Download Data

Download and unzip the Turbofan Engine Degradation Simulation Data Set from https://ti.arc.nasa.gov/tech/dash/groups/pcoe/prognostic-data-repository/ [2].

Each time series of the Turbofan Engine Degradation Simulation data set represents a different engine. Each engine starts with unknown degrees of initial wear and manufacturing variation. The engine is operating normally at the start of each time series, and develops a fault at some point during the series. In the training set, the fault grows in magnitude until system failure.

The data contains a ZIP-compressed text files with 26 columns of numbers, separated by spaces. Each row is a snapshot of data taken during a single operational cycle, and each column is a different variable. The columns correspond to the following:

Create a directory to store the Turbofan Engine Degradation Simulation data set.

dataFolder = fullfile(tempdir,"turbofan");
if ~exist(dataFolder,'dir')
    mkdir(dataFolder);
end

Download and extract the Turbofan Engine Degradation Simulation Data Set from https://ti.arc.nasa.gov/tech/dash/groups/pcoe/prognostic-data-repository/.

Unzip the data from the file CMAPSSData.zip.

filename = "CMAPSSData.zip";
unzip(filename,dataFolder)

Prepare Training Data

Load the data using the function processTurboFanDataTrain attached to this example. The function processTurboFanDataTrain extracts the data from filenamePredictors and returns the cell arrays XTrain and YTrain, which contain the training predictor and response sequences.

filenamePredictors = fullfile(dataFolder,"train_FD001.txt");
[XTrain,YTrain] = processTurboFanDataTrain(filenamePredictors);

Remove Features with Constant Values

Features that remain constant for all time steps can negatively impact the training. Find the rows of data that have the same minimum and maximum values, and remove the rows.

m = min([XTrain{:}],[],2);
M = max([XTrain{:}],[],2);
idxConstant = M == m;

for i = 1:numel(XTrain)
    XTrain{i}(idxConstant,:) = [];
end

View the number of remaining features in the sequences.

numFeatures = size(XTrain{1},1)

numFeatures = 17

Normalize Training Predictors

Normalize the training predictors to have zero mean and unit variance. To calculate the mean and standard deviation over all observations, concatenate the sequence data horizontally.

mu = mean([XTrain{:}],2);
sig = std([XTrain{:}],0,2);

for i = 1:numel(XTrain)
    XTrain{i} = (XTrain{i} - mu) ./ sig;
end

Clip Responses

To learn more from the sequence data when the engines are close to failing, clip the responses at the threshold 150. This makes the network treat instances with higher RUL values as equal.

thr = 150;
for i = 1:numel(YTrain)
    YTrain{i}(YTrain{i} > thr) = thr;
end

This figure shows the first observation and the corresponding clipped response.

Prepare Data for Padding

To minimize the amount of padding added to the mini-batches, sort the training data by sequence length. Then, choose a mini-batch size which divides the training data evenly and reduces the amount of padding in the mini-batches.

Sort the training data by sequence length.

for i=1:numel(XTrain)
    sequence = XTrain{i};
    sequenceLengths(i) = size(sequence,2);
end

[sequenceLengths,idx] = sort(sequenceLengths,'descend');
XTrain = XTrain(idx);
YTrain = YTrain(idx);

View the sorted sequence lengths in a bar chart.

figure
bar(sequenceLengths)
xlabel("Sequence")
ylabel("Length")
title("Sorted Data")

Choose a mini-batch size which divides the training data evenly and reduces the amount of padding in the mini-batches. Specify a mini-batch size of 20. This figure illustrates the padding added to the unsorted and sorted sequences.

miniBatchSize = 20;

Define Network Architecture

Define the network architecture. Create an LSTM network that consists of an LSTM layer with 200 hidden units, followed by a fully connected layer of size 50 and a dropout layer with dropout probability 0.5.

numResponses = size(YTrain{1},1);
numHiddenUnits = 200;

layers = [ ...
    sequenceInputLayer(numFeatures)
    lstmLayer(numHiddenUnits,'OutputMode','sequence')
    fullyConnectedLayer(50)
    dropoutLayer(0.5)
    fullyConnectedLayer(numResponses)
    regressionLayer];

Specify the training options. Train for 60 epochs with mini-batches of size 20 using the solver 'adam'. Specify the learning rate 0.01. To prevent the gradients from exploding, set the gradient threshold to 1. To keep the sequences sorted by length, set 'Shuffle' to 'never'.

maxEpochs = 60;
miniBatchSize = 20;

options = trainingOptions('adam', ...
    'MaxEpochs',maxEpochs, ...
    'MiniBatchSize',miniBatchSize, ...
    'InitialLearnRate',0.01, ...
    'GradientThreshold',1, ...
    'Shuffle','never', ...
    'Plots','training-progress',...
    'Verbose',0);

Train the Network

Train the network using trainNetwork.

net = trainNetwork(XTrain,YTrain,layers,options);

Test the Network

Prepare the test data using the function processTurboFanDataTest attached to this example. The function processTurboFanDataTest extracts the data from filenamePredictors and filenameResponses and returns the cell arrays XTest and YTest, which contain the test predictor and response sequences, respectively.

filenamePredictors = fullfile(dataFolder,"test_FD001.txt");
filenameResponses = fullfile(dataFolder,"RUL_FD001.txt");
[XTest,YTest] = processTurboFanDataTest(filenamePredictors,filenameResponses);

Remove features with constant values using idxConstant calculated from the training data. Normalize the test predictors using the same parameters as in the training data. Clip the test responses at the same threshold used for the training data.

for i = 1:numel(XTest)
    XTest{i}(idxConstant,:) = [];
    XTest{i} = (XTest{i} - mu) ./ sig;
    YTest{i}(YTest{i} > thr) = thr;
end

Make predictions on the test data using predict. To prevent the function from adding padding to the data, specify the mini-batch size 1.

YPred = predict(net,XTest,'MiniBatchSize',1);

The LSTM network makes predictions on the partial sequence one time step at a time. At each time step, the network predicts using the value at this time step, and the network state calculated from the previous time steps only. The network updates its state between each prediction. The predict function returns a sequence of these predictions. The last element of the prediction corresponds to the predicted RUL for the partial sequence.

Alternatively, you can make predictions one time step at a time by using predictAndUpdateState. This is useful when you have the values of the time steps arriving in a stream. Usually, it is faster to make predictions on full sequences when compared to making predictions one time step at a time. For an example showing how to forecast future time steps by updating the network between single time step predictions, see Time Series Forecasting Using Deep Learning.

Visualize some of the predictions in a plot.

idx = randperm(numel(YPred),4);
figure
for i = 1:numel(idx)
    subplot(2,2,i)
    
    plot(YTest{idx(i)},'--')
    hold on
    plot(YPred{idx(i)},'.-')
    hold off
    
    ylim([0 thr + 25])
    title("Test Observation " + idx(i))
    xlabel("Time Step")
    ylabel("RUL")
end
legend(["Test Data" "Predicted"],'Location','southeast')

For a given partial sequence, the predicted current RUL is the last element of the predicted sequences. Calculate the root-mean-square error (RMSE) of the predictions, and visualize the prediction error in a histogram.

for i = 1:numel(YTest)
    YTestLast(i) = YTest{i}(end);
    YPredLast(i) = YPred{i}(end);
end
figure
rmse = sqrt(mean((YPredLast - YTestLast).^2))
histogram(YPredLast - YTestLast)
title("RMSE = " + rmse)
ylabel("Frequency")
xlabel("Error")

References