## 5 Results
### Evaluation of the MLAs with the Higher Prediction Ability  
In this section, we provide a more detailed description about the performance of the MLAs with the higher prediction ability during the 10-fold procedure. In Figure 9, the error metrics are depicted comparatively for the qualified MLA of each damage index. In general, the extra trees regressor algorithm exhibits higher performance than the gradient boosting regressor algorithm considering the DI\({}_{\text{G,PA}}\) and DI\({}_{\text{DC}}\) structural damage indexes, respectively. Considering DI\({}_{\text{G,PA}}\), a generally smooth shift of the error is observed that expresses the probability of a given number of events occurring over a fixed period of time,  
Figure 8: Peformace metrics of the examined MLAs. taking into account the observations that occur at a known average constant rate and are independent of their appearance. There is only one case of significant error fluctuation which describes repetitive non-periodic alterations that could not be predicted by this algorithm. Regarding the DIDC, it is observed that there is higher dispersion of the error, which normalizes in the later folds. This fact translates the randomness of the samples into some folds, which are independent of the time period of their occurrence. The normalization and stabilization of the error after the initial fluctuations describes some possible repetitive non-periodic changes which are satisfactorily predicted by the specific algorithm. By this fact, the model can calculate reliable output values for inputs that are new and different from those with which it is trained. The 10-fold procedure is implemented iteratively in a progressively increasing subset in order to produce the learning curves. In both cross-validation and training sets, the average and the range of R\({}^{2}\) are calculated for each iteration. A major control procedure of the adjustment and the response of the algorithms is based on the learning curve, which depicts the learning performance as a function of the gained experience. It is a widely used tool that assesses the training and the validation data after each update of the measured error performance. Via this method, problems such as under- or over-fitting of the model, and the adequacy of the training or the validation data, could emerge. In Figure 10, the learning curves of the distinctive MLA for each dataset are depicted. Specifically, Figure 10a illustrates the learning curves of the extra trees regressor algorithm when the structural damage is assessed in terms of DI\({}_{\text{G,PA}}\), while Figure 10b presents the learning curves of the gradient boosting regressor considering structural damage in terms of DIDC. It is obvious that the training curve of Figure 10a improves as the experience of the model increases without any trends of over-fitting. That fact could be identified by small alterations similarly presented in both training and cross-validation curves. The prediction ability of the model is highlighted due to the high performance beginning at the starting point of the procedure with a score over 0.87. An increasing trend is depicted with a rather narrow confidence interval, a fact that reflects the quality of the model. Moreover, there is no loss of the training, and as such, the distance between training and the validation curve reduces in relation to the experience. This distance is referred to as the \"generalization gap\" and defines the quality of the model. It is obvious that smaller gaps between the two curves implies higher accuracy of the model. Figure 9: Evolution of performance metrics during 10-fold cross-validation for ETR and GBR algorithms in case of DI\({}_{\text{G,PA}}\) and DIDC damage indices, respectively. From the training and the validation curves of Figure 10b, it could be easily observed that the algorithm fits quite well. Specifically, there are no trends of under- or over-fitting.