% Data_Inputs=xlsread('1.xls'); % Import file %The training data sample are randmonized by using the function'randperm' %Shuffling_Inputs=Data_Inputs(randperm(end),1:2); % integers (training sample) Training_Set=Data_Inputs(1:end,1);%specific training set Target_Set=Data_Inputs(1:end,2); %specific target set Input=Training_Set'; %Convert to row Target=Target_Set'; %Convert to row X = con2seq(Input); %Convert to cell T = con2seq(Target); %Convert to cell %%2. Data preparation N = 365; % Multi-step ahead prediction % Input and target series are divided in two groups of data: % 1st group: used to train the network inputSeries = X(1:end-N); targetSeries = T(1:end-N); inputSeriesVal = X(end-N+1:end); targetSeriesVal = T(end-N+1:end); % Create a Nonlinear Autoregressive Network with External Input delay = 2; inputDelays = 1:2; feedbackDelays = 1:2; hiddenLayerSize = 100; net = narxnet(inputDelays,feedbackDelays,hiddenLayerSize); % Prepare the Data for Training and Simulation % The function PREPARETS prepares timeseries data for a particular network, % shifting time by the minimum amount to fill input states and layer states. % Using PREPARETS allows you to keep your original time series data unchanged, while % easily customizing it for networks with differing numbers of delays, with % open loop or closed loop feedback modes. [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) % Plots % Uncomment these lines to enable various plots. %figure, plotperform(tr) %figure, plottrainstate(tr) %figure, plotregression(targets,outputs) %figure, plotresponse(targets,outputs) %figure, ploterrcorr(errors) %figure, plotinerrcorr(inputs,errors) % Closed Loop Network % Use this network to do multi-step prediction. % The function CLOSELOOP replaces the feedback input with a direct % connection from the outout layer. 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) % Early Prediction Network % For some applications it helps to get the prediction a timestep early. % The original network returns predicted y(t+1) at the same time it is given y(t+1). % For some applications such as decision making, it would help to have predicted % y(t+1) once y(t) is available, but before the actual y(t+1) occurs. % The network can be made to return its output a timestep early by removing one delay % so that its minimal tap delay is now 0 instead of 1. The new network returns the % same outputs as the original network, but outputs are shifted left one timestep. 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) %%5. Multi-step ahead prediction inputSeriesPred = [inputSeries(end-delay+1:end),inputSeriesVal]; targetSeriesPred = [targetSeries(end-delay+1:end), con2seq(nan(1,N))]; [Xs,Xi,Ai,Ts] = preparets(netc,inputSeriesPred,{},targetSeriesPred); yPred = netc(Xs,Xi,Ai); perf = 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');
a. Rainfall vs time b. Water Level vs time c. Water Level vs Rainfall d. Autocorrelation function of Water Level e. Crosscorrelation function of Water Level and Rainfall 2. Calculate a. Significant values and lags of the Water Level autocorrelation function b. Significant values and lags of the Water-Level/Rainfall crosscorrelation function 3. Determine which time-series functions yield the best predictions. DO NOT use the default 'dividerand' which destroys correlations. Use 'divideblock'. a. Timedelaynet b. Narnet c. Narxnet 4. If b and/or c have a satisfactory openloop performance, close the loop and continue training with the original data.
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