## 1 Introduction  
Vibroacoustic diagnostics include vibrations, noise, medium pulsation, and acoustic emissions [1, 2]. Vibroacoustic signals are measured using sensors to process the primary physical quantities of objects:  
* Element displacement;
* The velocity of elements;
* The acceleration of elements;
* The phase shift of harmonic portions;
* Pressure;
* Strength;
* Stress. For the measurement of vibroacoustic signal generation, piezoelectric sensors, called accelerometers, are most often used, as they have a wide range of measurement frequencies, high dynamics, and good linearity and are stable for long periods [3]. Degradation processes in power facilities affect the evolution of load distribution, which indicates the desirability of using frequency analyses of vibration signal systems and studying the impact of damage development on signal changes. According to some authors, there are better tools than classical spectral analyses, in which an assumption of mutual independence of components is made [4]. Intelligent systems have been constructed and used in this field, operating according to algorithms that include the detection and localization of damage [5]; the assessment of the degree of criticality of a state; changes in parameters as a result of a response to a change in a technical state; and forecasting the remaining existence time. Algorithms for the adaptive control of internal combustion engines with changing dynamic properties as well as changing properties and stochastic disturbances have also been used, during which process and disturbance model parameters are estimated in order to update the control algorithm. When assessing risk, it is possible to use analysis methods such as fault and event trees, considering the influence of wear processes and impacts on the environment. Measuring energy bandwidth changes in the spectral width ratio can be used to assess damage development [6]. [PERSON] and [PERSON] [7] proposed a method of predicting and analyzing the gigacycl fatigue life of gear materials using a vibroacoustic signal. The authors carried out accelerated fatigue tests on a constructed stand operating in the natural frequency range of the samples. The vibroacoustic diagnostic methods enabled the detection of surface damage and damage in the core of the sample. Their research allows for an understanding of the nature of the increased fatigue life and to use of the parameters of vibroacoustic signals to predict fatigue life. [PERSON] et al. [8] indicated that changes in mild steel and high-strength steel samples cause changes in observed acoustic emission signals. Fatigue cracking shows different stages of development [8], namely substructural and microstructural changes, the microscopic formation of dominant cracks, the stable propagation of dominant cracks, and structural instability leading to the termination of the cracking. Although various methods have been developed to detect fatigue cracks [6; 8], detecting crack initiation remains a real challenge in nondestructive testing. The main problem of the early microstructural stage of fatigue cracking is its stochastic nature. [PERSON] found that higher-order central statistical moments reveal the most information when diagnosing damage using vibroacoustic signals [6]. Another study described a stress assessment methodology and a method of integrity loss detection for concrete beams using a technique based on vibroacoustic signal analysis [1]. The skeletal curve of nonlinearity changes obtained in the experiment, after the secondary processing of a time-frequency map, showed that the difference in the shape of the skeletal curve was correlated with the change in stresses in the structure. Qualitative changes in nonlinearity were used to detect the loss of cohesion in the examined systems. After the secondary processing of a time-frequency map, the nonlinearity changes obtained in the experiment skeletal curve were used to detect the examined system's cohesion loss.