## 7 Results and Discussion  
Experimental results are discussed in this section as well as comparative analysis among low-level and high-level models. In Table 3, the results of each metric described in Section 4.5 for the use of the DeepESN (our proposal) and LSTM (state-of-the-art) models in combination with the anomaly detector are described. The first results are related to effectiveness, while the latter results are related to efficiency. Regarding effectiveness metrics, our proposal is better than the state-of-the-art in terms of accuracy, recall, and F1 score, respectively, by around 2%, 9%, and 4%, while is worse in terms of precision by around 5%. In general, from the point of view of effectiveness, the use of DeepESN brings about better results than LSTM, except in terms of precision. In terms of efficiency, the use of DeepESN is better than the LSTM model. The time measured in training is improved by three orders of magnitude, while the time spent in inference is less than one-third of the state-of-the-art. Regarding CO\({}_{2}\) emissions, our proposal outperforms the state-of-the-art by two orders of magnitude in the training phase and one order of magnitude in the inference phase. Efficiency results prove that our proposal is highly efficient with respect to the state-of-the-art. This consideration promotes the usage of our proposal directly in on-the-edge devices instead of exploiting a remote server both for training and inference. The LSTM model is trained using the backpropagation through time (BPTT) algorithm, while the DeepESN model uses the ridge regression algorithm. BPTT is iterative (the iterations of the algorithm are called epochs), while ridge regression is one-shot. In the following analysis, the performance of the LSTM model combined with the anomaly detector during the iterations of training is compared with the one-shot-trained DeepESN. Figure 12 shows the evolution of accuracy and F1 score for the effectiveness metrics and time and CO\({}_{2}\) emissions for the efficiency metrics. In all the plots, the x-axis is related \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metrics** & **DeepESN** & **LSTM** \\ \hline Accuracy & 76.8\% & 74.74\% \\ Precision & 83.89\% & 88.58\% \\ Recall & 70.19\% & 60.75\% \\ F1 score & 76.43 \% & 72.05\% \\ \hline TR Time & 11.75 s & 2004.23 s \\ TS Time & 19.11 s & 72.29 s \\ TR CO\({}_{2}\) Emissions & \(4.76\times 10^{-5}\) & \(8.13\times 10^{-3}\) \\ TS CO\({}_{2}\) Emissions & \(7.75\times 10^{-5}\) & \(2.93\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results for individual metrics with the use of DeepESN and LSTM deep-learning models. to the epochs of the BPTT training algorithm, while the y-axis is related to the analyzed metric. The accuracy and F1 score metrics are computed on the test set, and they show that DeepESN outperforms LSTM at each epoch of training. In terms of efficiency, a low result is desired for both time and CO2 emissions. Both in terms of time and CO2 emissions, the LSTM is inefficient at the first epoch. Over the course of subsequent epochs, which bring with them an improvement in effectiveness, the methodology becomes more and more expensive, with a linear increase. The inefficiency of the BPTT algorithm promotes its usage inside of a server, while our proposal can be implemented directly inside of on-the-edge devices due to its good efficiency. In order to emphasize the results obtained, a graphic visualization has been chosen. In the representation, the left side of the graph offers a comparison between the two models, DeepESN and LSTM, regarding standard deviation. In the legend, the standard deviation values are indicated as follows:  
* **q**: Standard deviation of the error. * Anomaly threshold: This represents the average of the values used to calculate the upper (+\(\sigma\)). This dashed green band indicates the range in which the standard deviation of the error must remain in order to prevent a failure from occurring. * Actual anomaly: This indicates the start of the actual anomaly.