**4. Conclusions**

One of the great advantages of the research presented herein is that it is based on experimental measurements carried out on a set of laboratory models of real flange connections. The main assumption of the proposed approach was that elastic waves carry information about the axial force in the bolt in which they propagate. Due to the significant differences in the measured signals, their compression using the MLP encoder was of great importance. By adding the variable of the elongation of one screw to the input vector, it became possible not only to achieve satisfactory identification results, but to achieve generalization capabilities. Moreover, this was not only possible with respect to one single connection, but after merging the signal parameters, it was possible for several investigated connections. Therefore, it can be concluded that the use of the MLP encoder (signal compression) and the addition of a bolt elongation (a physical variable) made it possible to find the relationship (ANN trained) between the propagating elastic wave and the axial force in the bolt subjected to tension.

On the basis of the trained ANN, axial force prediction was carried out for bolts that were not equipped with force sensors. The values obtained were consistent with those of other bolts, which was not possible in previous studies [11,17]. In this work, the dimensionality reduction of measured wave signals (neural network encoder) gave meaningful improvement to the results of the identification of the force in the bolts. Moreover, this new approach enabled: (1) the prediction of forces in bolts where they were not directly measured; (2) simultaneous analysis of data related to several connections. Obtaining the expected values of the prediction of axial forces was completely impossible in the previously considered stage of the research due to a serious problem with achieving the generalizing ability of ANNs [11,17]. The approach presented in this paper has eliminated this problem.

The article also presents the preliminary results of the identification of the axial forces, in which instead of the elongation of a single screw, elongation increments were used. Thanks to this, the proposed approach also has the potential for practical applications in real non-destructive test (NDT) measurements. Therefore, in future studies, this idea will also be extended to other connections. It will also be a good opportunity to include, in addition to processing elastic wave signals, the filtering of data related to the measurement of axial forces in bolts, which also influence the prediction accuracy.

Furthermore, it is worth mentioning that during the static tensile test, the force applied by the testing machine was also recorded. Therefore, it is also possible to use this in the pattern database information regarding load increments, which, in practice, may be more useful than measurements of elongation changes.

**Author Contributions:** Conceptualization, P.N. and L.Z.; methodology, P.N. and L.Z.; software, L.Z.; validation, P.N. and L.Z.; investigation, P.N.; resources, P.N.; writing, original draft preparation, P.N.; writing, review and editing, L.Z.; visualization, P.N. and L.Z.; supervision, L.Z.; project administration, P.N.; funding acquisition, L.Z. All authors read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Polish Ministry of Science and Higher Education grant to maintain research potential.

**Conflicts of Interest:** The authors declare no conflict of interest.
