基于物理信息神经网络的桩基m法分析模型

    Physics informed neural networks for analyzing m-method in pile foundations

    • 摘要: 国内常用m法分析水平承载桩,现已有丰富的资料推荐m的取值,但目前该方法没有解析解,通常需采用数值方法计算。数值方法需要进行网格划分和迭代计算,且一次只能计算一组参数,对于需要大量计算的任务而言效率不佳。近年来,基于物理信息的神经网络(PINN)被提出来,该方法不需要划分网格,可解高维微分方程。基于此,提出一种考虑了m法所有输入参数(包括荷载、桩参数和土参数)的PINN模型,旨在分析任意输入参数而无需重新建模、迭代计算和训练。模型对输入参数进行了归一化,同时采用了硬约束方法,大幅提高模型的训练效率。对损失项的量纲进行了统一,解决了不同损失项差别过大的问题。通过与查表法的无量纲系数对比验证了PINN模型的准确性。PINN模型的优势在于:基于微分方程训练,不需要任何标签数据;相比查表有更好的计算精度,相比有限元法有更高的计算效率;能通过并行运算高效获得多组样本的结果,不需要重新建模和迭代计算,使其在可靠度分析中有显著的优势;能高效获取输出与输入的导数,使其在优化设计中具有巨大的优势;模型具有良好的扩展性,可运用于其他形式的桩基分析模型,如c法模型等。

       

      Abstract: The m-method is widely used to analyze laterally loaded piles, with extensive data available for recommended values of m. However, it currently lacks an analytical solution and typically requires numerical methods. Numerical methods necessitate meshing the model and iterative computations, and they can only compute one set of input parameters at a time, resulting in inefficiencies for tasks that demand extensive computations. Recently, Physics informed neural networks (PINN) have been proposed, which do not require meshing and can solve high-dimensional partial differential equations (PDEs). Based on this, a PINN model that considers all input parameters of the m-method, including loads, pile parameters, and soil parameters, is proposed to analyze arbitrary input parameters without the need for re-modeling or re-training. The model normalizes the input parameters and employs a hard constraint method, significantly enhancing training efficiency. The dimensions of the loss terms are unified, addressing the issue of large differences among them. The accuracy of the PINN model is validated by comparison with the dimensionless coefficients obtained from the tabular method. The advantages of the PINN model include: it is trained directly on differential equations without requiring labeled data; it provides higher accuracy than the tabular method and greater computational efficiency than FEM; it enables efficient parallel computations for multiple parameter sets without re-modeling, making it highly advantageous for reliability analysis; it efficiently computes input-output derivatives, offering significant benefits for optimization design; and it demonstrates excellent scalability, allowing application to other pile analysis models, such as the c-method.

       

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