Fractional-order neural network for detecting process deviations in optical fiber cable manufacturing.

Anomaly detection in industrial manufacturing processes is essential for reducing material costs and improving product quality. This study focuses on detecting anomalies in the production of fiber optic cables, where small deviations in process parameters such as temperature, extrusion pressure, and fiber tension can significantly impact the optical properties of the final product. Given the high-dimensional nature of process data and the challenge of automatically labeling anomalies, unsupervised learning techniques were applied to cluster and label production anomalies. To address this problem, we propose an FD-LSTM (Fractional Derivative - Long Short-Term Memory) network model incorporating fractional order derivatives, implemented using the Grünwald-Letnikov method. These specialized activation functions enable smooth modeling of complex temporal dependencies within the manufacturing process. The proposed models achieve high accuracy in detecting multiple types of anomalies, with predictive performance above 95% across the evaluated dataset. In particular, the FD-LSTM achieved an accuracy of 96.7% and an F1-score of 0.93 on real production data, compared with 94.8% accuracy for the classical LSTM baseline. The fractional-order gating mechanism reduced dominant misclassification flows and improved the separability of weak anomaly clusters, indicating its ability to capture subtle temporal deviations in the manufacturing process. Furthermore, a comparative analysis was conducted between conventional neural network models and those utilizing fractional order derivatives, indicating improved capability in capturing intricate process dynamics. This work integrates fractional calculus into recurrent network architectures to support anomaly detection in industrial manufacturing environments.