因果卷积网络可看作有限冲激响应滤波器，提升时序信号的可解释性。
Causal Convolutional Neural Networks as Finite Impulse Response Filters
- 将长卷积核的因果CNN视为FIR滤波器，用卷积结合律等效为单层优化滤波器
- 在模拟梁动力学和真实桥梁振动数据上验证，对稀疏频谱信号学习效果好
- 适合需要理解动态系统频谱特性的物理建模任务，如结构健康监测
本研究探讨了具有准线性激活函数的因果卷积神经网络（Causal CNN）在多模态频率内容的时间序列数据上的行为。结果表明，训练后此类网络表现出与有限冲激响应（FIR）滤波器类似的特性，尤其当卷积核长度远超标准CNN架构时。因果CNN能隐式和显式地捕捉频谱特征，提升了动态系统任务的可解释性。利用卷积的结合律，我们进一步证明整个网络可简化为一个等效的单层滤波器，该滤波器通过最小二乘准则优化，类似于FIR滤波器。这一等价关系揭示了CNN在稀疏频谱信号上的谱学习机制。方法在模拟梁动力学和真实桥梁振动数据集上得到验证，凸显其在建模与识别受动态响应支配的物理系统中的应用价值。
原文摘要 · Abstract (English)
This study investigates the behavior of Causal Convolutional Neural Networks (CNNs) with quasi-linear activation functions when applied to time-series data characterized by multimodal frequency content. We demonstrate that, once trained, such networks exhibit properties analogous to Finite Impulse Response (FIR) filters, particularly when the convolutional kernels are of extended length exceeding those typically employed in standard CNN architectures. Causal CNNs are shown to capture spectral features both implicitly and explicitly, offering enhanced interpretability for tasks involving dynamic systems. Leveraging the associative property of convolution, we further show that the entire network can be reduced to an equivalent single-layer filter resembling an FIR filter optimized via least-squares criteria. This equivalence yields new insights into the spectral learning behavior of CNNs trained on signals with sparse frequency content. The approach is validated on both simulated beam dynamics and real-world bridge vibration datasets, underlining its relevance for modeling and identifying physical systems governed by dynamic responses.
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