A deep learning-based prognostic approach for predicting turbofan engine degradation and remaining useful life

Data description

This study utilized NASA’s C-MAPSS (Commercial Modular Aero-Propulsion System Simulation), a tool designed for simulating turbofan engines, to generate the data. C-MAPSS simulates various operational, environmental, and control scenarios by adjusting input parameters².

C-MAPSS includes run-to-failure data for 249 engines, simulated across six operational parameters. To create a more realistic environment, each of these engines has unique manufacturing differences and varying initial wear levels. The initial wear is attributed to differences in module efficiency. Engine failures occur due to one of two malfunction modes: High-Pressure Compressor (HPC) degradation or fan degradation. At the beginning of each time series, the engine operates normally, but a fault is introduced at some point, eventually leading to engine failure².

A total of 21 sensors, installed across various engine modules, monitor the engine’s health. Table 2 provides a detailed list of all sensors. In addition to the 21 sensor readings, three extra parameters are recorded to reflect the engine’s operating conditions. Table 3 lists these operational parameters. All sensor and operational data are recorded once per engine cycle.

Table 4 summarizes key details of the C-MAPSS dataset, which consists of four sub-datasets—FD001, FD002, FD003, and FD004—each featuring different operational conditions and failure modes. Each sub-dataset is divided into training and test sets. The dataset contains 26 columns per row: the first five columns include the engine unit number, degradation time step, and operational settings, while the remaining 21 columns contain multivariate time-series data from the 21 sensors in the same operating cycle. As shown in Table 2, the sensor data include measurements of temperature, pressure, and speed, with additional details available in⁴.

Furthermore, this sensor data captures the engine’s progression from normal operation to initial wear and eventual failure. In this study, the proposed model is used to analyze the training dataset and predict the Remaining Useful Life (RUL) of engines in the test dataset.

Performance metrics

The system’s RUL prediction model utilizes multisensor monitoring data to forecast aircraft engine degradation, with the predicted RUL as the output. To evaluate the effectiveness of different techniques, three metrics are used: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and a scoring function.

1. 1.

   Root mean square error (RMSE)¹⁹ is a widely used metric for evaluating the performance of regression models. It measures the average magnitude of errors between predicted and actual values in a dataset. Here’s a simple explanation:

   $$\begin{aligned} RMSE_R{EMPTY}_U{EMPTY}_L=\sqrt{(1/N) \sum _{i=1}^{N}(Y_i – \hat{Y_i}^2)} \end{aligned}$$

   (26)

   where: N represents the total number of test data samples. \(Y_i\) is the true value of the engine life. \(\hat{Y_i}\) is the predicted value of the engine life.

2. 2.

   Mean absolute error (MAE) is known as the loss function, which is derived by averaging the absolute differences between the predicted and actual target values. It is represented as follows:

   $$\begin{aligned} MAE_R{EMPTY}_U{EMPTY}_L=\sqrt{(1/N) \sum _{i=1}^{N}|Y_i – \hat{Y_i}|} \end{aligned}$$

   (27)

   where: N represents the total number of test data samples. \(Y_i\) is the true value of the engine life. \(\hat{Y_i}\) is the predicted value of the engine life. \(|-|\) denotes the absolute value. It is often used as a loss function, particularly in regression problems aimed at predicting continuous values. During model training, the objective is to minimize the MAE loss, which represents the average absolute difference between the predicted and actual values.

3. 3.

   Scoring Function¹⁸ is often defined as a function that evaluates a model’s performance on a specific dataset. Scoring functions are used to assess a model’s ability to predict or classify data. It represents the average value of the test set fraction. A lower score indicates better performance. The calculation formula is:

   $$\begin{aligned} Score= {\left\{ \begin{array}{ll} \sum _{i=1}^{N} (e^{\frac{dif_i}{13}} – 1), & \text {if } dif_i < 0 \\ \sum _{i=1}^{N} (e^{\frac{dif_i}{10}} – 1), & \text {if } dif_i \ge 0 \end{array}\right. } \end{aligned}$$

   (28)

When employing deep learning models to predict RUL, Eq. 28 shows that the scoring function penalizes late predictions more heavily, whereas RMSE treats both early and late predictions equally. Late predictions are considered more critical as they can lead to severe accidents. Figure 3 illustrates the comparison between RMSE and the scoring function. It demonstrates that the penalty for late predictions is significantly higher than for RMSE, emphasizing the goal of preventing engine failures. The linear relationship between RMSE and error values suggests that RMSE has a well-defined physical meaning. The model’s predictive capability was evaluated using both RMSE and the scoring function, as they serve as crucial performance indicators.

