## Appendix A A Short Review on SHM  
For our purposes, some techniques look for the changes in the structure's damping ratio, the natural frequencies or the modes shapes [19, 33]. When considering dynamical responses, the analysis can be carried out in the time or the frequency domains. Frequency domain techniques take advantage of modal analysis. The literature is extremely abundant. They are based on the use of modal informations extracted from input-output measurements by means of the modal analysis methods or from only using output data measured under the ambient excitation [34, 35]. Time domain methods avoid issues related to the natural frequencies. In [15, 16, 17, 18, 19, 20], the authors identified modal parameters from time domain measurements and used the extracted vibration features and modal properties for detecting damage occurrence and/or location by comparing the identified modal properties with the original values. Wavelet analysis allows identifying changes in modal shapes, facilitating the damage quantification and its spatial location [21, 22, 23, 24, 25, 36, 37, 38].  
Reduced Order Modeling (ROM) techniques have been also extensively considered. In [39], the authors applied the proper orthogonal decomposition (POD) to track the structural behavior. In [40], the authors proposed a data-driven methodology for the detection and classification of damage by using multivariate data-driven approaches and PCA. A support vector machine (SVM) was used for damage detection in [41]. In [42], the authors used machine-learning algorithms to generate a classifier that monitors the damage state of the system and a reduced basis method to reduce the computational burden associated with model evaluations. Proper orthogonal decomposition approximations and self-organizing Maps (SOM) are combined to realize a fast mapping from measured quantities in order to propose a data-driven strategy to assist online rapid decision making for an unmanned aerial vehicle that uses sensed data to estimate its structural state [43].  
Data Mining techniques are also used in the context of the SHM. In [44], the authors combined data mining (GA), machine learning (PCA) and deep learning (neural networks) techniques in the damage identification context. Concerning Deep Learning techniques, in [45], a smart monitoring of aeronautical composites plates based on electromechanical impedance measurements and artificial neural networks is proposed.  
In our former work [46], we proposed a strategy based on the combination of model order reduction, which extracts a reduced basis from undamaged snapshots, that will serve for projecting any measured solution on it with data-mining techniques. When projecting into this reduced basis the measured field, undamaged regions are expected to be better approximated for the ones in which damage occurs. Thus, data-mining strategies could be then used to differentiate both regions (undamaged and damaged). Finally, in order to limit the number of points at which data are collected, the just-described methodology was combined with a data-completion strategy based on the use of dictionary learning.  
These techniques allow identifying and quantifying the damage based on the collected data and on the performed training; however, performing time predictions needed in accurate prognosis remains a challenge for techniques based on data analysis.