*2.1. The Idea of Force Monitoring in Bolts*

The idea of bolt force monitoring discussed in this paper is based on measurements of elastic waves. It was confirmed by Kim and Hong [14] and Ding et al. [15] that even a relatively small change in a bolt force will affect the signals measured (its time of flight, amplitude, frequency, etc.). Changes in the tension force have an influence on the shortening/elongation of the screw. This results in variations occurring in the distance traveled by waves and the time related to it. Thus, the propagation velocity and ToF are the parameters frequently used to determine and detect the stresses or forces of the monitored elements [16].

In this paper, two single PZT were implemented to excite and to measure the response signals in the bolts of the studied flange connections (Figure 1). These transducers were placed in pitch–catch configurations. At the beginning, a single screw was equipped with additional transducers (one on the end of the shank and two on the screw's head) in order to get a pulse–echo configuration. Nevertheless, due to the fact that both of them provided similar accuracy considering force identification, it was decided to use pitch–catch in subsequent studies because this enables one to obtain a higher signal-to-noise ratio (SNR).

**Figure 1.** Example of connections subjected to static tests and the elastic wave propagation measurements in bolts: (**a**) P1, (**b**) P2, (**c**) P3, (**d**) P4.

Taking into account the simplicity of conducting on-site inspections, the most convenient placement of measurement units would be probably an impulse–echo configuration, but this was not considered in this study. In the case of SHM systems, whether or not the structure is equipped with instrumentation during its construction can be seen as irrelevant (actuators and sensors can even be mounted inside the bolts).

A typical washer force sensor consists of three or four standard piezoelectric measuring elements or strain gauges inside the unit. This is to average the results over the entire sensor surface. This approach should be considered in future work related to the approach under consideration because of the possibility of the simultaneous tensioning and bending of bolts (Figure 2).

**Figure 2.** An example of visible bolts deformation at the end of the static test (P6 connection).

Parameters describing the force changes (e.g., physically measured or determined based on the measured signals) can be used for training an efficient diagnosis system that is based on ANNs. The advantage of this over existing solutions is that the application of the proposed approach may allow one to estimate not only changes in forces over time, but also detect yielding and fatigue damages and monitor the structural integrity.