Data preprocessing

Sensor selection

All of our analysis is based on sensor measurements. The first two columns of the training data contain engine and cycle information, which are not required for training the algorithm. Similarly, columns 3, 4, and 5 represent operating settings, which we will also exclude from training. It is worth noting that some researchers use operational setting values in their algorithms, but we will not.

We will train our algorithm solely using the values from columns 6 to 26, as they contain sensor measurements. Figure 4 presents boxplots of all sensor measurements from the FD001 training dataset.

From Fig. 4,we observe that sensors 1, 5, 10, 16, 18, and 19 have constant values. Additionally, sensor 6 appears to have only a few distinct values³³. Specifically, sensor 6 has two constant values: 21.61 and 21.60, with 21.61 occurring 20,225 times. Since these values are extremely close together, we can consider the entire column to be constant.

Constant values are not particularly useful for training algorithms. Moreover, normalizing data is sometimes necessary, but if a column has a constant value, its standard deviation becomes 0. As a result, normalization is impossible due to division by zero. Therefore, we will remove columns with constant values.

The selection of sensor measurements was conducted after a thorough investigation of feature importance. Some sensors exhibited little or no correlation with the degradation process, indicating that their inclusion would not significantly enhance prediction performance.

Figure 5 illustrates sensor measurements over time for a subset of randomly selected engines from the FD001 training data.

Data normalization

Data normalization is primarily considered the first step in deep learning. Thus, to retain data on the same scale, the dimensions of multiple sensors must be standardized⁴⁵. We use a StandardScaler approach (Z-score) to normalize the input data, ensuring it falls within the range of 0 to 1. The formula for Z-score is given by:

where: z represents the standardized data. x represents the original value of the feature. \(\mu\) is the mean value of the feature. \(\sigma\) is the standard deviation of the feature.

Correlation analysis of the sensors in dataset FD001 is presented in Fig. 6. From this figure, we can see the obvious relationships between all sensors in the dataset. Figure 7 presents the correlation analysis without the excluded sensors mentioned in the data selection.

Normalization is crucial in RUL prediction since it scales the input characteristics to a constant range, which helps the model’s convergence speed during training. It reduces the impact of different magnitudes of sensor readings, allowing the model to learn significant patterns more efficiently. Furthermore, it improves prediction accuracy and model generalization by ensuring that all features contribute equally.

It can be seen from Fig. 8 data signal of sensors before standardization and the standardized sensor data signal in Fig. 9.

Piecewise degradation model

To accurately anticipate RUL labels, it’s important to analyse the turbofan engine’s specific features. During regular use, the engine’s lifespan decreases in a predictable manner. To improve model prediction accuracy, it is assumed that the engine does not degrade during its first operation and has a constant lifetime. When the engine’s RUL reaches the turning point of lifetime decay, it begins to degrade linearly, resulting in its real lifetime³³.

In dataset FD001 there is no RUL data provided for the training set. It is easy to calculate RUL values directly from training data. Taking into account that training data includes run-to-failure data for all engines. Engine 1 fails at 192 cycles. So, during the first cycle of engine 1, the RUL is 191. After cycle two, the RUL is 190, and so on. It fails after 192 cycles, therefore its RUL is 0. This is known as a linear degradation model. It gradually diminishes from the beginning of the cycle until it reaches zero at the end. In addition to the linear degradation model, the piecewise linear degradation model is also commonly employed. In this concept, RUL is initially allocated to a fixed number (for a number of cycles). The fixed number is known as early RUL. When the RUL value hits the early RUL, it then follows a linear decline paradigm.

Piecewise linear degradation models are more flexible in reflecting different degradation patterns over time than exponential models, which assume a constant rate of decrease. They enable for more rapid changes in degradation behaviour, better representing real-world conditions. These models enhance interpretability, making it easier to identify critical operating stages. Furthermore, piecewise linear models are resistant to noise in sensor data, which reduces the danger of overfitting. When combined with CAELSTM, they can improve prediction accuracy by learning local trends and deterioration transitions. This results in more accurate maintenance planning and decision-making³⁵.

To demonstrate both degradation models, we shall present RUL values for engine 1 using both models in Fig. 10.The RUL of engine 1 is 192 (as mentioned above). For the piecewise linear degradation model, we set the early RUL to 125 according to the study⁴⁶. There is no set rule for selecting this value. Figure 11 shows that the RUL label degrades linearly with time, eventually failing completely.

