有限数据条件下石窟岩体参数空间变异性的不确定性量化与传播研究

    Uncertainty quantification and propagation for spatial variability of rock mass parameters for grottoes under limited data conditions

    • 摘要: 准确表征岩体力学参数的空间变异性是开展石窟等文化遗产可靠度分析的基础。针对数据稀疏与测试噪声导致的参数不可辨识性问题,本研究构建了一套基于层级贝叶斯推断的综合分析框架。该框架通过引入块金效应实现信号与噪声分解,并结合信息性先验以增强模型的可识别性。利用条件随机场模拟,系统传播参数后验不确定性,并结合概率失效准则开展空间可靠度评估。结果表明,所提出的五参数模型在MCMC后验推断中具有良好的收敛性与稳健性;先验敏感性分析揭示了信息性先验的关键正则化作用。生成的空间失效概率图与现场破坏现象高度一致,识别出最高失效概率达32.9%的潜在风险区。研究表明,该贝叶斯框架可在高噪声、有限数据条件下实现岩体参数的稳健推断与不确定性量化,为石窟文化遗产的风险识别与动态保护提供了科学的决策支持。

       

      Abstract: Accurately characterizing the spatial variability of rock mass mechanical parameters is essential for the reliability assessment of cultural heritage sites such as grottoes. To address the parameter non-identifiability caused by sparse data and high measurement noise, this study develops an integrated analytical framework based on hierarchical Bayesian inference. The framework introduces nugget effect to separate signal and noise components and incorporates informative priors to enhance model identifiability. Conditional random field simulations are employed to propagate posterior uncertainties of the parameters and, combined with probabilistic failure criteria, to evaluate spatial reliability. The proposed five-parameter model exhibits excellent convergence and robustness in MCMC posterior inference, while prior sensitivity analysis quantitatively reveals the critical regularization role of informative priors. The resulting spatial failure probability map aligns well with observed damage patterns, identifying potential high-risk zones with a maximum failure probability of 32.9%. Overall, the proposed Bayesian framework enables robust inference and comprehensive uncertainty quantification of geotechnical parameters under limited and noisy data conditions, providing a rigorous quantitative basis for risk identification and dynamic preservation of grotto cultural heritage.

       

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