*2.3. Flange Connections under Static Tests*

The investigated set of flange connections consisted of six M16 bolts (Figure 4). In each connection, only four of them were equipped with washer strain load cells (Bolt Nos. 1, 2, 4, and 5; see Figure 4). The other two had spacers that imitated the force sensors in order to ensure the similar nature of bolt work. The dimensions of the considered connections and the types of screws are listed in the Table 1.

**Figure 4.** A scheme of the flange connection (P1/P2), screw numbers, and sensor locations (all dimensions are given in mm; washer-type sensors are not included).

Unfortunately, as a result of technical complications (a lack of free hard disk space during the measurements) and the resulting differences in the number of recorded signals between the two oscilloscopes, measurement data from the P5\* connection were not used in this article.


**Table 1.** Dimensions of the investigated flange connections.

\* data related to this connection were not used – details are given in the text.

Two inductive sensors were mounted on screw S1 (from above and below; see Figure 1) to measure its displacement. Thanks to this, it was possible to determine the elongation of this screw during the tensile test. The other two inductive sensors were attached on the right and left side of the pipe rod. They were used to monitor possible rotational deformation, which was considered insignificantly small. On this basis, it was assumed that the investigated flange connections generally deform symmetrically, and the elongation of a single bolt can be used as an additional parameter describing their current condition. The conducted tests did not take into account the occurrence of a complex stress state, in which this assumption could be false.

The forces obtained during the static tests and the elongation in one representative screw were used to define an output vector for ANN training. The obtained relationship between these values in the case of single connections is shown in Figure 5. It can be seen there that the forces measured in the bolts were not exactly the same. This may be related to the geometric imperfections of the connection (non-symmetric holes) or measurement uncertainty (this type of applied force sensor is sensitive to the washer hardness or a screw touching the edge of the hole).

**Figure 5.** Elongation and forces measured in the bolts: (**a**) P1 connection; (**b**) P2 connection (see Table 1).

In addition, four bolts were equipped with piezoelectric transducers, but their numbers were different with respect to the force sensor locations, i.e., 2, 3, 4, and 5 (Figure 4). It was not possible to mount them at the S1 bolt because the inductive sensors were placed there. As a consequence, the signals measured in the S3 bolts (in all connections), which were not equipped with the washer load cell, were used to define the database with unknown force magnitudes. After the process of ANN training, these data were used to predict the forces in those bolts.

It is worth mentioning here that the completed test plan did not assume cyclical loading/unloading of the connections. In this particular case, each individual test was intended to cause damage in one of the following forms: bolts yielding or breaking, plastic deformation of pipes or head plates. The failure model depended on the connection dimensions and the class of bolts used. For example, in the P1 connection, there was plastic deformation of the pipe observed (Figure 5a), while in the case of the P2 connection (see Figure 5b), the deformation of the pipes was accompanied by yielding of the bolts. This explains the differences that can be seen in these charts. Despite this fact, an attempt was made to estimate the bolt forces regardless of the connection operation phase.

In the experimental studies carried out, it was not possible to obtain measurement data from the unloading phase of a damaged joint in the case of all considered models. When the load capacity of the connection was being approached, some of the sensors were disassembled due to the risk of their damage. Therefore, it was decided not to include these data in the ANN training process. However, the issue of cyclic loading is very important, and further research in this area is needed. Examples of experimental studies carried out so far and the preliminary results of the axial forces' identification can be found in the literature [11,17].
