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Article

Tool-Life Estimation Model in Milling Processes Using Multi-Head Cross-Covariance Attention Fusion-Based Dilated Dense Bi-Directional Gated Recurrent Unit

by
Hisham Alkhalefah
1,2
1
Advanced Manufacturing Institute, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
2
Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
Mathematics 2025, 13(23), 3798; https://doi.org/10.3390/math13233798
Submission received: 28 October 2025 / Revised: 19 November 2025 / Accepted: 22 November 2025 / Published: 26 November 2025
(This article belongs to the Special Issue Artificial Intelligence for Fault Detection in Manufacturing)

Abstract

When performing the milling process, it is essential to consider the life estimation and availability of the milling tool to achieve a reliable and optimized result at a lower cost. It is necessary to monitor the tool’s condition during the milling process due to its inherent wear nature. In earlier times, visual inspection was used to assess the condition of the milling tool, and it was considered a complex and specialized task. Due to this issue, the milling process requires further investigation. In the manufacturing and automation industry, deteriorated milling tools have led to several challenges, including a decline in product quality, reduced equipment utilization, and increased costs. The tool wear prediction is a challenging and complex task, as it includes several variables. The existing framework for tool condition monitoring, in terms of the degree, typically falls short in terms of real-time prediction and accuracy. Hence, in this research, a tool-life estimation model is developed to minimize unexpected failures during the milling process using deep learning techniques. Initially, the data are collected from benchmark sources. The statistical features, deep features via fuzzy autoencoders (FAEs), and t-Distributed Stochastic Neighbor Embedding (t-SNE)-based features are extracted from the input data to capture various information related to the machine. These features are passed to the proposed multi-head cross-covariance attention fusion-based dilated dense bi-directional gated recurrent unit (MCF-DD-BiGRU) for accurate prediction of tool life. The input features are fused using a multi-head cross-covariance attention mechanism to enhance the representation of interdependencies among features. The DBi-GRU network processes the fused features to improve the accuracy of tool-life prediction for milling machines. The prediction efficiency of the implemented model is compared with the existing models to ensure its effectiveness.
Keywords: tool-life estimation; feature extraction; machine learning; prediction; multi-head cross-covariance attention fusion; dilated dense bi-directional gated recurrent unit tool-life estimation; feature extraction; machine learning; prediction; multi-head cross-covariance attention fusion; dilated dense bi-directional gated recurrent unit

Share and Cite

MDPI and ACS Style

Alkhalefah, H. Tool-Life Estimation Model in Milling Processes Using Multi-Head Cross-Covariance Attention Fusion-Based Dilated Dense Bi-Directional Gated Recurrent Unit. Mathematics 2025, 13, 3798. https://doi.org/10.3390/math13233798

AMA Style

Alkhalefah H. Tool-Life Estimation Model in Milling Processes Using Multi-Head Cross-Covariance Attention Fusion-Based Dilated Dense Bi-Directional Gated Recurrent Unit. Mathematics. 2025; 13(23):3798. https://doi.org/10.3390/math13233798

Chicago/Turabian Style

Alkhalefah, Hisham. 2025. "Tool-Life Estimation Model in Milling Processes Using Multi-Head Cross-Covariance Attention Fusion-Based Dilated Dense Bi-Directional Gated Recurrent Unit" Mathematics 13, no. 23: 3798. https://doi.org/10.3390/math13233798

APA Style

Alkhalefah, H. (2025). Tool-Life Estimation Model in Milling Processes Using Multi-Head Cross-Covariance Attention Fusion-Based Dilated Dense Bi-Directional Gated Recurrent Unit. Mathematics, 13(23), 3798. https://doi.org/10.3390/math13233798

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