###### Abstract
Monitoring involves measuring and recording the selected output values over time, using measuring sensors, continuously or periodically. We refer specifically to the diagnostic process when the quality criteria of the measured quantity are defined. Diagnostic assessment consists of comparing the measured value with the criterion value [20]. Diagnostic processes refer to state diagnostics and process diagnostics. State diagnostics is considered in the context of a machine's efficiency (wear or damage to its parts and assemblies), while process diagnostics is related to disruptions in the process. Of course, a machine failure directly affects the processes it realizes. Diagnosing the technical condition of a machine, according to the literature, consists of measuring methods and technologies in relation to various monitored quantities and tested physical phenomena, such as vibration diagnostics [21; 22; 23; 24; 25; 26], thermal imaging diagnostics [27; 28; 29; 30; 31; 32; 33; 34], oil diagnostics [35; 36; 37; 38; 39; 40], vision diagnostics [41; 42; 43], acoustic diagnostics [44; 45; 46; 47; 48], or electrical diagnostics [49; 50; 51; 52]. In relation to machines with rotating components, vibration methods are most often used. In ref. [63], it was found that state monitoring based on vibrations allows detecting of as much as 90% of faults or failures in this type of machines. Depending on the type of machines and the processes they perform, three basic diagnostic strategies are used: a single-limit strategy, which assumes that exceeding the criterion limit results in stopping the machine; a two-boundary strategy, which assumes setting two thresholds, i.e., an alarm threshold and a threshold resulting in stopping the machine; a third strategy that involves comparing the waveforms of the monitored quantity with the reference waveform [20]. In the context of the efficient functioning of the manufacturing system in accordance with the I4.0 concept, non-destructive methods of monitoring and predictive diagnosis of machines are being sought. It is particularly important that these methods are sensitive and enable the detection of small changes in the monitored object at an early stage of damage propagation. This is important for planning the necessary machine downtime in advance. Currently, one of the most dynamically developing methods of monitoring and non-destructive diagnostics is vibration methods. This is mainly due to the emergence of small wireless sensors based on IoT technology, which makes continuous monitoring of the machine possible. This allows one to improve, and in advanced applications fully automate, the diagnostic reasoning process. This is important in the context of the I4.0 approach. Then, expensive, specialized and often invasive ad hoc inspection of machines is not required, but only automatic or remote analysis of continuously recorded data is needed. Therefore, structural health monitoring (SHM) methods based on the analysis of dynamic parameters of systems are currently being dynamically developed by researchers from many academic centers [64; 65; 66; 67; 68; 69]. The development of these methods results from the need to optimize costs related to broadly understood machine maintenance. Some of these methods make it possible not only to detect damage at the initial stage of its occurrence but also to localize it in the machine structure. These methods must then be highly sensitive to changes in the analyzed parameters. One of the most important groups in this context is model-based vibration methods. Vibration diagnostics based on a dynamic model consists of comparing the dynamic parameters identified for an undamaged object with the parameters measured during its operation. Based on the identified differences, it is possible to detect damage and the place of its occurrence [70; 71; 72]. In general, such methods can be divided based on the assessment of changes in the natural frequency, damping coefficient, natural vibration modes or frequency characteristics.