## 3 Feature Selection Algorithms
### Empirical Mode Decomposition
#### 4.2.3 Support Vector Machines (SVMs)
\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
[123] & Three-story building & Magnetwheelological & Laser kernel and & RMSE = 0.0380 (AR, & & & & \\ structure experimental & model & dampers & AGRW, WARM, DEF & Linear kernel and & RMSE = 0.0589(WN, & 100 samples from acceleration data and an SVM for damage detection purposes & 2013 \\ \hline
[114] & Simply supported bridge & Simulation & CA & GRRF & ACC\({}_{-100\%}\), damage localization, & & A GA algorithm was used to select the optimal & \\ numerical model & Simulation & CA & GRRF & ACC\({}_{-98.1\%}\) (triple & Not specified & hyperparameters for an SVM structural damage classification model & 2011 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Cont._[PERSON] and [PERSON] [117] proposed a two-step method using a differential evolution algorithm (DEA) and an SVM for damage identification in a steel structure. In the first step, the location of the potential damage is determined using an SVM, and in the second step, the severity of the damage and a more accurate location is obtained using the DEA. The results obtained showed high accuracy in the capabilities of the damage identification system. [PERSON] et al. [118] proposed the integration of a DNN and SVMs for the SHM damage identification framework. SVMs were used in the output layer of the DNN to detect data associated with an unlearned structural damage pattern. The added value of the proposed framework is the correct classification of unlearned damage patterns that may lead to misclassification, thereby improving the generalization feature of the classification model for damage identification. [PERSON] and [PERSON] [75] proposed a damage identification SVM system to determine the presence and location of damage using intensity-based features as damage-sensitive features. This SHM system achieved over 83% accuracy in damage classification. Intensity-based damage features were also used in a system proposed by [PERSON] and [PERSON] [74], in which an SVM classifier performed the classification task. The optimal damage-sensitive features and hyperparameters of the SVM were obtained using Bayesian optimization techniques. The proposed system showed robustness against signal distortion and reliability in detecting damage to building structures. [PERSON] et al. [119] presented a comprehensive comparative study among several ML algorithms, including BP-NN, LS-SVMs, ANFIS, RBFN, LMNN, ELM, GP, multivariate adaptive regression spline (MARS), random forests and Kriging, for damage identification classification, location and severity estimation tasks. The results obtained indicate that the Kriging and LS-SVM models better predict damage location and severity than the other ML models. [PERSON] [120] presented a two-step unmeasured mode prediction method using two LS-SVMs and limited sensor measurements. The first step estimates missing modal shapes through an LS-SVM. In the second step, when complete modal system information is available, a second LS-SVM performs structural damage identification. The effects of noise and modeling error interference were analyzed, showing that the proposed system is robust against these effects. In the damage identification proposal presented by [PERSON] et al. [41], transmissibility functions, WPEV and PCA were calculated on the acceleration response data and fed into an SVM damage classification model. WPEV and PCA were used as damage-sensitive feature extractors to construct the training samples of the ML model. As an improvement of the proposed damage identification scheme, the training data size was greatly reduced with the proposed strategy. The SVM classifier performed damage localization, and damage severity was obtained from the SVM regression result. [PERSON] et al. [121] presented a comparative study of optimization techniques combined with SVM models.