# Evolutionary Optimization of Spiking Neural P Systems for Remaining Useful Life Prediction
## 5 Numerical Results
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Methods** & **Test RMSE** & \(\boldsymbol{s}\)**-Score \(\boldsymbol{\times}\) (103)** & **Trainable Parameters** & **Test Execution Time (ms)** \\ \hline MLP [39] & 8.34 \(\pm\) 0.00 & 20.41 & 94,701 & 1223 \\ CNN [39] & **7.22 \(\pm\) 0.00** & **1.14** & 5722 & 1178 \\ SNPS (1) & 19.72 \(\pm\) 0.44 & 8.39 & 218 & 19 \\ SNPS (2) & 20.11 \(\pm\) 0.62 & 6.53 & 180 & 17 \\ SNPS (3) & 19.23 \(\pm\) 0.57 & 7.92 & 83 & 12 \\ SNPS (4) & 18.14 \(\pm\) 0.52 & 6.39 & **56** & **11** \\ SNPS (5) & 18.25 \(\pm\) 0.59 & 7.69 & 105 & 15 \\ SNPS (6) & 18.45 \(\pm\) 0.57 & 6.48 & 98 & 14 \\ \(R_{md}\) & 26.85 \(\pm\) 0.00 & 276.76 & - & - \\ \(R_{\mu}\) & 18.97 \(\pm\) 0.00 & 63.98 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Summary of the comparative analysis based on the test results on N-CMAPSS (DS02). The symbol “-” indicates not available data. For our SNPS methods, we report the RMSE in terms of mean \(\pm\) std. dev. across 10 independent runs. For the remaining methods, we report the results from the original papers (std. dev. not provided). The boldface indicates the best value per column. Figure 6: Trade-off between test RMSE and number of trainable parameters for the methods considered in the experimentation on CMAPSS (FD001). Another advantage of our method relates to memory consumption (which correlates to the number of parameters). Considering that in all the experiments we used the standard 32-bit floating point precision (so that each parameter takes 4 bytes), we can see that the method with the largest number of parameters, the MLP, consumes roughly 370 KB, while our SN P systems take much less than 1 KB. This difference may be crucial for some industrial environments characterized by stringent memory constraints, e.g., due to the use of embedded systems. Figure 8: Best SN P system evolved for the RUL prediction task on N-CMAPSS (DS02). Figure 7: Trade-off between test RMSE and number of trainable parameters for the methods considered in the experimentation on N-CMAPSS (DS02). Finally, as a further reference, we include in Table 8 two additional RMSE values, namely \(R_{rnd}\) and \(R_{\mu}\). The test RMSE value of \(R_{rnd}\) indicates the performance that may be obtained by randomly choosing an RUL value from the test labels and considering it as an RUL prediction. Therefore, the random performance can be calculated by the RMSE between the test labels and the randomly chosen values. In the case of \(R_{\mu}\), we take instead all the RUL values from the test labels and compute their mean. Then, the mean performance is computed by the RMSE between the test labels and their mean. We can see that our results are better than the result of \(R_{rnd}\), but only three NEAT configurations perform slightly better than \(R_{\mu}\). One additional note is that the test RMSE values of the BPNNs reported in Table 8 are different from those reported in [39], which are based on an early version of DS02 that has a lower noise level on the sensor readings and a sampling rate of 0.1 Hz.