# Evolutionary Optimization of Spiking Neural P Systems for Remaining Useful Life Prediction
## 4 Experimental Setup
### Compared Algorithms  
As we discussed in Section 1, the previous works have mostly used traditional neural networks as data-driven methods for RUL prediction. The performance of these methods is typically estimated by the RMSE of a trained network on test data that have not been observed during the training phase. To evaluate our work with comparative analysis, we specify the details of the compared methods taken from the literature. As for CMAPSS, we consider two feed-forward networks proposed in [13], i.e., a MLP and a CNN, and one LSTM proposed in [14]. The architecture of the MLP comprises one hidden layer of 50 neurons. For the CNN, the model consists of two pairs of convolutional layers and pooling layers, which are followed by an MLP. The first convolutional layer has eight filters of size 12, while the second convolutional layer is made up of 14 filters of size 4. Each pooling layer performs average pooling with size 1 \(\times\) 2 to halve the feature length. At the end of the last pooling layer, the feature map is flattened and passed to a fully connected layer of 50 neurons, which is followed by an output neuron. Both the MLP and the CNN use sigmoids as activation functions. The LSTM has four hidden layers: two stacked LSTM layers and two fully connected layers. The number of hidden units in each LSTM is 32, and the following two fully connected layers contain eight neurons in each layer. To demonstrate the performance of the proposed method compared to a machine learning method other than neural network-based models, we also consider for the comparisons an approach based on support vector machine (SVM), which is presented in [38]. The main drawback of this method is that it requires feature creation and a degradation model. For those two steps, in [38], the authors used an SVM classifier and a Weibull distribution, respectively. In the case of N-CMAPSS, we consider two feed-forward networks, again an MLP and a CNN, as proposed in [39]. Based on our preliminary experiments, large recurrent networks such as LSTM are not an efficient RUL prediction tool on this large dataset, since their computational cost and training time are too large to handle it. The MLP used for the N-CMAPSS dataset is much more complex than the one used for the CMAPSS dataset. The considered MLP consists in fact of four hidden layers: the first three have 200 neurons each, while the remaining one has 50 neurons. The architecture of the CNN is made up of three convolutional layers followed by a fully connected layer. Each of the first two \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Training Set (\(D_{train}\))**} & \multicolumn{3}{c}{**Test Set (\(D_{test}\))**} \\
**Unit** & \(m_{i}\) **(M)** & \(t_{EOL}\) & **Failure Mode** & **Unit** & \(m_{i}\) **(M)** & \(t_{EOL}\) & **Failure Mode** \\ \hline \(u_{2}\) & 0.85 & 75 & HPT & \(u_{11}\) & 0.66 & 59 & HPT + LPT \\ \(u_{5}\) & 1.03 & 89 & HPT & \(u_{14}\) & 0.16 & 76 & HPT + LPT \\ \(u_{10}\) & 0.95 & 82 & HPT & \(u_{15}\) & 0.43 & 67 & HPT + LPT \\ \(u_{16}\) & 0.77 & 63 & HPT + LPT & & & & \\ \(u_{18}\) & 0.89 & 71 & HPT + LPT & & & & \\ \(u_{20}\) & 0.77 & 66 & HPT + LPT & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overview of each unit in the DS02 sub-dataset of N-CMAPSS w.r.t. the number of samples \(m_{i}\) (in millions), the end-of-life time \(t_{EOL}\), and the failure modes. convolutional layers has 10 filters of size 10, while the last convolutional layer has merely one filter of size 10. The extracted convolutional features proceed to a fully connected layer that consists of 50 neurons. For both the MLP and the CNN, ReLU is used as an activation function for all the nodes in the networks. As far as we know, no methods other than neural network-based models have been proposed for N-CMAPSS yet; therefore, in this case, we consider for the comparisons only the aforementioned MLP and CNN. The details of the compared algorithms for the two different datasets are summarized in Table 3 and Table 4, respectively.