基于参数均衡-傅里叶特征PINN的结构动力响应分析研究

STRUCTURAL DYNAMIC RESPONSE ANALYSIS BASED ON PARAMETER-BALANCED FOURIER-FEATURE PINN

  • 摘要: 由于融合物理信息的神经网络(physics-information neural network , PINN)具备低数据依赖特性、高精度和普适性,其目前正成为研究微分方程数值求解热点方法。现有PINN求解结构动力响应研究多基于简单假设参数分析其精度及可行性,由于未考虑实际结构中物理参数尺度差异大、整体振动频率较高等问题,PINN在真实参数下逼近效果差。因此本文构建了适用于实际工程结构的参数均衡-傅里叶特征模型(parameter-balanced Fourier-feature PINN model, PBFF-PINN),该模型首先通过对结构振动方程进行参数均衡变换,以解决真实结构参数尺度差异过大而导致的PINN学习失衡、稳定性差的问题;其次提出引入多尺度傅里叶特征映射,变传统的时域输入为时频域输入,以提升PINN在实际结构振动问题中的表达能力和求解精度。通过对符合实际参数尺度的振动系统进行消融实验,验证了两个过程对于解决真实结构振动方程的必要性以及PBFF-PINN的适用性。

     

    Abstract: Due to the low data dependency, to the high accuracy, and to the universality, physics-information neural networks (PINNs) have become a useful method for solving differential equations. However, existing studies on PINN for solving structural dynamic response equations mostly base upon simple assumptions about parameters to analyze their accuracy and feasibility, which do not consider issues such as large differences in the physical parameter scales and high vibration frequencies in real structures, leading to poor approximation performance of PINN under real parameters. Therefore, this study constructs a parameter-balanced Fourier-feature PINN model (PBFF-PINN) suitable for practical engineering structures. Firstly, the model performs parameter scales transformation on the structural vibration equations, solving the problem of learning imbalance and poor stability in PINN caused by large differences in the parameter scales of real structures. Then, it introduces Fourier feature mapping to transform the traditional time-domain input into time-frequency domain input to enhance the expression capability and solution accuracy of PINN in practical structural vibration problems. Ablation experiments on vibration systems with practical parameter scales validate the necessity of these two processes for solving real structural vibration equations and the applicability of PBFF-PINN.

     

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