## 3 Road Anomaly Detection and Classification Approaches through Vibration-Based Techniques  
Vibration-based techniques to detect and classify road anomalies can be categorized into three approaches [17]. The first is threshold-based methods, the second is learning-based techniques employing feature extraction before the learning stage, and machine learning techniques without feature extraction, such as deep learning algorithms [1]. Figure 2 shows an overview of the road anomaly detection and classification approaches based on vibrations collected from accelerometer and gyroscope data. As depicted in Figure 2, threshold techniques do not require a training process however an empirical calibration is needed before the validation. In the feature extraction and deep learning approaches, a step of model generation is performed through the training process and, consequently, a validation stage is performed. This section provides a brief overview and examples of these approaches and the authors' reported methods and results.  
Figure 1: Schematic representation of the search process performed for this narrative review that focuses on vibration-based techniques used for the detection and classification of anomalies on the road surface.  
Figure 2: Overview of the approaches used for the detection and classification of road surface anomalies based on vibration-based techniques.  
In the case of the threshold-based methods, the metrics commonly reported are the true positives and false positives [21]. However, other metrics, such as the F1-score or the area under the receiver operating characteristic (ROC), have been reported [22; 23]. On the other hand, the learning-based techniques with feature extraction or deep learning approaches are commonly evaluated through the accuracy and the metrics derived from the confusion matrix (i.e., recall, precision, and F1-score). Figure 3 shows a confusion matrix illustration along with the metrics derived from it, and Table 2 shows a summary of commonly reported validation metrics used to evaluate algorithms for detecting and classifying road surface anomalies based on vibration-based methods.  
The accuracy represents the proportion of correctly identified observations among all the observations tested. The sensitivity indicates the percent of real positive cases accurately recognized, whereas specificity is the proportion of real negative data points accurately  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Metrics** & **Equation** \\ \hline Accuracy & \(\frac{TP+TN}{TP+TN+FP+FN}\) \\ \hline True Positive Rate/Recall/Sensitivity & \(\frac{TP}{TP+FN}\) \\ \hline Specificity & \(\frac{TN}{TN+FP}\) \\ \hline Precision & \(\frac{TP}{TP+FP}\) \\ \hline False Positive Rate & \(\frac{FP}{FP+TN}\) \\ \hline F1-Score & \(2\frac{(Precision)(Recall)}{Precision+Recall}\) \\ \hline TP: true positives, TN: true negatives, FP: false positives, FP: false negatives \\ \hline \hline \end{tabular}
\end{table}
Table 2: Metrics used to evaluate the performance of threshold-based methods and machine learning models for the detection and classification of road surface anomalies [24; 25].  
Figure 3: Confusion Matrix and the formulas of accuracy, precision, specificity, recall, and negative predictive value. TP refers to True Positives, TN refers to True Negatives, FP refers to False Positives, and FN refers to False Negatives.  
classified. The sensitivity and specificity are used to determine a classification model's individual class performance. Otherwise, precision is defined as the ratio of true positives to true positives plus false positives. The F1-score value is calculated using the recall and precision parameters as shown in Table 2. Its value ranges from 0 to 1, with 0 indicating a poor forecast and 1 indicating a good forecast [25]. The F1-score is used to compare the performance across models.