## 3 Data and Application
### Method 3: Machine Learning Algorithms (e.g., Support Vector Machines)  
The first example shows a synthetic nonlinear signal generated as a combination of sinusoidal components with added nonlinearity (see Figure 8). In Figures 8 and 9, the SVM classifier attempts to detect these changes based on the features extracted from the signal. The accuracy of the change detection calculated as the percentage of correctly classified instances is shown in the title of the subplot. A new example of the SVM method is represented in Figure 10.  
In the top subplot of Figure 10, the synthetic signal is plotted over time. The amplitude spikes, representing changes in the signal, are highlighted in red. These spikes indicate moments where significant deviations from the normal pattern occur. In the bottom subplot, the true labels (indicating the presence of changes) are plotted in green, while the predicted labels generated by the SVM classifier are plotted as red dashed lines. The agreement between the true and predicted labels is visualized, showing how well the classifier identifies changes in the signal. The accuracy of change detection using SVM classification is provided in the title, indicating the percentage of correctly classified samples. This accuracy metric quantifies the performance of the machine learning approach in detecting changes in the synthetic data. Figure 5: Change detection using mean and standard deviation method. (**Top**) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations and fluctuations in amplitude. (**Bottom**) The red line represents the results of change detection using the mean and standard deviation method. Figure 6: Change detection using Wavelet Transform. (**Top**) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations and fluctuations in amplitude. (**Bottom**) The bottom subplot displays the results of change detection using the Wavelet Transform method. Changes in the signal are represented by localized regions of high wavelet coefficients, indicating deviations from the background signal. Figure 7: Change detection using Wavelet Transform. (**Top**) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations  
and fluctuations in amplitude. (**Bottom**) The bottom subplot displays the results of change detection using the Wavelet Transform method. Changes in the signal are represented by localized regions of high wavelet coefficients, indicating deviations from the background signal. Figure 8: Change detection in synthetic signal using Support Vector Machine (SVM) classification. (**Top**) Synthetic nonlinear signal plotted against time and shown in blue. This signal exhibits complex behavior over time, characterized by variations and fluctuations in amplitude. (**Bottom**) Change detection results using Support Vector Machine (SVM) classifier, where red indicates predicted change points based on the trained model. Figure 9: _Cont._  
Figure 10: Change detection in synthetic signal using Support Vector Machine (SVM) classification. (**Top**) Synthetic signal with complex patterns and amplitude spikes indicating changes (highlighted in red). (**Bottom**) Detected changes indicated by green (true labels) and red dashed lines (predicted labels) using SVM classification. The accuracy of change detection is shown in the title. Figure 9: Change detection in synthetic signal using Support Vector Machine (SVM) classification. (**Top**) Synthetic signal with a sinusoidal pattern over a duration of 5 s. Random changes have been introduced into the signal to simulate anomalies, indicated by the red markers. These changes represent potential abnormalities or deviations from the expected signal pattern.