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<p>In the context of Industry 4.0, improving the reliability and efficiency of rotating machinery remains a relevant challenge, particularly for systems employing Gas Foil Bearings (GFBs). This paper investigates the development of surrogate models based on Bayesian Neural Networks (BNNs) and Random Forests (RF) to predict GFB stability, addressing the high computational cost associated with their strongly coupled fluid–structure interactions and nonlinear dynamic behavior. A comprehensive dataset is generated using physics-based numerical simulations, representing the dynamic response of GFBs with different geometrical configurations under identical operating conditions. This dataset is used to train and validate surrogate models. The proposed framework combines BNNs and RF models to exploit their complementary characteristics. BNNs are employed for probabilistic modeling, using Monte Carlo dropout to approximate Bayesian inference and to provide predictive uncertainty estimates. RF models are used as an ensemble-based alternative, offering robust predictions and supporting sensitivity analysis and the identification of influential input parameters. The implementation of these two strategies represents the main methodological contribution to this work, given their high computational efficiency. The surrogate models show high predictive capability in estimating GFB stability metrics. The BNN ensemble captures the main trends of simulation data while providing consistent confidence intervals associated with the predictions. Comparisons with conventional Artificial Neural Networks (ANNs) and other Gradient Boosting approaches demonstrate the advantages of incorporating uncertainty quantification into the modeling framework. In addition, a reliability analysis is performed by evaluating the area under the probability density function (PDF) of the predicted stability indicator, enabling a quantitative assessment of instability risk.</p>

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Probabilistic surrogate modeling for gas foil bearing stability

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月31日

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  • Matheus de Moraes,
  • Marian Franz Sarrazin,
  • Robert Liebich,
  • Helio Fiori de Castro

摘要

In the context of Industry 4.0, improving the reliability and efficiency of rotating machinery remains a relevant challenge, particularly for systems employing Gas Foil Bearings (GFBs). This paper investigates the development of surrogate models based on Bayesian Neural Networks (BNNs) and Random Forests (RF) to predict GFB stability, addressing the high computational cost associated with their strongly coupled fluid–structure interactions and nonlinear dynamic behavior. A comprehensive dataset is generated using physics-based numerical simulations, representing the dynamic response of GFBs with different geometrical configurations under identical operating conditions. This dataset is used to train and validate surrogate models. The proposed framework combines BNNs and RF models to exploit their complementary characteristics. BNNs are employed for probabilistic modeling, using Monte Carlo dropout to approximate Bayesian inference and to provide predictive uncertainty estimates. RF models are used as an ensemble-based alternative, offering robust predictions and supporting sensitivity analysis and the identification of influential input parameters. The implementation of these two strategies represents the main methodological contribution to this work, given their high computational efficiency. The surrogate models show high predictive capability in estimating GFB stability metrics. The BNN ensemble captures the main trends of simulation data while providing consistent confidence intervals associated with the predictions. Comparisons with conventional Artificial Neural Networks (ANNs) and other Gradient Boosting approaches demonstrate the advantages of incorporating uncertainty quantification into the modeling framework. In addition, a reliability analysis is performed by evaluating the area under the probability density function (PDF) of the predicted stability indicator, enabling a quantitative assessment of instability risk.