Time window processing

Time window processing is a data improvement technique. Sliding window processing captures the dependencies between time series data³³. Figure 12 depicts the time window processing. Set the sliding time step to 1 and use the previous time step to forecast the next. The length of the window depends on the original data. Longer time windows offer more valuable information. The length of the time window should not exceed the minimal life cycle. To achieve satisfactory results, we choose an appropriate window length for FD001 and FD003. The minimum life cycle of training subsets is 128 and 145 respectively. The minimum life cycle of testing subsets is 31 and 38 respectively. the time window size is equal 30 this is shown in Table 5. The window size is determined through experimental design. The experiment try window sizes of 30, 35, 40, and 45. when the window size is 30, the proposed model can obtain the best results. Therefore, 30 is selected as the window size.

Experimental analysis and results

Experimental setting and description

The training and testing procedure uses Tensorflow 2.16.1, Numpy 1.26.4, Pandas version 2.2.3 and Scikit-learn 1.2.2. The hardware platform includes an Intel(R) Core(TM) i7, 8 GB of RAM, and Windows 10 as the operating system. A Kaggle Platform is used for speeding up the processing of deep learning computation. We run all of our experiments on it to use it’s capabilities. Table 6 lists the suggested model’s hyper-parameters.

We present a model based on convolutional autoencoders, LSTMs, and an attention mechanism to predict the RUL of aero-engines. Figures 13 and 14 show the predicted RUL values for 100 engine units from the FD001 and FD003 sub-datasets alongside the actual RUL values. The results demonstrate that the proposed model’s predictions closely match the actual values.

In Table 7, we report the RMSEs for the proposed model with the two datasets: 14.44 for FD001 and 13.40 for FD003; MAEs are 10.49 and 10.68, respectively, with scores of 282.38 and 264.47. During training, we calculated the Mean Absolute Error (MAE) and loss for both training and validation sets to assess model performance and monitor for overfitting or underfitting. Figures 15 and 16 illustrate the performance accuracy of the proposed model across the two sub-datasets, indicating an ideal range for model complexity. Figures 17 and 18 show that the training and validation loss values align well over 25 epochs, confirming that the model’s predictions are consistent with actual data, with no signs of overfitting or underfitting.

Impact of learning rate

It is a crucial hyper-parameter in deep learning, affecting the model’s ability to reach the local minimum within a reasonable time frame. In experiments we included learning rates of 0.0001, 0.0005, 0.001, 0.005, and 0.01. All other model parameters stay unaltered. Figures 19 and 20 display the results For FD001 and FD003. The proposed model performs optimally at a learning rate of 0.001 for FD001 and 0.0001 For FD003 (minimum RMSE, MAE, and score).Therefore, two values were chosen as the ultimate learning rates.

Impact of batch size

It determines the quantity of training data and impacts model speed and optimisation. In experiments we included batch sizes of 32, 64, 128, 256, and 512. Figures 21 and 22 show that with a batch size of 512 (FD001) and 32 (FD003), the proposed model yields the best results. Therefore, two values are chosen as the ultimate batch size.

Impact of dropout

It is a key hyperparameter that prevents overfitting and enhances model performance. In experiments we included dropout values of 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 and 0.8. Figures 23 and 24 show that a dropout of 0.4 (FD001) and 0.6 (FD003) results in the least RMSE and Score for the model.

Comparison with different methods

The proposed method is compared with existing state of the art methods including CNN¹⁸, MODBNE¹⁹, Deep LSTM²⁰, GRU LSTM²¹, RNN²³, bi-RNN-autoencoder²⁴, Attention-LSTM²⁵, Chain-graph²⁶, Deep quantile regression²⁹, PCA-LSTM³⁰, CNN-BGRU-SA³, VAE-RNN³², ABGRU³³, CNN-LSTM-Attention³⁵ and THGNN⁴⁷ . RMSE and Score function are used to evaluate the performance of different methods. The comparison results of different methods are shown in Table 8. The proposed model results for the sub-datasets FD001 and FD003 are smaller than other methods. ABGRU³³ has results smaller than the proposed model for FD001 and FD003 except score for FD003. CNN-BGRU-SA³ and Deep quantile regression²⁹ have smaller RMSE and score for FD001 results than the proposed model. It outperforms other methods in some cases due to the prepossessing steps done on dataset and normalize it to be with in specific range. A linear degradation model has benefit also affect on the results of the proposed model. Using a fixed sliding window let also the proposed model obtain better results. The structure of the proposed model performs well in predicting RUL on two sub-datasets according to experimental results.