Parameter Identification of Bearing Stiffness for a Centrifugal Compressor Using an Artificial Neural Network

The design of modern high-tech equipment (pumps, compressors, turbines) is inevitably related to the need to ensure vibration reliability, especially at high shaft rotation speeds, which is particularly relevant for flexible rotors. Therefore, the research aims to provide vibration reliability of energy-intensive rotary machines by developing a hybrid parametric identification approach that leverages analytical dependencies in rotor dynamics, numerical simulations to study rotor behavior, and artificial intelligence systems. While implementing the proposed solution, the Monte Carlo method and Moore–Penrose pseudoinversion are also applied. As a result, modified linear and nonlinear parameter identification approaches are developed. They are based on an improved finite element model that accounts for the analytical dependence of bearing stiffness on rotor speed, with the parameters evaluated numerically. The corresponding algorithms were implemented in the PTC MathCAD 14 computer algebra system and the Python 3.13 programming language, using the authors’ program code and an artificial neural network. The developed methods and algorithms were proven in the case study of a natural gas compressor station’s multistage centrifugal compressor, S325 GC2-650/6-56M12. As a result, stiffness parameters of bearing supports were identified with a 0.2–0.7% accuracy for the first two critical frequencies compared with the available data from the accelerating-balancing stand “Schenck” with a vacuum chamber. The proposed parameter identification approach can also be extended to evaluate stiffness parameters for high-precision bearing supports with speed-dependent stiffness in multistage centrifugal pumps, turbochargers, turbines, and turbopump units.