基于物理信息神经网络(PINN)方法的结构动力响应分析

STRUCTURAL DYNAMIC RESPONSE ANALYSIS UPON PHYSICAL INFORMATION NEURAL NETWORK (PINN) METHOD

  • 摘要: 经典逐步积分方法通常用于求解结构动力响应,然而时间步长取值过大,精度和稳定性会下降;时间步长取值过小,计算效率会特别低。机器学习可以显著提高学习效率,然而传统的机器学习方法需要大量训练数据才能进行结构动力响应计算。为提高基于数据驱动机器学习方法的可解释性和泛化性,该文使用一种基于物理信息神经网络(PINN)方法来求解结构动力响应分析,将结构动力响应方程引入到损失函数中作为物理约束使神经网络具有物理含义。该方法本质上是将直接求解动力学微分方程的问题转换为损失函数的优化问题来得到常微分方程的解。随后开展不同激励下结构动力响应的算例分析,验证了所提出方法的可行性和有效性,并且讨论了不同神经网络参数对PINN模型收敛性的影响。数值算例结果表明,与数据驱动机器学习方法相比,PINN方法能够在不需要任何系统响应数据的前提下对结构动力响应进行有效分析;与经典逐步积分方法相比,所提出方法属于空间域优化过程,与时间域无关,因此不受时间步长影响。

     

    Abstract: The classical stepwise integration method is usually used to solve the dynamic response of structures, but the accuracy and stability will be reduced if the time step is too large. If the time step is too small, the calculation efficiency will be particularly low. Machine learning can significantly improve learning efficiency, but traditional machine learning methods require a large amount of training data to perform structural dynamic response calculations. In order to improve the interpretability and generalization ability of data-driven machine learning methods, this paper adopts a physics-informed neural network (PINN) approach to solve structural dynamic response analysis, and introduces the structural dynamic response equation into the loss function as a physical constraint to endow the neural network with physical meaning. In essence, the method converts the problem of directly solving the dynamic differential equation into the optimization problem of the loss function to obtain the solution of the ordinary differential equation. Subsequently, the feasibility and effectiveness of the method proposed are verified by a numerical analysis of the dynamic response of the structure under different excitations, and the influence of different neural network parameters on the convergence of the PINN model is discussed. Numerical results show that compared with the data-driven machine learning method, the PINN method can effectively analyze the structural dynamic response without any system response data. Compared with the classical stepwise integration method, the method proposed belongs to the spatial domain optimization process, which is independent of the time domain, thusly it is not affected by the time step.

     

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