GFKAN: An interpretable graph Fourier Kolmogorov-Arnold network for multi-sensor signal fusion and machine fault diagnosis

In machine condition monitoring, reliable intelligent fault diagnosis is often challenged by the complexity of measurement signals acquired from multiple sensors operating in harsh environments and the poor interpretability of the deep neural network. To address these issues, this paper proposes an interpretable Graph Fourier Kolmogorov-Arnold Network (GFKAN) for multi-sensor signal fusion and machine fault diagnosis. In the proposed GFKAN, multi-sensor measurements are first represented as graph-structured signals to capture cross-sensor relationships. Then, a novel Graph Fourier Kolmogorov-Arnold Convolution (GFKAConv) layer is proposed to model signal interactions in the graph spectral domain. By integrating a learnable Fourier-based Kolmogorov-Arnold kernel, the proposed layer decomposes graph signals into interpretable frequency components and enables physically meaningful feature propagation during message passing. Unlike conventional graph neural networks that primarily rely on spatial topology aggregation, the GFKAConv layer performs spectral-aware feature learning, facilitating the extraction of fault-related spectral structures. Furthermore, a Dynamic Sensor Optimization (DSO) module is designed to adaptively identify informative sensor channels and enhance multi-sensor signal fusion without manual sensor selection. Extensive experiments demonstrate that the proposed GFKAN consistently outperforms several state-of-the-art models under complex operating conditions, while simultaneously providing more interpretable signal representations that align with the physical characteristics of measurement signals.