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<p>Efficient and accurate reliability assessment of high-dimensional nonlinear structural problems remains a persistent challenge. Traditional analytical methods often struggle with complex failure boundaries of intricate structures. Meanwhile, the intersection area division method faces computational intractability despite its accuracy, and the improved approximate integral method is limited by fixed empirical formulas that fail to fully compensate for projection-induced bias. To address these limitations, this paper proposes a Geometry-Informed Machine Learning method using XGBoost (GMLX). By extracting topologically consistent geometric parameters from the limit state surface as feature descriptors, GMLX constructs a data-driven model to adaptively compensate for projection-induced bias. The GMLX architecture exhibits notable dimension universality: once trained offline, the model enables correction without retraining for a wide range of engineering problems of the same dimension within the trained geometric bounds, regardless of specific physical limit state functions. Validation through diverse numerical and engineering examples, including a complex thermo-mechanical turbine blade analysis, demonstrates that GMLX successfully bridges analytical precision and machine learning efficiency, providing a robust and practical tool for the reliability analysis of complex structures.</p>

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A geometry-informed machine learning method using XGBoost for reliability analysis

  • 期刊论文

  • 发表日期：

    2026年6月2日

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  • Zhenzhong Chen,
  • Yujie Zeng,
  • Peiyu Wang,
  • Qianghua Pan,
  • Ying Jin,
  • Lei Wang,
  • Xiaoke Li,
  • Yuewei Bai,
  • Ge Chen

摘要

Efficient and accurate reliability assessment of high-dimensional nonlinear structural problems remains a persistent challenge. Traditional analytical methods often struggle with complex failure boundaries of intricate structures. Meanwhile, the intersection area division method faces computational intractability despite its accuracy, and the improved approximate integral method is limited by fixed empirical formulas that fail to fully compensate for projection-induced bias. To address these limitations, this paper proposes a Geometry-Informed Machine Learning method using XGBoost (GMLX). By extracting topologically consistent geometric parameters from the limit state surface as feature descriptors, GMLX constructs a data-driven model to adaptively compensate for projection-induced bias. The GMLX architecture exhibits notable dimension universality: once trained offline, the model enables correction without retraining for a wide range of engineering problems of the same dimension within the trained geometric bounds, regardless of specific physical limit state functions. Validation through diverse numerical and engineering examples, including a complex thermo-mechanical turbine blade analysis, demonstrates that GMLX successfully bridges analytical precision and machine learning efficiency, providing a robust and practical tool for the reliability analysis of complex structures.