# Vibration Signal Diagnostic Information of Reinforced Masony Elements Destruction
## 2 Materials and Methods
### Coherence Function  
The measure of two vibration processes \(x(t)\) and \(y(t)\) is called the coherence function defined, which is as follows [25; 26; 27; 28]. \[\gamma_{xy}^{2}(f)\equiv\frac{\left|G_{xy}(f)\right|^{2}}{G_{xx}(f)G_{yy}(f)} \tag{13}\]  
When calculating the spectral densities for the formula given above, as a function of the density of source process \(u(t)\) and known transmittances \(H1(f)\) and \(H2(f)\), the results are as follows. \[G_{xy}(f)=H_{1}(f)H_{2}(f)G_{uu}(f)\]  
\[G_{xx}(f)=\left[H_{1}(f)\right]^{2}G_{uu}(f) \tag{14}\]  
\[G_{yy}(f)=\left[H_{2}(f)\right]^{2}G_{uu}(f)\]  
From here, the following result is obtained:  
\[\gamma_{xy}^{2}(f)=\frac{\left|H_{1}(f)H_{2}(f)\right|^{2}G_{uu}^{2}(f)}{ \left|H_{1}(f)\right|^{2}G_{uu}(f)|H_{2}(f)\right|^{2}G_{uu}(f)}=1 \tag{15}\]  
The coherence function always takes the value 1 if only signals \(x(t)\) and \(y(t)\) come from the same source. In the applications of this work, the coherence function will be smaller than unity now when any damage to the masonry element occurs. From the above calculations, it can  
Figure 2: Determination of natural frequency from the stabilization diagram. be concluded that the coherence function has effective diagnostic properties because the appearance of a new fault signal violates the coherence of the previous ones, which reduces the coherence function. Therefore, the coherence function, which is a local measure of the similarity of processes, has significant diagnostic properties in relation to the objects called linear and stationary in the domain of dynamic time T. Even greater possibilities of diagnostic applications of coherence functions can be found in complex systems. Currently, research on the quality of construction segments is identified based on constructed structural models or experiments conducted on real objects. New tools in vibration research concern the possibility of using modal analysis methods for obtaining new diagnostic information. The developed recommendations for the methodology and method of testing destruction were verified in terms of their usefulness on selected brick segments. Segments made of ceramic elements and silicate blocks were selected for verification tests, and for the purposes of the tests, they were marked depending on the execution method, which is shown in Table 1. The table also includes the determined values of the breaking force of segments on a testing machine. Considering the destructive values of the segment samples, the values of loads during the research were selected by the authors, as shown below, at the level of up to 200 kN. The tested wall segments of ceramic bricks (as appropriately marked) were made without reinforcements, with steel mesh reinforcements, and Ruredil mesh reinforcements. Figures 3-5 show the measured segment samples before and after testing. During the tests, they were subjected to a compression test to determine the failure limit of a given segment. The samples were subjected to a variable load from the value of 0 kN to the value of the destructive force (the values of the destructive force for individual wall segments are given in Table 1). The courses of destruction from scratching to buckling to failure were observed in \(\sigma\)-\(\varepsilon\) diagrams. The waveform changes with respect to the value of the load force (in kN) from 0 to the failure limit allowed for the further selection of load points for each segment, and state destruction studies were carried out. The following figures show the results of such a procedure presented successively: the excitation force waveforms; responses to the given excitations in the form of a vibration acceleration amplitude; vibration spectra of these signals; FRF waveforms; transmittance; and the coherence function. C1 SAMPLE