A High-Precision Random Forest-Based Maximum Lyapunov Exponent Prediction Model for Spherical Porous Gas Bearing Systems

Spherical porous air bearing (SPAB) systems have been extensively used in various mechanical engineering applications. SPABs are promising materials in high-rotational speed, high-precision, and high-stiffness instruments. In SPAB systems, a rotor is supported by gas bearings, which provides higher rotational speed and lower heat generation environment than oil bearings do. Furthermore, SPAB does not cause deformation. Although, the supporting force of gas bearings is less, their stability is better than that of oil films. However, because the pressure distribution in the gas films is nonlinear, they are prone to failure at specific critical speeds, rotor imbalances, or inappropriate operations, which results in nonperiodic or chaotic motion and causes structural fatigue to the system. To understand and control the operating conditions of the SPAB systems during the nonperiodic motion, first, the governing equations of the SPAB system were solved to obtain the dynamic behavior of the rotor center. Then, the performance of the SPAB system were examined under different operating conditions by generating the maximum Lyapunov exponents (MLEs). However, the calculation process of MLE is extremely time consuming and complex. To solve this problem efficiently, a high-precision machine learning (ML)-based MLE prediction model was proposed in this study. The results show that the training process can be finished within few minutes, and the prediction process is able to be completed within few seconds. Meanwhile, the results demonstrate the merit of using the machine learning method for solving the MLE prediction problem and shorten the calculation time significantly. The proposed prediction model achieves excellent prediction outcome and it is more efficient and precise than traditional iteration scheme for the calculation of MLE. The feasibility of the proposed model is validated and the results also are the major contribution of this study.