## 3 Feature Selection Algorithms
### Empirical Mode Decomposition
#### 4.2.3 Support Vector Machines (SVMs)  
A support vector machine (SVM) is a popular machine-learning algorithm used for classification and regression problems. Its working principle is essential to maximize the distance value between a set of vectors, named support vectors, and a defined hyperplane. The maximizing goal in SVM can be seen as an optimization problem, and several approaches can be used to solve this problem. An exciting feature of the SVM decision boundary is that this boundary is the best possible boundary between a set of data classes for a given set of data and an SVM formulation. Table 10 shows that several SVM structural approaches for damage identification have high accuracy. However, SVM models' training stage is usually computationally expensive and unsuitable for real-time SHM systems that rely on post-training updates and ML model improvement. A common practice to reduce this computational cost is to combine SVM models with signal processing techniques such as PCA, WT and HHT, or damage-sensitive feature extraction methods such as RFR. Figure 4 shows an example of an SVM-based structural damage identification system. [PERSON] et al. [115] proposed a combination of PSO and SVM for structural damage identification, location and severity. Four ML algorithms, including ANN, DNN, ANFIS and SVM, were trained and compared to predict damaged elements and damage severity. The proposed PSO-SVM combination achieved the highest accuracy among the compared techniques and correctly predicted all damage locations in the validation test. In a proposal by [PERSON] and [PERSON] [116], Bayesian optimization (BO) was used in the hyperparameter search of an SVM, in which the SVM was used to perform damage identification. A comparison between BO and PSO in hyperparameter optimization search showed that BO was an efficient method that accelerated the optimization problem. [PERSON] et al. [52] designed an SHM damage identification system, in which MEEMD and HHT were applied to acceleration measurements to extract damage characteristics through Hilbert spectrum energy. The SVM trained with Hilbert energy identified, located and estimated the severity of the damage in the structure, and the theoretical and experimental validation of the proposed method was provided. Figure 4: An example of an SVM-based structural damage identification system [114]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Publication** & **Structure** & **Excitation Source** & **Signal Processing** & **Type of Kernel** & **Classification Error** & **Dataset Size** & **Purpose** & **Year** \\ \hline \multirow{3}{*}{[115]} & \multirow{3}{*}{Transbridge structure FE model} & \multirow{3}{*}{Simulation} & \multirow{3}{*}{PSO} & \multirow{3}{*}{GRBF} & RMSE = 0.0461 & \multirow{3}{*}{1000 samples} & Propose an ML-based method & \multirow{3}{*}{2021} \\  & & model and two-story & & & & (trans structure), & (dance stamps), & to detect and locate structural & \multirow{3}{*}{2021} \\  & & frame structure FE model & & & & (frames stamps) & & \\ \hline \multirow{3}{*}{[116]} & \multirow{3}{*}{The Phase II LASC-ACE structure FE model} & \multirow{3}{*}{Simulation} & \multirow{3}{*}{PSO} & \multirow{3}{*}{GRBF} & \multirow{3}{*}{ACC = 100\%} & \multirow{3}{*}{1768 samples} & Propose a method