固有频率嵌入物理信息神经网络:克服PINN谱偏差的结构动力响应方法

EIGENFREQUENCY-EMBEDDED PHYSICS-INFORMED NEURAL NETWORK: A STRUCTURAL DYNAMIC RESPONSE METHOD TO OVERCOME THE SPECTRAL BIAS OF PINNS

  • 摘要: 结构动力学旨在分析结构在地震等动力荷载下的响应,其核心是结构动力学微分方程的求解。物理信息神经网络(PINN)因融合物理约束与数据驱动,为结构动力微分方程的求解提供了新思路,但存在频谱偏差,难以准确捕捉地震动高频成分的问题。为此,本文提出固有频率嵌入物理信息神经网络(EE-PINN),通过在激活函数中显式嵌入结构自振频率,构造多频基函数以增强网络的高频表达能力。基于神经正切核(NTK)理论分析表明,EE-PINN能减缓特征值衰减,改善高频梯度传播,从根本上缓解PINN的高频学习瓶颈。数值算例显示,与传统PINN相比,EE-PINN在位移、速度与加速度模拟中显著提升精度,并在不同地震输入情形下保持稳健表现。即便在中等噪声干扰及部分观测缺失的情况下,该方法仍具有良好的鲁棒性,展现出在实际环境中结构动力响应中的潜在应用优势。

     

    Abstract: Structural dynamics aims to analyze the structural responses under dynamic loads such as earthquakes, and it requires solving governing differential equations of motions. Physics-informed neural networks combine physical constraints with data-driven learning for this purpose, but spectral bias limits their ability to represent high-frequency seismic components. An eigenfrequency-embedded physics-informed neural network is proposed. Structural natural frequencies are embedded into activation functions to construct multifrequency basis functions. This design enhances high-frequency representation. Neural tangent kernel analysis shows slower eigenvalue decay and improved gradient propagation in high-frequency ranges. The high-frequency learning limitation of standard physics-informed neural networks is therefore alleviated. Numerical examples show improved accuracy in displacement, velocity, and acceleration responses compared with conventional physics-informed neural networks. Stable performance is observed under different seismic excitations, moderate noise levels, and partial observation losses. These results indicate the applicability of the proposed method to structural dynamic response analysis.

     

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