基于物理驱动深度学习的结构形状优化设计  

Structural Shape Optimization Design Based on Physics-Informed Deep Learning

作　　者：唐和生[1] 李度 廖洋洋 李荣帅 TANG Hesheng;LI Du;LIAO Yangyang;LI Rongshuai(College of Civil Engineering,Tongji University,Shanghai 200092,China;Shanghai Construction Group Co.,Ltd.,Shanghai 200080,China)

机构地区：[1]同济大学土木工程学院,上海200092 [2]上海建工集团股份有限公司,上海200080

出　　处：《湖南大学学报（自然科学版）》2024年第11期33-42,共10页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(52378184)。

摘　　要：结构形状的优化设计本质上是一类泛函极值求解问题.在求解高维度泛函极值问题时,传统的变分法往往面临着求解目标函数类型有限、求解过程呈现振荡行为等问题.利用深度学习模型的高维非线性映射能力,建立了一种基于物理驱动深度学习的泛函极值求解模型.首先将描述结构形状优化问题的物理信息(控制方程、初始条件和边界条件等)作为正则化项嵌入深度学习模型中,基于性能目标构建损失函数;采用随机梯度下降法完成深度学习模型的训练,进而实现泛函极值的求解和结构形状的优化设计;通过分析最优曲面和最优拱轴线问题验证模型的有效性,并与遗传算法进行对比,结果表明该模型在小样本的目标任务上具有较高的预测精度和效率.作为一种非参数模型化技术,物理驱动深度学习模型对解决数据采集成本高、难度大的工程问题具有重要意义.The optimization design of structural shapes is fundamentally a problem of solving functional extremum.Traditional variational methods often encounter challenges,such as limited functional types and oscillation in the solution process when solving high-dimensional functional extreme value problems.In this paper,a functional extremum numerical solution method based on physics-informed deep learning(PIDL)is proposed by using the high-dimensional nonlinear mapping ability of deep learning model.The method first embeds the physical information(control equations,initial conditions and boundary conditions,etc.)of the shape optimization problem as regularization terms into the deep learning model,and a loss function based on the objective functional extremum is constructed.Then,a random gradient descent algorithm is used to train the deep learning model,further realizing the solution of functional extremum and optimization design of structural shape.The proposed method is verified through numerical examples of optimizing the shape of surfaces and arch axes,and a comparative analysis is conducted with the computational results obtained from genetic algorithms.The results demonstrate that the method has high prediction accuracy and efficiency for the target task of small samples.As a non-parametric modeling technology,the method is of great significance for solving engineering problems characterized by high data acquisition costs and data collection challenges.

关 键 词：物理驱动深度学习 形状优化设计 泛函极值 遗传算法 

分 类 号：TU318[建筑科学—结构工程]