## 2 Research Methodology
### Measurement Noises and Computational Complexity  
Exploring the studies, we can distinguish several of the most common attendant issues researchers encountered during their investigations. Along with the crucial issues, they challenge researchers to apply their ingenuity to solve them. Ways of solving such problems are also important, so it is also reasonable to pay attention to them. The issues, such as measurement noise, computational complexity, iteration divergence, and nonlinear relationship of parameters, will be observed below. Measurement noise is one of the significant issues affecting rotor systems' diagnostic and analytical accuracy. It can arise from many sources, such as electromagnetic interference, transients, random vibration input from other monitored system components, environmental effects, temperature variations, and inaccurate measurement equipment. In the study by [31], the Kalman filter was applied to reduce noise during measurements. According to the authors, the method demonstrated the worst results from the considered method set. Moreover, in the studies [68; 87], the authors note this method as unsuitable for problems they solve because the Kalman filter requires an accurate mathematical model derived from prior knowledge of the signal, and model inaccuracies can result in significant estimation errors. The results of the paper by [31] demonstrated the joint input-state estimation method, which compensates for noise excitations during measurement. Moreover, in the paper, the authors considered a modal expansion approach, which decomposes the signal into its main components and suppresses noise. Reduction of low-frequency noise with high-pass filtering was applied in [51]. This method demonstrated promising sustainability for artificially added noise. The paper by [87] used the moving average filter (MAF) to eliminate harmonic components in the measured signal. The authors concluded that this method shows suitable efficiency with a number of stages more than five. In the study by [55], the authors successfully used the Daubechies wavelet to separate the helpful signal from noise components. The researchers recognized the affiliation of decomposition fragments without using any automation. The Fourier synchro-squeezed transform was utilized in [86] for isolating multi-component signals and cleaning the spectrum. An extremely popular tool to reduce noise is a type of Fourier transformation. For instance, in [51], the noise reduction method is based on the discrete Fourier transform (DFT) algorithm. In the study by [14], the equivalent loads minimization method also demonstrates high sustainability to noise. Here, noise excitations are removed during the minimization procedure. Methods of artificial intelligence and machine learning take a separate place in the problem of noise reduction. In the study by [90], the authors used generative-competitive networks (GAN) to recover synthetic signals and compensate for noise components. However, noise reduction can also be performed using hardware devices. For instance, the authors in the paper [68] considered the noise reduction technique of measuring signal synchronization with rotation frequency. Thus, it can be concluded that digital filters are most appropriate for preliminary signal cleaning. Signal transformation-based methods are more suitable for removing undesirable harmonics. Depending on the architecture, AI-based filters can perform a wide range of signal cleaning and restoration tasks. Finally, signal quality can be improved at the measurement stage by synchronizing measurements with rotation and amplifying specific frequency bands. In contemporary rotor system analysis, it is highly crucial to maintain precise results and, at the same time, minimize computational expenses.