基于微调DeepONet模型的非饱和边坡参数贝叶斯反分析 English Version
Bayesian inverse analysis of unsaturated slope parameters using fine-tuning deep operator network model
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摘要: 贝叶斯方法可以结合参数先验信息与监测数据有效推断参数后验分布,这一过程通常需要调用成千上万次耗时的数值模型计算,计算量十分可观。为降低计算成本,一般采用代理模型替代耗时的数值计算。然而,目前参数贝叶斯反分析方法不能考虑模型输出响应的时空演化特征。对于时空变化的监测数据,只能针对不同时间点和空间点分别构建代理模型。另外,融合大量时间序列监测数据需要进行多次贝叶斯更新,始终使用基于参数先验信息构建的代理模型进行参数反分析,计算精度较差。为此,本文通过结合贝叶斯更新与深度算子网络(Deep operator network, DeepONet),提出了基于微调(Fine-tuning)DeepONet模型的贝叶斯反分析方法,一方面可利用考虑时空特征的DeepONet模型替代数值计算,将输出响应时空演化特征嵌入到参数反分析中,另一方面可通过在每层子集中挑选额外样本微调DeepONet模型,保证参数后验分布推断精度。最后以香港某边坡为例,验证了提出方法的有效性。/t/n提出方法通过构建反映模型输出响应时空演化特征的代理模型并实时进行微调,为解决基于大量时间序列监测数据的边坡参数后验分布推断难题提供了一种有效的工具,同时为降雨入渗下非饱和边坡稳定性演化规律研究奠定了基础。Abstract: The Bayesian method is an effective tool for inferring the posterior distribution of parameters by combining prior information with monitoring data. This process typically requires thousands of computationally expensive numerical model evaluations, leading to substantial computational costs. To alleviate this, surrogate models are often used as substitutes for time-consuming numerical computations. However, the current Bayesian inverse analysis methods fail to account for the spatio-temporal evolution characteristics of the output response. For monitoring data with spatio-temporal variations, surrogate models must be constructed separately at different temporal and spatial points. Additionally, the integration of a large number of time-series monitoring data requires multiple Bayesian updates. Traditional methods generally rely on surrogate models based solely on prior information for Bayesian inverse analysis, which leads to poor computational accuracy in the posterior inference. To address these challenges, this paper proposes a Bayesian inverse analysis method based on fine-tuning deep operator network (DeepONet) model by combining Bayesian updating methods with DeepONet. This method incorporates spatiotemporal characteristics into the Bayesian inverse analysis by replacing the numerical model with DeepONet model that reflects the spatiotemporal evolution of the output response. Additionally, extra samples are selected in each subset simulation layers to fine-tune the surrogate model, ensuring the accuracy of the 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 effectively addresses the challenge of inferring the posterior distribution of slope parameters from a large number of time-series monitoring data by constructing a surrogate model that reflects the spatiotemporal evolution characteristics of output responses and performing real-time fine-tuning. Furthermore, this method lays the foundation for studying the evolution of unsaturated slope’s stability under rainfall infiltration.
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