External influences such as traffic and environmental factors induce vibrations in structures, leading to material degradation over time. These vibrations result in cracks due to the material's lack of plasticity compromising structural integrity. Detecting such damage requires the installation of vibration sensors to capture the internal dynamics. However, distinguishing relevant eigenmodes from external noise necessitates the use of Deep Learning models. The detection of changes in eigenmodes can be used to anticipate these shifts in material properties and to discern between normal and anomalous structural behavior. Eigenmodes, representing characteristic vibration patterns, provide insights into structural dynamics and deviations from expected states. Thus, we propose ModeConv to automatically capture and analyze changes in eigenmodes, facilitating effective anomaly detection in structures and material properties. In the conducted experiments, ModeConv demonstrates computational efficiency improvements, resulting in reduced runtime for model calculations. The novel ModeConv neural network layer is tailored for temporal graph neural networks, in which every node represents one sensor. ModeConv employs a singular value decomposition based convolutional filter design for complex numbers and leverages modal transformation in lieu of Fourier or Laplace transformations in spectral graph convolutions. We include a mathematical complexity analysis illustrating the runtime reduction.

翻译：交通和环境因素等外部影响会诱发结构振动，导致材料随时间推移发生性能退化。由于材料缺乏塑性，这些振动会产生裂缝，从而损害结构完整性。检测此类损伤需要安装振动传感器以捕捉内部动态。然而，从外部噪声中区分相关本征模态必须借助深度学习模型。通过检测本征模态的变化，可以预测材料特性的转变，并区分正常与异常的结构行为。本征模态作为特征振动模式，能够揭示结构动力学特性及其与预期状态的偏差。为此，我们提出ModeConv方法，旨在自动捕捉并分析本征模态的变化，从而实现对结构及材料特性的有效异常检测。在实验验证中，ModeConv展现出计算效率的提升，显著降低了模型计算的运行时间。这种新型ModeConv神经网络层专为时序图神经网络设计，其中每个节点代表一个传感器。ModeConv采用基于奇异值分解的复数卷积滤波器设计，并在谱图卷积中利用模态变换替代傅里叶或拉普拉斯变换。我们通过数学复杂度分析证明了该方法在运行时间上的优化效果。