xic Aic Ts] = preparets( netc, X, {},T );
ysc1 = cell2mat(netc(Xsc,Xic,Aic));
figure(2)
hold on
plot(ts,'k--')
plot(ysc1,'g')
[ netc trc Ysc2 Esc2 Xfc Afc ] = train(netc, Xsc,Ts,Xic,Aic);
ysc2 = cell2mat(Ysc2);
figure(3)
hold on
plot(ts, 'k--')
plot(ysc2,'r')
trc = trc
toc

Have fun with the other nndatasets.

Greg



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