## 5 Results and Discussion
### Discussion  
In this paper, we conducted a comprehensive evaluation of four autoencoder-based models for time-series anomaly detection: TCN-Autoencoder, GRU-Autoencoder, LSTM-Autoencoder, and VAE. The main focus was on three key performance metrics [39; 40]: Mean Squared Error (MSE), Equation (1), Root Mean Squared Error (RMSE), Equation (2),and Mean Absolute Error (MAE), Equation (3). The MSE measures the average squared difference between the predicted values (\(\hat{y}\)) and the actual values (y). The RMSE is a variation of the MSE that takes the square root of the MSE value. It provides the standard deviation of the errors and is in the same units as the original data. The MAE measures the average absolute difference between the predicted values (\(\hat{y}\)) and the actual values (y). It is less sensitive to the MSE [41]. The equations are as follows:  
\[\text{MSE }=\left(\frac{1}{\text{n}}\right)\times\ \Sigma(\text{y }-\hat{y})^{2}, \tag{1}\]  
\[\text{RMSE }=\sqrt{\text{MSE}} \tag{2}\]  
\[\text{MAE }=\left(\frac{1}{\text{n}}\right)\times\ \Sigma|\text{y }-\hat{y}| \tag{3}\]  
where n is the number of data points. The results reveal that the TCN-Autoencoder exhibited the most promising performance in all three metrics, with an MSE of 1.447, RMSE of 1.193, and MAE of 0.712. This shows that the TCN-Autoencoder excels in accurately reconstructing time-series data and reveals its potential as a robust model for anomaly detection. In contrast, GRU-Autoencoder and LSTM-Autoencoder displayed slightly higher MSE values of 1.824 and 1.822, respectively, along with RMSE values of 1.343 for both models. The MAE for these models was also relatively close, with the GRU-Autoencoder at 0.741 and the LSTM-Autoencoder at 0.725. While these models perform adequately, their results indicate that they may not be as effective as the TCN-Autoencoder in capturing complex patterns in the data. Finally, VAE exhibited an MSE of 1.825, RMSE of 1.343, and MAE of 0.707 when competing. While its performance is similar to the GRU-Autoencoder and LSTM-Autoencoder, it falls slightly behind the TCN-Autoencoder in terms of accurately reconstructing time-series data. Based on our comprehensive evaluation, the TCN-Autoencoder emerges as the most promising choice for time-series anomaly detection with superior performance in terms of MSE, RMSE, and MAE. However, further research and testing may be required to explore the full potential of these models and their application in specific real-world scenarios. In Figure 7, the TCN-Autoencoder model demonstrates its effectiveness in identifying anomalies in the vibration data collected from the Kirkuk power plant. The figure presents two distinct parts where anomalies are encircled with dashed lines, indicating critical deviations from normal operating patterns, and potentially pointing to mechanical issues. Figure 7 presents an anomaly detected during a period of increased load on the turbine. The model identified an unusual pattern that deviated significantly from the baseline vibration sign. Further investigation attributed this to a slight misalignment in one of the turbine blades, exacerbated by load conditions. Such misalignments, if not addressed quickly, can lead to increased wear and tear. Figure 7 depicts an anomaly that coincides with a transient spike in vibration that is accurately captured by the model. This spike is attributed to a temporary obstruction in the air inlet, possibly caused by debris, momentarily disrupting the airflow dynamics inside the turbine. The TCN-Autoencoder's ability to detect these anomalies can be attributed to its architectural features, which include multiple dilated convolutions that help capture a wide range of temporal dependencies in sequential data. The Multi-Head Attention mechanism allows the model to simultaneously focus on different temporal segments of the data, increasing its sensitivity to subtle anomalies indicative of underlying mechanical issues.