MATLAB: Input and feedback delay in narxnet

feedback delaysinput delaysnarxnet

if true
  % code
endHello,
I have recently started working on neural network with MATLAB. I am dealing with gas turbine dynamic model and facing problems in determining optimal value of input and feedback delays. I have gone through similar posts that suggests to look for target auto-correlation and input target cross-correlation but I am unable to read the graph to determine delays.I am attaching the graph for target auto-correlation and input target cross-correlation along with the code.(Code is taken from one of the example given for simplenarx data)
close all, clear all, clc,
tic
plt=0;
%[X,T] = simplenarx_dataset; % simplenarx_dataset;
load GT_complete.dat %data
FuelFlowLhr = GT_complete(:,12);
N1RPM = GT_complete(:,15);
x_1 = FuelFlowLhr(150:800,:);
t_1 = N1RPM(150:800,:);
X1 = x_1';
T1 = t_1';
X = con2seq(X1);
T = con2seq(T1);
x = cell2mat(X);
t = cell2mat(T);
[ I N ] = size(x); % [ 1 651 ]

[ O N ] = size(t); % [ 1 651 ]
% Define data for training
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)) % Product of element
MSE00 = var(t',1) % 0.1021
% Calculate Z-Score for input (x) and target (t)
zx = zscore(x, 1);
zt = zscore(t, 1);
zxtrn = zscore(x(trnind), 1);
zttrn = zscore(t(trnind), 1);
% Plot Input & Output for both original and transformed (Z-scored)
plt = plt+1,figure(plt);
subplot(221)
plot(x)
title('Fuelflow INPUT SERIES')
subplot(222)
plot(zx)
title('STANDARDIZED INPUT SERIES')
subplot(223)
plot(t)
title('RPM OUTPUT SERIES')
subplot(224)
plot(zt)
title('STANDARDIZED OUTPUT SERIES')
rng('default')
L = floor(0.95*(2*N-1)) 
for i = 1:1000 % Number of repetations to use for estimating summary statistics
  % This is for Target (T) Autocorrelation
  n = zscore(randn(1,N),1);
  autocorrn = nncorr( n,n, N-1, 'biased');
  sortabsautocorrn = sort(abs(autocorrn));
  thresh95T(i) = sortabsautocorrn(L);
    % This is for Input-Target (IT) Crosscorelation
    nx = zscore(randn(1,N),1);
    nt = zscore(randn(1,N),1);
    autocorrnIT = nncorr( nx,nt, N-1, 'biased');
    sortabsautocorrnIT = sort(abs(autocorrnIT));
    thresh95IT(i) = sortabsautocorrnIT(L);
end
% For Target Autocorrelation
sigTthresh95 = median(thresh95T)
meanTthresh95 = mean(thresh95T) 
minTthresh95 = min(thresh95T) 
medTthresh95 = median(thresh95T) 
stdTthresh95 = std(thresh95T)
maxTthresh95 = max(thresh95T) 
% For Input-Target Autocorrelation
sigITthresh95 = median(thresh95IT)
meanITthresh95 = mean(thresh95IT) 
mintIThresh95 = min(thresh95IT) 
medtIThresh95 = median(thresh95IT) 
stdtIThresh95 = std(thresh95IT) 
maxtIThresh95 = max(thresh95IT) 
%%CORRELATIONS
%%%%%TARGET AUTOCORRELATION %%%%%%%
%



autocorrt = nncorr(zttrn,zttrn,Ntrn-1,'biased');
sigflag95 = -1+ find(abs(autocorrt(Ntrn:2*Ntrn-1))>=sigTthresh95); 
sigflag95(sigflag95==0)=[]; 
%
plt = plt+1, figure(plt);
hold on
plot(0:Ntrn-1, -sigTthresh95*ones(1,Ntrn),'b--')
plot(0:Ntrn-1, zeros(1,Ntrn),'k')
plot(0:Ntrn-1, sigTthresh95*ones(1,Ntrn),'b--')
plot(0:Ntrn-1, autocorrt(Ntrn:2*Ntrn-1))
plot(sigflag95,autocorrt(Ntrn+sigflag95),'ro')
title('SIGNIFICANT TARGET AUTOCORRELATIONS (FD)')
%
%%%%%%INPUT-TARGET CROSSCORRELATION %%%%%%
%
crosscorrxt = nncorr(zxtrn,zttrn,Ntrn-1,'biased');
sigilag95 = -1 + find(abs(crosscorrxt(Ntrn:2*Ntrn-1))>=sigITthresh95) 
plt = plt+1, figure(plt);
hold on
plot(0:Ntrn-1, -sigITthresh95*ones(1,Ntrn),'b--')
plot(0:Ntrn-1, zeros(1,Ntrn),'k')
plot(0:Ntrn-1, sigITthresh95*ones(1,Ntrn),'b--')
plot(0:Ntrn-1, crosscorrxt(Ntrn:2*Ntrn-1))
plot(sigilag95,crosscorrxt(Ntrn+sigilag95),'ro')
title('SIGNIFICANT INPUT-TARGET CROSSCORRELATIONS (ID)')

Best Answer

 1. Ntrn ~  0.7*651 ~  456 
 2. Use Ntrn for significant correlation threshold estimates
 3. 1000 repetitions seems extreme. How much difference if 
    you only  use 100 or 200?
 4. Mislabeled crosscorr as autocorr
 5. Print out all significant correlations. Do not try to 
    read them from the graphs.
Hope this helps.
Thank you for formally accepting my answer*
Greg
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