【作者】 陈健；

【导师】 王东东；

【作者基本信息】 厦门大学 ， 建筑与土木工程， 2022， 硕士

【摘要】 物理信息神经网络作为一类深度学习算法,将计算区域的采样点坐标作为输入信息,在损失函数中引入物理问题微分控制方程的残差项作为物理信息,可显著改进网络预测精度,在结构静动力分析中有良好的应用前景。对于控制方程中的微分项,物理信息神经网络常采用自动微分器进行计算,但自动微分采用链式求导法则,导致了计算所占内存大、效率低。因此,如何高效计算物理损失函数中的微分项是一个值得关注的问题。再者,在结构动力分析中,通常需要通过逐步递推得到每个时间步的动力响应,计算效率相对较低。此外,在大变形损伤破坏模拟中,例如边坡失稳分析,本构关系中的应力迭代计算也十分繁杂低效。针对这些问题,本文研究物理信息神经网络的高效梯度计算方法,然后通过构建结构动力分析和本构模型的代理模型,提升无网格法动力分析和损伤破坏模拟的计算效率。首先,通过研究物理信息神经网络与无网格法在梯度计算方式上的内在相似性,在物理信息神经网络自动微分计算中引入无网格递推光滑梯度理论,建立了基于递推梯度的改进物理信息神经网络。在递推梯度构造中,基于低阶基函数可直接构造无网格形函数的任意高阶光滑梯度,避免了损失函数中高阶导数项的复杂冗长计算,显著提高整体网络的计算效率。在此基础上,通过将递推光滑梯度理论与循环神经网络相结合,构建了物理信息与数据双重驱动的无网格动力分析代理模型,实现了结构动力响应的高效预测。然后,借鉴结构动力分析代理模型,提出了边坡大变形无网格损伤破坏模拟的本构关系代理模型,避免了复杂的应力迭代计算,为损伤破坏模拟提供了 一种高效智能本构计算方法。文中通过系列静动力分析和大变形损伤破坏模拟算例,系统地验证了递推梯度物理信息神经网络和无网格动力分析代理模型的计算精度和效率。更多还原

【Abstract】 As atypical deep learning algorithm,the physics-informed neural networks(PINN)take the sampling point coordinates of the computational domain as the network inputs,and introduce the residuals of governing differential equations for the problems under consideration into the loss function in order to improve the network prediction accuracy.Due to its sound accuracy,PINN has been widely used in many areas and is a very promising method to enhance the efficiency and robustness of structural static and dynamic analysis.It is noted that the governing differential equations in PINN involves successive differentiation operations which are often carried out by the automatic differentiation.However,the automatic differentiation is based upon the chain rules and requires large memory reservation,which significantly reduces the computational efficiency.Consequently,the efficiency improvement of differentiation computation in the loss function of PINN has been an important topic.Meanwhile,the step by step updating of structural responses in dynamic analysis is also quite time-consuming.Another noticeable issue in large deformation meshfree simulation of slope failure is the costly and complex stress iteration in constitutive modeling.To resolve these issues,this thesis aims to develop an efficient gradient evaluation strategy for PINN and improve the meshfree dynamic analysis and failure simulation through formulating proper surrogate models.In this thesis,a comparison study is presented to disclose the inherent similarity regarding gradient computation between meshfree methods and PINN.Accordingly,the fast recursive smoothed meshfree gradients are introduced to replace the automatic differentiation in PINN and an improved PINN with recursive gradients is rationally developed.It is noted that in the recursive gradient formulation,the low order gradients,i.e.,the first order gradients,can be recursively used to efficiently construct arbitrary order smoothed gradients since the complex high order gradient computation is completely avoided in the loss function calculation.Accordingly,through merging the recursive smoothed meshfree gradients and the recurrent neural networks,a meshfree dynamic analysis surrogate model driven by both physical information and data is presented,which leads to a fast prediction of structural dynamic responses.This surrogate model is subsequently generalized to develop a smart surrogate model for the constitutive relationship in large deformation meshfree simulation of slope failure.The smart constitutive surrogate model bypasses the complicated and costly iterative stress updating process,and then provides a highly efficient way for meshfree failure simulation.The accuracy and efficiency of the proposed recursive gradient PINN and surrogate models for dynamic analysis and constitutive updating are systematically verified through a series of static,dynamic as well as large deformation slope failure problems.更多还原