## 3 Selected Research Results
### Analysis in the Frequency Domain  
To obtain reliable signal analysis results, it is advisable to conduct an analysis of the time domain and frequency domain, either separately or together. Figure 6a shows the spectra in Figure 4a for cylinder No. 1 in the suitability state, and before the damage in No. 5. Figure 6a shows that this is a polyharmonic and polyperiodic complex signal. Polyharmonic signals, in addition to the fundamental component at frequency \(f_{p}\) (usually rotational), contain superharmonic components at frequency \(if_{p}\) (\(i\) = 1, 2, 3, \(\ldots\) \(n\)) [3]. Polyharmonic signals consist of multiple polyharmonic signals with different fundamental frequencies [3]. The vibration acceleration spectra were divided into third-octave bands (Figure 6b), in which the powers of \(N_{H}\) harmonics, recorded in terms of mean and \(rms\) values, were determined in the octave (thirds) band of the spectrum according to the following relationship:  
\[\widetilde{H}_{o,t}=\sqrt{N_{H}}=\left[\sum_{i=1}^{n}\frac{H_{i}^{2}}{2} \right]^{\frac{1}{2}} \tag{9}\]  
where \(\widetilde{H}_{o,t}\) is the partial \(rms\) value in the \(i\)-\(th\) octave (third) band, and \(H_{i}\) is the component of the amplitude spectrum. Analyzing the frequency domain signals, damage-oriented symptoms were sought in octave and one-third octave bands (Figure 6). The measurement results in the frequency domain in the one-third octave bands are shown in Figure 6, in which, in (a), the average values of the amplitudes for cylinders No. 1 and No. 5 are presented. Figure 6b shows a  
Figure 5: Sample results of the analysis of vibration acceleration signals for cylinders No. 1–6 in the domain of amplitude (a) and root-mean-square (\(rms\)) values measured relative to the limit values (b): \(p\)-\(p\)—peak-to-peak value, _aver_—average value, _llv_—lower limit value and _ulv_—upper limit value. significant variation in some components' average amplitudes of the vibration acceleration signals (_aver_). Figure 6b displays the _rms_ values of the amplitudes in the one-third octave bands for cylinders No. 1-6, along with the limit values (_llv_ and _ulv_). Figure 6c shows that the upper limit value (_ulv_) for cylinder No. 5 exceeded that of the precritical damaged state. After 247 h of test operation, the combustion engine was halted due to an increase in exhaust gas temperature to 600 \({}^{\circ}\)C at a 37.5% load. A breakage was found in the injector nozzle of cylinder No. 5 (Figure 7a). The cracking of the injector nozzle body resulted in intense fuel leakage, which is shown in Figure 7b for an exemplary nozzle in a suitable state (\(q_{m}=0.0419\) kg/s) and another nozzle with a cracked body (\(q_{m}=0.1094\) kg/s). A large fuel leak occurred due to a broken-off section of the injector nozzle of cylinder No. 5, which diluted the lubricating oil with fuel. The oil analysis showed it was unsuitable for further operation due to its low flash point (165 \({}^{\circ}\)C) and reduced viscosity. Repeated cyclic loading during operation under high pressure and thermal loads [15,20] tends to cause unexpected fatigue cracks. The lack of resistance, which led to failure, was observed using semiempirical growth formulas for defects that increased due to cyclic loading and caused severe damage. The data for injector nozzle cracking are presented in Table 2 to distinguish the phases of damage development in the marine engine's injector nozzles. Figure 6: Amplitude-frequency spectrum (**a**), the average values of vibration acceleration amplitudes in one-third octave bands for cylinder No. 1 in suitability state and cylinder No. 5 before damage (**b**), and _rms_ values of vibration acceleration amplitudes \(H_{a}\) in one-third octave bands for \(f_{aver}=160\) Hz with limit values (**c**): \(f_{aver}\)—center frequency, _llv_—lower limit value, and _ulv_—upper limit value. Analysis of the signals in the frequency domain also showed the existence of a large number of diagnostic symptoms related to damage development.