How can I simulate a NARX neural network after being trained and tested?

Hi,

Using the NN tool box (MATLAB R2012b), I trained a NARX NN with data vectors X for input and Y for output. Now I would to know if the NARX NN developped is capable to predict the output of a given input A for example. Could someone tell me how can i do that? is there any specific command to use? I tried sim(A) but it didn't work.

Thank you in advance for your reponse,

Amine

Answer 1

[Greg Heath]

% How can I simulate a NARX neural network after being trained and tested?

1. You have not suggested a MATLAB nndataset to use as an example. Please choose one or post one of your own.

help nndatasets

Input-Output Time-Series Prediction, Forecasting, Dyanamic modelling
Nonlinear autoregression, System identification and Filtering

Input-output time series problems consist of predicting the next value
of one time-series given another time-series. Past values of both series
(for best accuracy), or only one of the series (for a simpler system)
may be used to predict the target series.

   simpleseries_dataset  - Simple time-series prediction dataset.
   simplenarx_dataset    - Simple time-series prediction dataset.
   exchanger_dataset     - Heat exchanger dataset.
   maglev_dataset        - Magnetic levitation dataset.
   ph_dataset            - Solution PH dataset.
   pollution_dataset     - Pollution mortality dataset.
   refmodel_dataset      - Reference model dataset
   robotarm_dataset      - Robot arm dataset
   valve_dataset         - Valve fluid flow dataset.

 inputSeries = tonndata(x,true,false);   % Change notation to  cell seqences X,

 targetSeries = tonndata(t,true,false);   % T and corresponding matrices x,t

% Create a Nonlinear Autoregressive Network with External Input

 inputDelays = 1:2; feedbackDelays = 1:1;

2. Have the correlation values at the lags in the chosen row vectors ID and FD been investigated to make sure that they are significant for the target autocorrelation function and target/input crosscorrelation function?

3. Given the number of outputs, and trn/val/tst data division ratio, how many training equations, Ntrneq, do you have?

 hiddenLayerSize = 10;

4. Given ID, FD and H = 10, how many unknown weights, Nw, do you have to estimate? Do you have more unknowns than equations? What is the estimation number of degrees of freedom, Ndof = Ntrneq-Nw? Are you considering to change H or try a range of values?

 net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize);

 [inputs,inputStates,layerStates,targets] = preparets(net,inputSeries,{},targetSeries);

% Setup Division of Data for Training, Validation, Testing

 net.divideParam.trainRatio = 70/100; net.divideParam.valRatio = 15/100;
 net.divideParam.testRatio = 15/100;

5. These are defaults. Why bother?

6. Why are you accepting the default random data division function 'dividerand' that destroys serial correlations? Override with 'divideblock' or 'divideind' to maintain order and spacing.

7.Separate t into ttrn/tval/ttst partitions and calculate the reference MSEs obtained from the naive constant output model estimate ytrn00 = mean(ttrn,2).

 MSEtrn00 = mean(var(ttrn,1)); MSEtrn00a = Ntrn*MSEtrn00/(Ntrn-1)

 MSEval00 = mse(tval-ytrn00); MSEtst00=mse(ttst-ytrn00);

8. Set practical training goals

 if Ndof > 0
    net.trainParam.goal = 0.01*Ndof*MSEtrn00a/Ntrneq; % R2trna = 0.99
 else
    net.trainParam.goal = 0.01*MSEtrn00;    % R2trn = 0.99
end
 net.trainParam.min_grad = MSEtrn00/200;

% Train the Network

 [net,tr] =train(net,inputs,targets,inputStates,layerStates);

% Test the Network

 outputs = net(inputs,inputStates,layerStates); 
 errors = gsubtract(targets,outputs); 
 performance = perform(net,targets,outputs)

9. ALTERNATIVE: Forget this and get all of your information (training, validation, test and total) from the training structure tr:

 tr = tr

10. The best evaluation criterion is the test coefficient of determination (R2tst) evaluated at the maximum of R2val

 R2val = 1-tr.vperf(tr.best_epoch)/MSEval00

 R2tst = 1-tr.tperf(tr.best_epoch)/MSEtst00

% View the Network

 view(net)

% Obtain the Closed Loop Design

 netc = closeloop(net); netc.name = [net.name ' - Closed Loop'];
 view(netc);

