**1. Introduction**

Measurements of the physical quantities that describe structural elements' state are significant in many engineering and industrial applications, including civil engineering. They are often conducted pending trial loads of new structures and prototype solutions in laboratory tests. This allows a better understanding of the behavior of the entire structure and its individual elements. Non-destructive tests (NDT) and structural health monitoring systems (SHM) are very useful in this task. Their constant use also increases the safety and reliability of the structure. There are also several tasks that can be carried out with their help [1–6]:


There is a group of structure connections where the pretension force level has an influence on the strength of the slip resistance connection. Changing pretension forces, i.e., due to the structure's usage over time, may become a highly relevant matter for the structural integrity. It is especially important in cyclically loaded constructions like telecommunication towers, bridges, and wind turbines.

Besides the necessity to monitor the state of strategic structures, the precision of the tightening method implemented to accomplish an accurate preload level is equally important. One of the hazards related to the occurrence of failure or structural damage may be the insufficient stress ratio of screw connections. Among the methods used to control their tightening level, two main features can be

distinguished: accuracy and practical applicability. Determining the prestressing force in everyday applications is most often based on the tightening torque measured with a dynamometer wrench. The accuracy of this approach is defined as ±25%. The best accuracy here is accomplished by using ultrasonic sensing (±1%) or strain gauges. There are already a few commercial solutions that can be used to estimate the axial forces in bolts. One of them concerns ultrasonic load-monitoring devices, which most often require access to bolts in a joint from both sides. The second solution is related to piezoelectric load cells or washer-type strain. The measurement uncertainty in this case amounts to ±10%. Fric et al. compared some of these methods [7]. However, their costs cannot be ignored, and therefore, in long-term research, strain gauges are used, either fitted inside the bolt shank or glued onto the bolt. For this reason, the article presents the results of laboratory research aimed at the use of commonly available and relatively inexpensive piezoelectric transducers (PZT) that can be used to excite and receive elastic waves.

In this work, the elastic wave propagation phenomenon was implemented due to the possibility of adjusting their parameters to the applied task, their sensitivity, and their ease of implementation in SHM systems. To measure and introduce the time signals of elastic waves, piezoelectric transducers were used. Nazarko and Ziemia ´nski [8] used this idea also in the field of non-destructive damage detection in a variety of elements and materials. Chaki and Bource [9] examined guided ultrasonic waves to monitor and observe the stress levels in steel strands. In these approaches, including ultrasonic testing, the most frequently used parameters are changes in longitudinal and transverse wave propagation velocities or time of flight/arrival (ToF/ToA). In the discussed problem of identifying axial forces in bolts of flange connections, this turned out to be insufficient. Therefore, in order to obtain reliable signal parameters, their deep compression was applied. Additionally, as the inference tool, artificial neural networks (ANNs) were used [10].

The results presented in the article concern a series of laboratory tests carried out on flange connections under tension in a static test machine. It appeared that force changes have an impact on the signals measured by the sensors [11]. This was reflected also in the calculated principal components, which are often used to compress signals (see Nazarko [12] or Chen et al. [13], where other methods concerning signal compression were compared). This article presents new results where ANNs were used both for signal compression and as an inference tool. The value of these results is increased by the fact that they refer to experimental studies, where there are a number of factors (measurement noise, apparatus limitations) that are quite difficult to examine in numerical simulations and analytical calculations. In this case, the research concerned the possibility of predicting axial forces in tension bolts of flange connections. The elastic waves were regularly excited and recorded (by PZT sensors) during the connection tensile test. After extending the set of patterns (compressed signal parameters) with information about the elongation of one of the bolts, it became possible to estimate (using ANNs) the magnitude of axial forces not only within a single connection, but also to generalize the results within several analyzed connections. Moreover, these preliminary results show that ANNs are able to predict the axial forces in bolts with reasonably good accuracy. This also indicates the significant potential of the approach being developed for real-life NDT inspections.
