基于微调DeepONet模型的非饱和边坡参数贝叶斯反分析

    Bayesian inverse analysis of unsaturated slope parameters using fine-tuned deep operator network model

    • 摘要: 贝叶斯方法通过融合参数先验分布与现场时序监测数据推断边坡参数后验分布,但需大量调用耗时的数值模型,导致计算成本高。尽管代理模型可替代数值模型,但是现有贝叶斯反分析方法仍有不足。一方面,传统代理模型难以准确描述边坡输出响应的时空演化特征,对于时空变化的监测数据,需要针对不同时间点和空间点分别构建代理模型;另一方面,融合时序监测数据需进行多次贝叶斯反分析,先验分布会逐渐过渡至后验分布,出现分布偏移现象,而基于固定先验分布构建的代理模型进行参数反分析时计算精度较差。为此,提出了结合微调深度算子网络(deep operator network, DeepONet)与子集模拟的贝叶斯反分析方法。首先利用DeepONet模型构建边坡输出响应的时空演化代理模型,接着在各子集模拟层中挑选额外训练样本微调DeepONet模型,确保后验分布推断精度。以香港某边坡为例,验证了提出方法的有效性。结果表明:提出方法提高了贝叶斯反分析的计算效率,并保证了参数后验估计的精度。为解决基于时序监测数据的边坡参数后验分布推断问题提供了一种有效的工具。

       

      Abstract: Bayesian method infers the posterior distribution of slope parameters by combining prior distribution with filed time-series monitoring data. This process requires extensive computational resources due to repeated calls to time-consuming numerical models. While surrogate models can replace numerical models to improve efficiency, current Bayesian inversion methods still exhibit limitations. On the one hand, conventional surrogate models inadequately capture the spatiotemporal evolutionary characteristics of slope output responses, requiring separate model constructions for distinct temporal and spatial points. On the other hand, integrating time-series monitoring data requires multiple Bayesian inversions. During this process, the prior distribution progressively transitions into the posterior distributions, leading to the phenomenon of distribution shift. Employing surrogate models constructed based on a fixed prior distribution results in poor computational accuracy during parameter inversion. To address these issues, this study proposes a Bayesian inversion method that combines subset simulation with a fine-tuned deep operator network (DeepONet). Specifically, the DeepONet model is employed to construct a spatio-temporally evolutionary surrogate model. Subsequently, additional training samples are selected in each subset simulation layer to fine-tune the DeepONet model, ensuring the accuracy of posterior distribution inference. The proposed method is validated using a case study of a slope in Hong Kong. The results demonstrate that the proposed method enhances the computational efficiency of Bayesian inverse analysis while ensuring the accuracy of posterior parameter estimation. This study provides an effective tool for addressing the problem of posterior distribution inference of slope parameters based on time-series monitoring data.

       

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