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Efficient visibility algorithm for high-frequency time-series: application to fault diagnosis with graph convolutional network

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Abstract

Time series is a popular data type that is collected from various machines for fault diagnosis. Although most time-series models for fault diagnosis reflect local relations well, they cannot extract the global patterns that contain valuable information that can be used to recognize faults. To reflect the global structural information of a time series, many recent studies have used a graph constructed by visibility algorithms (VAs) that convert a time series into a graph. However, applying the VAs to high-frequency time series—which the machines typically generate—is challenging because the computational burden of the VAs increases with the length of a time series. Therefore, we propose a novel graph-based fault diagnosis framework for high-frequency time series. First, we propose an efficient VA (EVA) that extracts essential data points to characterize a time series and constructs a graph from a high-frequency time series. Not only do the EVAs convert a given time series faster into a graph than the VAs, but the resulting graphs also characterize the time-series structure with simplicity and clarity by selecting essential data points. Then, we adopt a graph convolutional network to analyze the resulting graphs and diagnose faults. We verified the characteristics of the EVAs and the fault diagnosis performance of the proposed framework using toy time series and public rotating machinery datasets, respectively. The results demonstrated that, compared to the VAs, the EVAs are efficient in terms of computational cost, and the proposed framework is effective for fault diagnosis.

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Acknowledgements

This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (MSIT) of Korea (Nos. 2020R1C1C1003425 and 2020R1A4A3079710) and also by Korea Institute of Planning and Evaluation for Technology in Food, Agriculture, Forestry (IPET) through Smart Agri Products Flow Storage Technology Development Program, funded by Ministry of Agriculture, Food and Rural Affairs (MAFRA) of Korea (No.322050-3).

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Dongguk University – Seoul, Seoul, 04620, South Korea

    Sangho Lee & Youngdoo Son

  2. Data Science Laboratory (DSLAB), Dongguk University – Seoul, Seoul, 04620, South Korea

    Sangho Lee & Youngdoo Son

  3. Department of Management Information Systems, West Virginia University, Morgantown, WV, 26505, USA

    Jeongsub Choi

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Appendix

Appendix

Here, to demonstrate the effect of global structural information on fault diagnosis, we compared the results of our framework with some baseline models using the CWRU bearing dataset. The baseline models include random forest (RF), one nearest neighbor (1-NN), SVM with the Gaussian kernel, multilayer perceptron (MLP), and one-dimensional fully convolutional neural network (FCN). Many previous studies have demonstrated that these baseline models are effective in time-series classification (Bagnall et al., 2017; Ismail Fawaz et al., 2019).

We set the experimental setup as the same with Sect. 5. The optimal hyperparameters of the baseline models were determined through a random search; the search ranges are shown in Table  9 where the optimal hyperparameters are highlighted in boldface.

Table 9 Table captionSearch ranges for hyperparameters of each baseline model. The optimal values are highlighted in boldface
Full size table
Table 10 Fault diagnosis performances of baseline models and GCN models with BVA, HVA, EBVA, and EHVA for the CWRU bearing dataset
Full size table

Table 10 shows the fault diagnosis performances of the baseline models, and GCNs with VAs and EVAs. For a fair comparison, we considered four evaluation metrics in the experiment: the accuracy, precision, recall, and F1-score. (AUC is excluded because SVM only provides the binary outputs.) In the experiment, it was observed that the FCN model, known for its decent performances in various studies, showed the best performance among the baseline models. However, the performance of the GCN with EHVA outperformed the others, including the baseline models, in terms of all the metrics. In addition, the performances of four GCN models, which reflect the structural information of time series, were generally better than those of the baseline models. Thus, we demonstrated that the graphs derived by either VAs or EVAs can provide useful information to diagnose faults, reflecting global structural patterns of time series.

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Lee, S., Choi, J. & Son, Y. Efficient visibility algorithm for high-frequency time-series: application to fault diagnosis with graph convolutional network. Ann Oper Res 339, 813–833 (2024). https://doi.org/10.1007/s10479-022-05071-x

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