10.57647/ijm2c.2026.1602.12

Efficient Multi-Path CNN Architecture for Anomaly Detection in Control Charts with Imbalanced Data

PDF
  • Amir Azar1,
  • Sadigh Raissi*1,
  • Paria Soleimani1,
  • Shahrooz Bamdad1,
  1. Department of Industrial Engineering, ST.C., Islamic Azad University, Tehran, Iran

Received: 15-08-2025

Revised: 30-09-2925

Accepted: 15-11-2025

Published in Issue 30-06-2026

Published Online: 22-11-2025

Copyright (c) 2025 Amir Azar, Sadigh Raissi, Paria Soleimani, Shahrooz Bamdad (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Azar, A., Raissi, S., Soleimani, P., & Bamdad, S. (2026). Efficient Multi-Path CNN Architecture for Anomaly Detection in Control Charts with Imbalanced Data. International Journal of Mathematical Modelling & Computations, 16(2). https://doi.org/10.57647/ijm2c.2026.1602.12
Crossref
Scopus
Google Scholar
Europe PMC

Abstract

Control Chart Pattern Recognition (CCPR) is critical for early anomaly detection in industrial processes, yet data imbalance poses a significant challenge, leading to biased models that overlook rare but critical anomalies. This study introduces a novel Multi-Path SMOTE-CNN framework to address this issue, enhancing classification performance under moderate (1:20) and severe (1:200) imbalance ratios. The methodology integrates univariate and dual-channel Synthetic Minority Over-sampling Technique (SMOTE) extensions with a multi-path Convolutional Neural Network (CNN) that processes raw time-series and recurrence plot images in parallel, extracting complementary temporal and spatial features. The model was evaluated on simulated datasets and the real-world Wafer dataset using accuracy, sensitivity, specificity, and G-mean metrics. Results demonstrate significant improvements over the baseline CSCNN model, achieving G-mean values up to 0.9928 for cyclic patterns under severe imbalance and 0.9987 on the Wafer dataset. The MP-SMOTE-CNN’s ability to handle extreme imbalance, reduce manual feature engineering, and ensure computational efficiency highlights its potential for real-time industrial applications. This work advances CCPR by offering a robust, scalable solution for anomaly detection, with implications for quality control in manufacturing and beyond.

Keywords

  • Control Chart Pattern Recognition (CCPR),
  • Convolutional Neural Network,
  • Imbalanced Data,
  • Synthetic Minority Over-sampling Technique (SMOTE),
  • Anomaly Detection,
  • Recurrence Plot
PDF

