## 4 Experiment and Results
### Results  
Figure 8 illustrates the application of synthetic outlier generation methods to the original data. We utilized four types of synthetic outliers: soft replacement, uniform replacement, length adjustment, and peak noise. Each method was designed to allow the model to indirectly learn the characteristics of abnormal data without requiring labeled anomaly data. * Soft Replacement: This method introduces subtle changes by replacing portions of the original data with smoothed values. It reflects gradual anomalies that appear over time, enabling the model to detect progressive deviations. * Uniform Replacement: This method replaces parts of the original data with random values generated from a uniform distribution. It simulates abrupt and unpredictable changes, mirroring sudden failures or external disturbances in sensor data. * Length Adjustment: Segments of the time series data are modified to reflect changes in periodicity or amplitude. This mimics real-world phenomena such as equipment wear or performance degradation. * Peak Noise: Sharp, isolated spikes are injected into the data to represent transient anomalies caused by mechanical impacts or electrical disturbances. This type of noise is designed to handle highly localized yet critical anomaly scenarios effectively. By generating synthetic outliers from normal data, the proposed SPT-AD model reduces reliance on labeled anomaly data and strengthens its generalization ability for diverse real-world scenarios. These techniques also minimize preprocessing requirements for large-scale sensor data, lowering the barriers to industrial deployment. Figure 9 shows the comparison of performance metrics (accuracy, precision, recall, and F1-score) between the LSTM Autoencoder, AnomalyBERT, and proposed SPT-AD model. Each metric was used as the main criterion to evaluate the anomaly detection performance of the model. This demonstrates that the design utilizing data degradation techniques and multi-resolution processing was effective, showing that the SPT-AD model provides higher accuracy and balanced precision and recall in anomaly detection compared to the existing models. Figure 8: Synthetic outlier methods applied to original data (soft replacement, uniform replacement, length adjustment and peak noise) (X-axis: seconds; Y-axis: V/g). In this study, we conducted an experiment to assess the performance of SPT-AD, a transformer-based time series anomaly detection model using self-supervised learning. We evaluated the performance of three models--LSTM AutoEncoder, MSCRED, USAD AnomalyBERT--that are widely used in unbalanced data problems and the proposed model, SPT-AD and used Accuracy, precision, recall, and F1-score as evaluation metrics. The results can be seen in Table 6. Since it is an anomaly detection problem utilizing only normal data, the performance metrics tended to be low, and the recall was somewhat low, but overall, the SPT-AD model proposed in this paper performed well. Table 7 shows a comparison of the computational effort of AnomalyBERT and SPT-AD. Computation was mainly calculated based on the Floating Point Operation (FLOP) complexity of the model. The AnomalyBERT model uses multi-head self-attention (MSA), which requires high computational effort that scales squarely with the length of the input sequence. The SPT-AD model uses the Pyramidal Attention Mechanism (PAM) to optimize the computation. The input data were reduced by multiple resolutions to efficiently reduce the length of the input sequence. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Accuracy** & **Precision** & **Recall** & **F1-Score** \\ \hline LSTM Autoencoder & 0.621 & 0.645 & 0.585 & 0.614 \\ \hline MSCRED & 0.590 & 0.612 & 0.568 & 0.589 \\ \hline USAD & 0.709 & 0.763 & 0.655 & 0.705 \\ \hline AnomalyBERT & 0.768 & 0.856 & 0.652 & 0.740 \\ \hline SPT-AD & 0.814 & 0.882 & 0.746 & 0.809 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison with other models.