## 2 Research Methodology
### Unbalance
During operation, relative deflection vectors classified by rotational speeds were fed into the neural network, resulting in relative imbalance values as the desired output. Sensors on a test rig measured the deflections. The example case study considered three rotational speed regimes and three deflection measuring positions, providing a nine-element input vector. To validate the results, actual imbalance values were measured on the test rig as reference values, and the deflection values were to be evaluated from simulations. The imbalance values were first estimated using linear regression but with unsatisfactory precision. By contrast, the imbalance values computed with the trained NN deviated by no more than 2% from the reference values, demonstrating the greater accuracy of the NN approach. Almost all experimental studies in rotor dynamics face the problem of noise in measured data, which can dramatically affect the accuracy of a study's results. The paper by [68] explores a real-time diagnostic technique for rotor unbalance using noise elimination that is accomplished by synchronizing the signal with the rotational speed. The authors employed a steady-state model rotor that balances centrifugal forces due to unbalance. The model's geometric parameters are given in parameterized terms so that the simulation of many various geometric configurations is possible. A matrix equation for computing the centrifugal forces is derived from the state of equilibrium. The imbalance angles and masses are calculated for the rotor's support locations as a function of the rotor's centrifugal force, section radius, and rotational speed. For noise suppression, a photoelectric tachometer is employed together with accelerometers; the tachometer quantifies the rotor rotation frequency and delivers a reference signal that amplifies the respective accelerometer signals, consequently suppressing the noise in measurements. Furthermore, the researchers created a graphical interface for graphically displaying the analysis results, plotting them as radial maps for two segments that show both the angular positions and the respective unbalanced mass values. Experimental tests validated the method, which were conducted on various geometric configurations of rotors to validate the geometric parameterization's correctness. According to the authors, the measurement error was maintained at 1-5% for mass and 0.5-2% for the angle measurements, which is consistent even under variations in the rotor's rotation speed. Moreover, parameterization of the geometric features of the rotor aids in standardizing the methods employed in the calculations, thereby making it more straightforward to research a large variety of rotor systems with various geometries. Nevertheless, the suggested model is a case of static equilibrium. It treats the specific centrifugal forces created in the rotor without regard to the inherent origin of the forces or their influence upon the dynamic oscillatory motion of the rotor. Furthermore, the model is limited by the measurement of the angular coordinates of the location of the unbalance only. Similarly, for modeling nonlinear effects that rule rotor behavior, the study by [26] proposes a new approach to imbalance localization in rotary machines using machine nonlinearities and an artificial neural network (ANN). A data-driven method was developed to address this issue: vibration signals were collected, and spectral characteristics were analyzed on an experimental test rig with a rotor and four disks. The key idea is that the machine's inherent nonlinear effects, such as sub-synchronous vibration components, contain information about the imbalance location. In the test rotor, such nonlinearity was identified: a slight bearing clearance in the housing caused the appearance of subharmonics, and the intensity of these components depended on which disk the imbalance was applied to. An artificial neural network (ANN) was used to automate the analysis of spectral features.