## 6 Conclusions  
The paper presents the DS-SHC method, which can determine the severity of a crack involving just four static tests, one for the intact beam and three for the beam affected by a defect for which the positions are changed successively. From the tests performed for the defective beam, deflection is determined at the free end of a cantilever. Subsequently, using the SHC algorithm, the theoretical deflection that occurs when the crack is at the fixed end is determined. The matching of the three points is carried out on the function proposed in this paper, which expresses the deflection with the crack position. This theoretical deflection is different from the deflection achieved when the crack is at the fixed end because of constructive reasons. Finally, the severity is calculated from the capability of the beam with a crack to store energy, which is reflected by the increase of deflection at the free end. To prove the reliability of the DS-SHC method, we compared the frequencies of the damaged beam calculated with the severity derived by employing the theoretical deflection with the frequencies obtained for the damaged beam using the FEM. The normalized differences between these frequencies are extremely low, less than \(\pm 0.001\), which proves the reliability of the DS-SHC method. Moreover, we demonstrated here that the theoretical deflection for the damaged beam has to be considered when calculating the damage severity. Figure 13: Compared RFS values between the experimental measurements and analytical determined ones. (**a**) Damage scenario C(0.8, 310, 2); (**b**) Damage scenario C(1.2, 587, 2); (**c**) Damage scenario C(1.2, 395, 2); (**d**) Damage scenario C(2, 795, 2). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Damage** & \(x\) & \(a\) & \(w\) & \multicolumn{3}{c}{**ANN Predicted Values**} \\ \cline{4-7}
**Scenario** & **[mm]** & **[mm]** & **[mm]** & \(x\) [mm]** & \(\epsilon_{x}\) [\%] & \(a\) [mm] & \(\epsilon_{a}\) [mm] \\ \hline Beam 1 & 310 & 0.8 & 2 & 321.07 & 1.107 & 1.06 & 0.26 \\ Beam 2 & 587 & 1.2 & 2 & 598.01 & 1.101 & 1.49 & 0.29 \\ Beam 3 & 395 & 1.2 & 2 & 394.41 & \(-\)0.059 & 1.38 & 0.18 \\ Beam 4 & 795 & 2 & 2 & 791.09 & \(-\)0.391 & 1.94 & \(-\)0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Predicted locations and depths of the damage. An additional check was made to find out whether the prediction of the frequency changes made with the severity calculated based on the theoretical deflection permits assessing the damage. In the laboratory experiments we conducted, we were able to localize the damage with high accuracy, the errors being less than 1.1%. The damage depth was also found with high accuracy; the difference between the depth of the generated damage and the prediction is smaller than 0.3 mm. In the next studies, we will focus on finding whether the severity derived for the cantilever beam can be used for beams with other boundary conditions, and how accurate the severities for structures with other shapes of the cross-section can be determined. Conceptualization, G.-R.G. ; methodology, N.G. ; software, C.V.R., C.S., and C.T. ; validation, G.-R.G. and C.V.R. ; formal analysis M.V.P. ; investigation N.G. and C.T. ; writing--original draft preparation, M.V.P. and C.O.H. ; writing--review and editing, G.-R.G. ; visualization, M.V.P. ; supervision, G.-R.G. All authors have read and agreed to the published version of the manuscript. This research received financial support through the project \"Entrepreneurship for innovation through doctoral and postdoctoral research\": POCU/380/6/13/123866, a project co-financed by the European Social Fund through the Operational Program Human Capital 2014-2020. Not applicable.