融合傅里叶特征与KAN架构的改进PINN:结构地震动力响应计算方法

IMPROVED PINN INTEGRATING FOURIER FEATURES AND KAN ARCHITECTURE: A COMPUTATIONAL METHOD FOR STRUCTURAL SEISMIC DYNAMIC RESPONSE

  • 摘要: 随着土木工程智能化的发展,物理信息神经网络(PINN)能够在少量甚至无传感器数据的条件下实现结构动力响应的快速预测。然而,受限于多层感知机(MLP)的“黑箱”特性表示能力,传统PINN难以准确刻画包含高频与多频耦合特征的结构响应,且物理可解释性不足。在地震作用下,结构动力响应往往同时包含低频主振型与高频局部振动成分,这种显著的多尺度频谱特性进一步加剧了PINN的频谱偏差、收敛退化以及物理可解释性问题。为此,本文提出一种融合傅里叶特征映射(FF)与Kolmogorov–Arnold网络(KAN)的新型物理信息框架—SDR-FPIKAN,用于结构地震动力响应分析。该方法在网络输入端引入傅里叶特征映射,将时间投影到多尺度频率空间,从而显式增强模型对高频与多频成分的解析能力;在网络主体中采用KAN结构,用可学习的单变量函数替代传统固定激活函数,使结构响应能够被表示为由三角函数与多项式函数组成的显式解析表达式,并与动力学控制方程形成一致的物理约束。FF与KAN的深度融合使模型同时具备良好的频谱表达能力与可解释的函数表示能力,从根本上缓解了传统PINN的频谱偏差和可解释问题。以地震动作用下的十层剪切框架结构与二层钢框架结构为算例,对SDR-FPIKAN与传统PINN进行了系统对比。数值结果表明,SDR-FPIKAN在预测精度、收敛效率、物理可解释性以及数值稳定性方面均优于传统PINN方法,验证了其在复杂结构动力学问题中的有效性。

     

    Abstract: With the advancement of intelligent civil engineering, physics-informed neural networks (PINNs) have demonstrated the capability to rapidly predict structural dynamic responses under conditions of limited or even absent sensor data. However, constrained by the black-box representational nature of multilayer perceptrons (MLPs), conventional PINNs struggle to accurately characterize structural responses involving high-frequency components and multifrequency coupling, and they generally exhibit limited physical interpretability. Under seismic excitations, structural dynamic responses typically consist of low-frequency dominant modes coupled with high-frequency local vibrations, and this pronounced multiscale spectral characteristic further exacerbates spectral bias, convergence degradation, and interpretability issues in PINNs. To address these challenges, this study proposes a novel physics-informed framework, termed SDR-FPIKAN, which integrates Fourier feature mapping (FF) with the Kolmogorov–Arnold network (KAN) for seismic structural dynamic response analyses. In this framework, Fourier feature mapping is introduced at the network input to project the temporal domain into a multiscale frequency space, thereby explicitly enhancing the model’s ability to resolve high-frequency and multifrequency components. Within the network architecture, a KAN structure is employed to replace conventional fixed activation functions with learnable univariate functions, enabling the structural response to be expressed as explicit analytical forms composed of trigonometric and polynomial functions, while remaining the consistent with the governing dynamic equations. The deep integration of FF and KAN endows the model with both enhanced spectral representation capability and interpretable functional representations, fundamentally alleviating the spectral bias and interpretability limitations inherent in conventional PINNs. Numerical case studies involving a ten-storey shear frame structure and a two-storey steel frame structure under seismic excitations are conducted to systematically compare SDR-FPIKAN with the conventional PINN. The numerical results demonstrate that SDR-FPIKAN outperforms the traditional PINN in terms of prediction accuracy, of convergence efficiency, of physical interpretability, and of numerical stability, thereby validating its effectiveness in addressing complex structural dynamics problems.

     

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