References

  1. He, H., & Garcia, E. A. (2009). Learning from imbalanced data. IEEE Transactions on Knowledge and Data Engineering, 21(9), 1263-1284. DOI: https://doi.org/10.1109/TKDE.2008.239
  2. Chawla, N. V., Bowyer, K. W., Hall, L. O., & Kegelmeyer, W. P. (2002). SMOTE: synthetic minority over-sampling technique. Journal of Artificial Intelligence Research, 16, 321-357. DOI: https://doi.org/10.1613/jair.953
  3. Fernández, A., Garcia, S., Herrera, F., & Chawla, N. V. (2018). SMOTE for learning from imbalanced data: progress and challenges, marking the 15-year anniversary. Journal of Artificial Intelligence Research, 61, 863-905. DOI: https://doi.org/10.1613/jair.1.11192
  4. Farsi, M. N., Amirfakhrian, M., & Vasiq, A. (2014). An improved controlled chaotic neural network for pattern recognition. International Journal of Mathematical Modelling and Computers, 4(3), 267-276.
  5. Buda, M., Maki, A., & Mazurowski, M. A. (2018). A systematic study of the class imbalance problem in convolutional neural networks. Neural Networks, 106, 249-259. DOI: https://doi.org/10.1016/j.neunet.2018.07.011
  6. Fuqua, D., & Razzaghi, T. (2020). A cost-sensitive convolution neural network learning for control chart pattern recognition. Expert Systems with Applications, 150, 113275. DOI: https://doi.org/10.1016/j.eswa.2020.113275
  7. Wang, S., Zhong, Z., Zhao, Y., & Zuo, L. (2021). A variational autoencoder enhanced deep learning model for wafer defect imbalanced classification. IEEE Transactions on Components, Packaging and Manufacturing Technology, 11(12), 2055-2060. DOI: https://doi.org/10.1109/TCPMT.2021.3114639
  8. Swana, E. F., Doorsamy, W., & Bokoro, P. (2022). Tomek link and SMOTE approaches for machine fault classification with an imbalanced dataset. Sensors, 22(9), 3246. DOI: https://doi.org/10.3390/s22093246
  9. Duan, F., Zhang, S., Yan, Y., & Cai, Z. (2022). An oversampling method of unbalanced data for mechanical fault diagnosis based on MeanRadius-SMOTE. Sensors, 22(14), 5166. DOI: https://doi.org/10.3390/s22145166
  10. Xue, L., Wu, H., Zheng, H., & He, Z. (2023). Control chart pattern recognition for imbalanced data based on multi-feature fusion using convolutional neural network. Computers & Industrial Engineering, 182, 109410. DOI: https://doi.org/10.1016/j.cie.2023.109410
  11. Cheng, C. S., Chen, P. W., Hsieh, Y. C., & Wu, Y. T. (2023). Multivariate process control chart pattern classification using multi-channel deep convolutional neural networks. Mathematics, 11(15), 3291. DOI: https://doi.org/10.3390/math11153291
  12. Naser, M. M. R., Varnamkhasti, M. J., Mohammed, H. J., & Aghajani, M. (2024). Artificial Intelligence as a Catalyst for Operational Excellence in Iraqi Industries: Implementation of a Proposed Model. International Journal of Mathematical Modelling and Computers, 14(2).
  13. Li, Y., Dai, W., & He, Y. (2024). Control chart pattern recognition under small shifts based on multi-scale weighted ordinal pattern and ensemble classifier. Computers & Industrial Engineering, 189, 109940.DOI: https://doi.org/10.1016/j.cie.2024.109940
  14. Chu, H., et al. (2024). Pattern recognition of control charts based on data feature enhancement and ensemble learning of classifiers for dimensional accuracy of products. International Journal of Production Research, 1-20.DOI: https://doi.org/10.1080/00207543.2024.2326213
  15. Xue, L., Zhu, D., Li, R., Si, S., & Wu, H. (2025). Control chart pattern recognition with variable window size for imbalanced data based on convolutional neural network with a convolutional block attention module. Neurocomputing, 131226. DOI: https://doi.org/10.1016/j.neucom.2024.131226
  16. Zan, T., Jia, X., Guo, X., Wang, M., Gao, X., & Gao, P. (2025). Research on variable-length control chart pattern recognition based on sliding window method and SECNN-BiLSTM. Scientific Reports,15(1),5921.DOI: https://doi.org/10.1038/s41598-025-89997-7
  17. Khan, S. H., Hayat, M., Bennamoun, M., Sohel, F. A., & Togneri, R. (2017). Cost-sensitive learning of deep feature representations from imbalanced data. IEEE Transactions on Neural Networks and Learning Systems, 29(8), 3573-3587. DOI: https://doi.org/10.1109/TNNLS.2017.2730018
  18. Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017). ImageNet classification with deep convolutional neural networks. Communications of the ACM, 60(6), 84-90. DOI: https://doi.org/10.1145/3065386
  19. Murray, N., & Perronnin, F. (2014). Generalized max pooling. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (pp. 2473-2480). DOI: https://doi.org/10.1109/CVPR.2014.317
  20. Kamal, H., & Mashaly, M. (2024). Advanced hybrid transformer- CNN deep learning model for effective intrusion detection systems with class imbalance mitigation using resampling techniques. Future Internet, 16(12), 481. DOI: https://doi.org/10.3390/fi16120481

Most read articles by the same author(s)