An interpretable graph neural network inspired by graph signal processing for mechanical fault diagnosis

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As mechanical equipment grows more complex, multi-sensor monitoring and data fusion are essential for accurate fault diagnosis. While graph neural networks (GNNs) are popularly used in this field, their performance evaluations remain largely empirical, lacking a unified theoretical framework to explain and assess their underlying propagation mechanisms. To address this, we propose a unified GNN framework from the perspective of graph signal processing (GSP). We mathematically demonstrate that each propagation layer in representative GNNs (including graph convolutional networks, graph attention networks, and GraphSAGE) is equivalent or approximately equivalent to performing a single-step proximal gradient descent to solve a specific instance within this framework. The framework also provides an interpretable foundation, revealing the commonalities, differences, and limitations of representative GNNs. To overcome the limitations, we design a more principled GSP optimization objective by removing the activation regularizer and adopting a multi-step gradient descent strategy. Using algorithm unrolling, we derive a novel architecture named gradient descent unrolled GNN (GDUGNN), which adopts a decoupled architectural paradigm where feature transformation is performed by a convolution and max-pooling module, and feature aggregation is implemented by unrolling the gradient descent algorithm into multiple propagation layers with learnable step sizes. This design naturally introduces skip connections from both the current and the first-layer inputs, effectively mitigating over-smoothing while ensuring inherent interpretability. A fault diagnosis model based on GDUGNN is developed and evaluated on a wind turbine simulator and a rock drill. Experiments demonstrate that GDUGNN achieves superior diagnostic performance with stronger resistance to overfitting and over-smoothing compared to mainstream GNNs and their variants. Our code will be available at https://github.com/CUG-FDGroup .