Neural Network - Multi Step Ahead Prediction Using NARX

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Abhishek Guhe
Abhishek Guhe el 26 de Oct. de 2015
Editada: Greg Heath el 6 de En. de 2016
I am modeling the network to predict the turning on and off the pump depending on the two variables. So the network is 2 inputs and 1 output with delay of 2 and hidden layer of 10. I have tried different combinations of transfer function, hidden layer and delays but the results are good enough. Output of pump is 0 or 1. Not sure if that is causing the problem.
Size(In)=Size(Out)=11,800
I have 5 inputs and 1 target. Is the data sufficient for the model?
I have tried with set of hiddenlayers and delays but not able to figure out what is the suitable number for current problem.
Is there any rule of thumb for for deciding these numbers for particular problem?
Here is the code:
X=tonndata(In,false,false);
T=tonndata(Out,false,false);
% % Input and target series are divided in two groups of data:
N = 50; % Multi-step ahead prediction
% 1st group: used to train the network
inputSeries = X(1:end-N);
targetSeries = T(1:end-N);
% % 2nd group: this is the new data used for simulation. inputSeriesVal will
be used for predicting new targets. targetSeriesVal will be used for network validation after prediction
inputSeriesVal = X(end-N+1:end);
targetSeriesVal = T(end-N+1:end);
%% Choose a Training Function
trainFcn = 'trainlm'; % Levenberg-Marquardt
% trainFcn = 'trainbr'; % Bayesian regularization
%% Create a Nonlinear Autoregressive Network with External Input
delay=2;
inputDelays = 1:delay;
feedbackDelays = 1:delay;
hiddenLayerSize = 10;
net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize,'open',trainFcn);
%% Prepare the Data for Training and Simulation
[x,xi,ai,t] = 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,x,t,xi,ai);
%% Test the Network
[Y,xf,af] = net(x,xi,ai);
e = gsubtract(t,Y);
performance = perform(net,t,Y)
%% Closed Loop Network
netc = closeloop(net);
netc.name = [net.name ' - Closed Loop'];
% view(netc)
[xc,xic,aic,tc] = preparets(netc,X,{},T);
yc = netc(xc,xic,aic);
closedLoopPerformance = perform(netc,tc,yc)
%% Step-Ahead Prediction Network
nets = removedelay(net);
nets.name = [net.name ' - Predict One Step Ahead'];
% view(nets)
[xs,xis,ais,ts] = preparets(nets,X,{},T);
ys = nets(xs,xis,ais);
stepAheadPerformance = perform(nets,ts,ys)
%% Prepare Input and Target Data for Testing the Network
[Xs1,Xio,Aio] = preparets(net,inputSeries(1:end-delay),{},targetSeries(1:end-delay));
[Y1,Xfo,Afo] = net(Xs1,Xio,Aio);
[netc,Xic,Aic] = closeloop(net,Xfo,Afo);
[yPred,Xfc,Afc] = netc(inputSeriesVal,Xic,Aic);
multiStepPerformance = perform(net,yPred,targetSeriesVal);
figure;
plot([cell2mat(targetSeries),nan(1,N);
nan(1,length(targetSeries)),cell2mat(yPred);
nan(1,length(targetSeries)),cell2mat(targetSeriesVal)]')
legend('Original Targets','Network Predictions','Expected Outputs')
Any comments and suggestions are very much appreciated.
Regards and thanks,
Abhishek
  3 comentarios
Abhishek Guhe
Abhishek Guhe el 28 de Oct. de 2015
Editada: Abhishek Guhe el 28 de Oct. de 2015
I think this code only calculates MSE. With the below equations which I found in one of the Greg's answer will help in determining NMSE. I did not quite get the idea in point 6.
MSE = mse(e)
MSE00 = mean(var(e',1))
NMSE = MSE/MSE00 % Normalized MSE
I have updated the code.
Thanks Greg for suggestions.
Greg Heath
Greg Heath el 29 de Oct. de 2015
Editada: Greg Heath el 6 de En. de 2016
ERROR:
MSE00 is the mean of the TARGET variance, NOT the ERROR variance.
MSEtrn00, MSEval00 and MSEtst00 are the means of the training, validation and testing subset target variances.
NMSE = MSE/MSE00 is the fraction of target variance that is modeled by the net.
6DEC2016 CORRECTION:
NMSE = MSE/MSE00 is the fraction of target variance that is NOT modeled by the net.
Rsq = 1 - NMSE is the fraction of target variance that IS modeled by the net.
https://www.google.com/?gws_rd=ssl#q=wikipedia+r+squared
END OF 6JAN2016 CORRECTION
For typical nets 0 <= NMSE <= 1. Similar inequalities hold for NMSEtrn, NMSEval and NMSEtst.
The training subset estimate is optimistically biased because the same data is used to both estimate weights and evaluate the performance obtained from using those weights. This bias can be mitigated by adjusting the training performance estimates to take into account the number of degrees of freedom that are lost by using the same data for estimating parameters and performance.
I = input vector dimensionality
O = output vector dimensionality
NID = No. of input delays
NFD = No. of feedback delays
H = No. of hidden nodes
Nw = (NID*I+NFD*O+1)*H+(H+1)*O % No. of unknowns weights
Ntrneq = Ntrn*O % No. of training equations
Ndof = Ntrneq-Nw % No. of degrees of freedom
SSEtrn = sse(etrn)
MSEtrn = SSEtrn/Ntrneq
MSEtrna = SSEtrn/Ndof % DOF "a"djusted
MSEtrn00 = mean(var(ttrn,1))
MSEtrn00a = mean(var(ttrn,0))
NMSEtrn = MSEtrn/MSEtrn00
NMSEtrna = MSEtrna/MSEtrn00a
For openloop training I favor the goal
NMSEtrna <= 0.005
or
MSEtrn <= 0.005*Ndof*MSEtrn00a/Ndof
Additional details can be obtained by searching the NEWSGROUP and ANSWERS using the above notation.
Hope this helps.
Greg

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Respuestas (1)

Nick Hobbs
Nick Hobbs el 28 de Oct. de 2015
An alternative to using the code for the neural network is to use the command 'nnstart'.
'nnstart' will launch a tool which would allow you to set options for your network more easily. You could then try various settings on the network to determine how it affects your results.
  1 comentario
Abhishek Guhe
Abhishek Guhe el 28 de Oct. de 2015
Thanks Nick for suggestion. I have exported the code from the nnstart and made changes for trying different combinations.

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