基于扩散增强傅立叶算子的弓网系统动力学快速求解方法

Fast Dynamics Solution Method for Pantograph-Catenary System Based on Diffusion-Enhanced Fourier Operator

  • 摘要: 受电弓–接触网(Pantograph-catenary system, PCS)系统的动态特性直接影响高速列车的受流质量与运行安全. 由于弓网耦合作用存在强非线性与时变特性,传统有限元方法虽能精确表征其力学行为,但存在计算复杂度高、实时预测能力差等瓶颈,难以满足高频振动分析与多参数耦合工况快速评估需求. 为此,本文提出融合自适应傅立叶神经算子(Adaptive fourier neural operator, AFNO)与条件扩散模型(Conditional diffusion model, CDM)的数据驱动框架—自适应傅里叶神经算子扩散模型(Adaptive fourier neural operator diffusion model, AFNODM). 首先,通过AFNO在频域动态捕捉接触网振动主模态,设计可变形卷积核实现频谱感知范围的自适应调整,解决传统FNO类模型因固定频带截断导致的高频成分漏失问题;其次,构建CDM驱动的后处理框架,以AFNO输出为条件,通过隐空间渐进式生成策略补偿高频振动细节. 最后,实验结果表明本文所提方法能够高效快速地求解弓网动力学方程,在位移、速度、加速度场的均方根误差分别为0.06730.16030.8503,相较于深度算子网络(Deep operator network, DeepONet)和物理信息增强型傅里叶神经算子(Physics-informed enhanced fourier neural operator, PI-EFNO)等主流基准方法,预测误差降低了50%以上.

     

    Abstract: The dynamic characteristics of the pantograph-catenary system (PCS) directly affect the current collection quality and operational safety of high-speed trains. While traditional finite element methods (FEM) that utilize nonlinear cable-truss equivalent models accurately characterize the strong nonlinearity and time-varying mechanical behaviors of the PCS, they suffer from prohibitive computational complexity that hinders real-time prediction and digital twin deployment. To address these computational bottlenecks, data-driven surrogate models have emerged. However, standard Fourier neural operators (FNO) rely on fixed-frequency band truncation, which effectively captures low-frequency principal modes but systematically discards critical high-frequency transient details, such as localized contact force mutations and wave reflections. Purely data-driven models also lack explicit physical constraints, leading to severe error accumulation during long-term dynamic simulations. To overcome these multiscale modeling challenges, this paper proposes adaptive fourier neural operator diffusion model (AFNODM), a novel physics-informed framework that synergistically integrates an adaptive fourier neural operator (AFNO) with a conditional diffusion model (CDM) to establish a time-frequency collaborative generation paradigm. In the first stage, the AFNO acts as a global physical skeleton generator to capture dominant vibration modes (0–20 Hz). Crucially, we introduce a velocity-based frequency modulation mechanism equipped with deformable convolution kernels, allowing the model to adaptively adjust its spectral receptive field in response to real-time train speeds and neutralize Doppler effects. In the second stage, a CDM-driven post-processing architecture is deployed. Conditioned on the AFNO’s output, the diffusion model executes a progressive reverse denoising strategy in the latent space to seamlessly reconstruct the missing high-frequency residual details (above 20 Hz), while kinematic constraint losses are embedded via automatic differentiation to ensure absolute derivative consistency across spatial-temporal fields. Extensive evaluations on a high-fidelity PCS dataset (200–380 km·h–1) demonstrate that AFNODM efficiently solves complex dynamic equations with an unprecedented balance of speed and precision. At 350 km·h–1, the root mean square errors (RMSE) for the displacement, velocity, and acceleration fields are remarkably low at 0.0673, 0.1603, and 0.8503, respectively, representing an error reduction of over 50% compared with mainstream baselines such as deep operator network (DeepONet) and physics-informed enhanced fourier neural operator (PI-EFNO). Frequency-domain analysis confirmed that CDM integration significantly suppressed the high-frequency relative spectral error (RSE) from 16.80% (using pure AFNO) to 6.55%. Cross-line robustness tests across three distinct high-speed railway configurations (Beijing—Shanghai, Guangzhou—Shenzhen, and Beijing—Tianjin) validated the exceptional generalization capabilities of the model under varying structural parameter perturbations. Ultimately, the proposed AFNODM framework provides a highly accurate, resolution-independent, and real-time capable computational engine, paving the way for next-generation digital twins and intelligent predictive maintenance in modern electrified railways.

     

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