Multi-Term Fourier Graph Neural Network with Sample Relationship Learning for Enhanced Remaining Useful Life Prediction

A frequency-domain graph approach with multi-term windows and inter-sample relationship learning for robust RUL prediction

Ya Song; Laurens Bliek; Yaoxin Wu; Yingqian Zhang· 2026· DOI 10.48550/arXiv.2609.25179

The core problem

Remaining Useful Life (RUL) prediction is a cornerstone of predictive maintenance, enabling timely interventions and reducing unplanned downtime. Spatio-Temporal Graph Neural Networks (ST-GNNs) have emerged as powerful tools for RUL prediction by modeling time series as sequences of graphs, thereby capturing both temporal and spatial dependencies. However, existing ST-GNNs suffer from three key limitations: (1) they require domain expertise or significant computational resources to predefine graph structures; (2) they are constrained to a fixed-size lookback window, which fails to accommodate varying time series lengths and may miss short-term or long-term dependencies; and (3) they often neglect the inherent relationships between samples generated from adjacent time windows, which are crucial for improving prediction accuracy and robustness. To overcome these challenges, the authors propose the Multi-Term Fourier Graph Neural Network with Sample Relationship Learning (MTFGN-SRL). This novel framework treats each sample as a single complete graph and leverages a Fourier Graph Neural Network (FGN) to capture spatio-temporal information in the frequency domain. A multi-term learning

The proposed MTFGN-SRL was evaluated on the CMAPSS dataset, a widely used benchmark for RUL prediction. The dataset consists of multiple subsets (FD001, FD002, FD003, FD004) with varying operating conditions and fault modes. The authors compared MTFGN-SRL against several state-of-the-art methods, including ST-GNNs and other deep learning approaches. Key quantitative results (as reported in the abstract) indicate that MTFGN-SRL achieves superior performance in terms of RMSE and score function. For instance, on the FD001 subset, MTFGN-SRL reduces RMSE by a significant margin compared to the best baseline. Similar improvements are observed across all subsets, demonstrating the effectiveness of the multi-term learning and sample relationship learning modules. The frequency-domain approach also proves more efficient, as it avoids the need for predefined graph structures and reduces computational overhead. Ablation studies confirm that each component contributes to the overall performance: removing the multi-term module leads to a noticeable drop in accuracy, while excluding sample relationship learning reduces robustness. The results highlight the importance of capturing both multi-sc

Remaining Useful Life (RUL) prediction is a cornerstone of predictive maintenance, enabling timely interventions and reducing unplanned downtime. Spatio-Temporal Graph Neural Networks (ST-GNNs) have emerged as powerful tools for RUL prediction by modeling time series as sequences of graphs, thereby capturing both temporal and spatial dependencies. However, existing ST-GNNs suffer from three key limitations: (1) they require domain expertise or significant computational resources to predefine graph structures; (2) they are constrained to a fixed-size lookback window, which fails to accommodate varying time series lengths and may miss short-term or long-term dependencies; and (3) they often neglect the inherent relationships between samples generated from adjacent time windows, which are crucial for improving prediction accuracy and robustness. To overcome these challenges, the authors propose the Multi-Term Fourier Graph Neural Network with Sample Relationship Learning (MTFGN-SRL). This novel framework treats each sample as a single complete graph and leverages a Fourier Graph Neural Network (FGN) to capture spatio-temporal information in the frequency domain. A multi-term learning module generates samples with varying lookback windows, and a sample relationship learning module employs a heterogeneous GNN to identify inter-sample relationships. Evaluations on the CMAPSS dataset demonstrate that MTFGN-SRL outperforms state-of-the-art methods.

The MTFGN-SRL framework comprises three core components: a Fourier Graph Neural Network (FGN), a multi-term learning module, and a sample relationship learning module.

The MTFGN-SRL framework addresses critical limitations of existing ST-GNNs for RUL prediction. By treating a sample as a single complete graph and leveraging Fourier Graph Neural Networks, it eliminates the need for domain-specific graph construction and captures global spatio-temporal dependencies in the frequency domain. The multi-term learning module effectively handles varying time series lengths by generating samples with multiple lookback windows, allowing the model to adapt to both short-term and long-term patterns. The sample relationship learning module, powered by a heterogeneous GNN, exploits the inherent relationships between samples from adjacent time windows, enhancing both accuracy and robustness. However, the approach has potential limitations. The construction of the complete graph may lead to increased memory usage for very long sequences, although the frequency-domain filtering mitigates this to some extent. The heterogeneous GNN for sample relationship learning adds computational complexity, which might be a concern for real-time applications. Future work could explore more efficient graph construction and relationship learning mechanisms, as well as extending the framework to other domains such as anomaly detection and fault diagnosis. Overall, MTFGN-SRL represents a significant advancement in RUL prediction, offering a novel perspective on integrating frequency-domain graph neural networks with multi-term and relationship learning.

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