% Change notation upper/lower case for cell/matrix, 'r' for removedelay

 [ Xsc, Xic, Aic, Tsc ] = preparets(netc, inputSeries, {},targetSeries);
 Ysc = netc(Xsc,Xic,Aic); 
% MSEc  = perform(netc,Tsc,Ysc)%    closedLoopPerformance
 ysc = cell2mat(Ysc);
 tsc  = cell2mat(Tsc);
 MSEc00 = mse(tsc-ytrn00)
 MSEc = mse(tsc-ysc)
 R2c = 1-MSEc/MSEc00

 netr = removedelay(net); 
 netr.name = [netr.name ' - Predict One Step Ahead']; 
 view(netr) 

 [Xsr,Xir Air Tir] = preparets(netr,inputSeries,{},targetSeries); 
 Ysr  = nets(Xsr,Xir Air);
%  MSEr= perform(netr,Tsr,Ysr) % earlyPredictPerformance
 ysr = cell2mat(Ysr);
 tsr  = cell2mat(Tsr);
 MSEr00 = mse(tsr-ytrn00)
 MSEr = mse(tsr-ysr)
 R2r = 1-MSEr/MSEr00

X and T dimension are the same and equal to 100. Now for example I would test the network with an input defined by:

 for i=1:100 T(i)=(1+i)^-1 end

how can i do that? net(T)? sim(T)? netc(T)?

NO!

YOU CAN NOT DO THAT! THE NET IS ONLY VALID FOR SERIES THAT HAVE, APPROXIMATELY, THE SAME MEANS, VARIANCES, AND SIGNIFICANT AUTO AND CROSSCORRELATION LAGS!!

HOPE THIS HELPS.

THANK YOU FOR FORMALLY ACCEPTING MY ANSWER

Greg

[Platon]

Thank you

[Gizo Bro]

Dear Greg

Is it a must to make both the input and output dimensions the same in NARX?

i gave different dimensions and got error "data selection has different time steps "

[mukesh meharda]

After training and testing the NARX model, I want to use it into simulink model then how can I use it with another inputs data and I extracted the simulink model but

[Tanmoy Majhi]

My question is related to this NARX neural networks. Input data having 3 different parameters (rainfall, temp, evaporation) and output data having 1 parameter(runoff). If I apply NARX neural network then input delays applied to all three parameters of input data and feedback delay applies to output to run the NARX network. My question is I want to add input delay to only 1 parameter (rainfall) of input data (and no delays to temp and evaporation parameter of input data). What is the correct procedure to solve this? Thank you in advance for your reponse.

Answer 2

[Shashank Prasanna]

If your trained network object is 'net' then you can say

net(A)

You can use SIM and it has the following input arguments:

http://www.mathworks.com/help/nnet/ref/sim.html

[Greg Heath]

Incorrect. With timeseries you have to include the delays. For example, see above

Ysc = netc(Xsc,Xic,Aic);

[Shashank Prasanna]

I agree, thanks for correcting.

[Platon]

Thank you for your reponse.

here is the code:

inputSeries = tonndata(u,true,false); targetSeries = tonndata(y,true,false);

% Create a Nonlinear Autoregressive Network with External Input inputDelays = 1:2; feedbackDelays = 1:1; hiddenLayerSize = 10; net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize);

[inputs,inputStates,layerStates,targets] = preparets(net,inputSeries,{},targetSeries);

% Setup Division of Data for Training, Validation, Testing net.divideParam.trainRatio = 70/100; net.divideParam.valRatio = 15/100; net.divideParam.testRatio = 15/100;

% Train the Network [net,tr] = train(net,inputs,targets,inputStates,layerStates);

% Test the Network outputs = net(inputs,inputStates,layerStates); errors = gsubtract(targets,outputs); performance = perform(net,targets,outputs)

% View the Network view(net)

netc = closeloop(net); netc.name = [net.name ' - Closed Loop']; view(netc) [xc,xic,aic,tc] = preparets(netc,inputSeries,{},targetSeries); yc = netc(xc,xic,aic); closedLoopPerformance = perform(netc,tc,yc)

nets = removedelay(net); nets.name = [net.name ' - Predict One Step Ahead']; view(nets) [xs,xis,ais,ts] = preparets(nets,inputSeries,{},targetSeries); ys = nets(xs,xis,ais); earlyPredictPerformance = perform(nets,ts,ys)

u and y dimension are the same and equal to 100.

Now for example I would test the network with an input defined by:

for i=1:100 T(i)=(1+i)^-1 end

how can i do that? net(T)? sim(T)? netc(T)?