用于联合估计材料强度与应力分布的贝叶斯最弱链接框架
A Bayesian Weakest-Link Framework for Joint Estimation of Material Strength and Stress Profile
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中文总结 AI 辅助
该研究针对现有可靠性模型的局限，提出分层贝叶斯最弱链接模型，联合估计材料强度与应力分布，经模拟及花旗松横担真实数据分析验证了其有效性。
中文摘要 AI 辅助
对于失效遵循最弱链接理论的结构构件，现有可靠性模型通常要么假设潜在力学模型已知，要么忽略利用观测失效位置包含的空间信息。然而实际中，理想化力学模型可能因简化或错误假设而系统性偏离实际应力。为解决此局限，我们提出分层贝叶斯最弱链接模型，从配对的失效载荷与失效区域观测中联合估计潜在材料强度与应力分布。在该模型中，应力分布通过B样条基展开估计，不可微的最弱链接机制由可微的Softmin函数近似，以考虑未观测的材料缺陷并便于贝叶斯推断。模拟研究表明，所提框架在多种实验配置下均能提供准确且稳健的估计；应用于花旗松横担的真实数据分析时，该模型识别出理想化梁理论无法捕捉的系统性偏差。
英文摘要
For structural components whose failure is governed by the weakest-link theory, existing reliability models typically either assume that the underlying mechanical model is known or neglect to exploit the spatial information contained in observed failure locations. In practice, however, idealized mechanical models may systematically deviate from the actual stress due to simplifying or incorrect assumptions. To address this limitation, we propose a hierarchical Bayesian weakest-link model that jointly estimates the latent material strength and stress profile from paired failure load and failure zone observations. In our formulation, the stress profile is estimated via a B-spline basis expansion, and the non-differentiable weakest-link mechanism is approximated by a differentiable Softmin function to account for unobserved material flaws and facilitate Bayesian inference. Simulation studies demonstrate that the proposed framework provides accurate and robust estimation under various experiment configurations. Applied to a real-data analysis of Douglas-fir crossarms, the proposed model identifies systematic deviations from idealized beam theory that cannot be captured by deterministic stress derivations.
