## 1 Introduction  
Energy exchange between machine parts can cause harmful changes, being common in technology. Practically, with any real movement of the object, vibration occurrence in the environment can be expected. The source of vibrations may include vehicle traffic, rail transport, equipment operations, construction works, and mine operations [1, 2]. Building structures and occupant comfort are both affected by vibrations. Historic buildings are susceptible to physical, chemical, and biological processes. Vibrations may damage elements of objects and potentially lead to a construction disaster [3]. Historical buildings in cities are subjected to long-term vibrations from public transport vehicles, which requires monitoring of the condition of the buildings over long periods of time [3]. With mechanical devices, vibration information can be used as diagnostic information. This can help to find whether the machine element works correctly or is damaged. Wind turbines can be used as an example. Turbines are structures susceptible to wear during operation. Full vibration monitoring and analysis systems allow early failure detection, reduce downtime, and maximise efficiency [4]. The turbine blade monitoring system is based on dynamic properties of the blade and depends on the blade's material (stiffnessand damping). Vibration monitoring can detect a reduction in blade stiffness caused by a damaged blade [5]. Coal mills are another exemplary group of devices, whose health can be monitored by recording vibrations. Incorrect loading and vibration of the mill can disrupt the coal pulverisation process. The regrinding efficiency cannot then be guaranteed, which has a negative effect on the entire pulverisation system. When monitoring the correct operation of the mill, vibration and load signals are first collected, corresponding to typical damage to a coal mill. Based on them, models of the mill's operation are built on various scales. The models are compared with those obtained during the mill operation. By analysing these vibration characteristics and estimating the coal level in the mill, various operational problems, such as overload and lack of carbon, are identified [6]. Bearings are an element commonly used in machines. The analysis of vibration signals is so advanced that signal modelling is used by analysing combined signals from a physical object and a material model based on physical properties [7]. Vibration monitoring allows for early detection and replacement of the damaged element. Explosions and controlled explosions are processes that release large amounts of energy. An example is rock breaking, where an effective part of the blast energy crushes the rock. Energy is transferred to the atmosphere as air movement, thermal energy, and ground vibrations. Ground vibrations are transmitted to buildings and other structures, causing movements. Explosions started in mines have a direct impact on mine office buildings, industrial structures, and surrounding residential buildings, power lines, and pipelines. Vibration monitoring detects the level of vibrations threatening the condition of objects surrounding the mine [8; 9]. The problem of vibration monitoring includes both small free-standing objects and large structures. A unique structure is the Large Hadron Collider (LHC) on the border of France and Switzerland. In order to reduce the influence of external factors on the research results, the LHC was built underground. Due to specialised research, it is necessary to conduct ongoing monitoring of the vibrations' impact, including seismic vibrations. Research on vibration monitoring considers both the measurement systems' construction and implementing new methods of signal processing [10; 11]. In [11], the researchers confirmed a practical possibility of using the Probabilistic Power Spectral Density analysis of signals from seismic stations in determining the long-term ground vibrations. As mentioned before, a significant source of long-term vibrations is public transport.