## 4 Developed Testing Methodology and Test Results
### Test Results  
As part of this research work, a series of tests were conducted to confirm the method formalized in this work with respect to its possibility of using it to identify the area of damage in the monitored machine component (Tables 2-4). The tests consisted of introducing the damage to a given shaft stage and determining the characteristics of the monitored machine component state using the developed methodology, taking into account its operating environment (Section 2). Based on the obtained test results, it can be seen that there are deviations in the state characteristics of the tested machine component in all tested intervals, regardless of the location of its damage. However, in the case of the theoretical model (discrete systems), deviations in the characteristics occur only on the displacements of inertial elements between which a change in stiffness has been introduced. The remaining inertial elements of the theoretical model would overlap the current characteristic with the reference characteristic (\(\Delta\varphi_{\mathrm{n}}=0\)). Therefore, in the tested system, an additional criterion for the deviation of the current characteristics from the reference ones was adopted. The process of identifying the area where damage occurs can therefore be presented in the following steps:  
* Identify in the characteristics of the machine component's state the form of deviation of the current characteristic from the reference characteristic consistent with theoretical considerations (the characteristics between two sensors defining the searched area with damage should form a minority sign when viewed from the bottom of the characteristics);  
Figure 9: Monitoring and diagnostics of the tested machine component state using the developed methodology. * If the state characteristics contain only one form of deviation consistent with theoretical considerations, the damaged area is located between the sensors on which these deviations were recorded (Table 2, items 4 to 7, Table 3, items 1 to 6, Table 4, item 4);
* If the state characteristics appear more than once in a form consistent with theoretical considerations, then the sum of the absolute values of deviations between the sensors monitoring these areas should be taken into account. The damaged area should have a higher value of the described sum (Table 2, items 2 to 4, Table 4, item 1). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Geometric Form and Place** & \begin{tabular}{c} **Characteristics of** \\ **Monitored Machine** \\ **Component State** \\ \end{tabular} & \begin{tabular}{c} **Deviation of the** \\ **Characteristics [rad]** \\ \end{tabular} & \
\begin{tabular}{c} **Volume Loss** \\ **[\%]** \\ \end{tabular} &
\begin{tabular}{c} **Natural Vibrations** \\ **Frequency [Hz]** \\ \end{tabular} \\ \hline No damage & & & & \(\Delta\varphi_{1}=0\) & & \(f_{1}=3.995*10^{3}\) \\  & & & \(\Delta\varphi_{2}=0\) & & \(f_{2}=4.063*10^{3}\) \\  & & & \(\Delta\varphi_{3}=0\) & & \(f_{3}=9.015*10^{3}\) \\  & & & \(\Delta\varphi_{4}=0\) & & \(f_{4}=9.163*10^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Determining the characteristics of the monitored machine component state when introducing damage in the area confined by sensors S1 and S2.