{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T05:23:17Z","timestamp":1767417797721,"version":"3.48.0"},"reference-count":53,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Future Internet"],"abstract":"<jats:p>Data-driven quality control (QC) systems for the hot forming of steel parts increasingly rely on deep learning models deployed at the network edge, making multivariate sensor time series a critical asset for both local decisions and management information system (MIS) reporting. However, these models are vulnerable to adversarial perturbations and realistic signal disturbances, which can induce misclassification and distort key performance indicators (KPIs) such as first-pass yield (FPY), scrap-related losses, and latency service-level objectives (SLOs). To address this risk, this study introduces a Digital-Twin-Conditioned Diffusion Purification (DTCDP) framework that constrains latent diffusion-based denoising using process states from a lightweight digital twin of the hot-forming line. At each reverse-denoising step, the twin provides physics residuals that are converted into a scalar penalty, and the diffusion latent is updated with a guidance term. This directly bends the sampling trajectory toward reconstructions that adhere to process constraints while removing adversarial perturbations. DTCDP operates as an edge-side preprocessing module that purifies sensor sequences before they are consumed by existing long short-term memory (LSTM)-based QC models, while exposing purification metadata and physics-guidance diagnostics to the plant MIS. In a four-week production dataset comprising more than 40,000 bars, with white-box \u2113\u221e attacks crafted on multivariate sensor time series using Fast Gradient Sign Method and Projected Gradient Descent at perturbation budgets of 1\u20133% of the physical range, combined with additional realistic disturbances, DTCDP improves the robust classification performance of an LSTM-based QC model from 61.0% to 81.5% robust accuracy, while keeping clean accuracy (\u224893%) and FPY on clean data (\u224897%) essentially unchanged. These results indicate that physics-aware, digital-twin-guided diffusion purification can enhance the adversarial robustness of edge QC in hot forming without compromising operational KPIs.<\/jats:p>","DOI":"10.3390\/fi18010023","type":"journal-article","created":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T09:56:23Z","timestamp":1767347783000},"page":"23","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Physics-Aware Latent Diffusion Framework for Mitigating Adversarial Perturbations in Manufacturing Quality Control"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4563-714X","authenticated-orcid":false,"given":"Nikolaos","family":"Nikolakis","sequence":"first","affiliation":[{"name":"Laboratory for Manufacturing Systems & Automation (LMS), Department of Mechanical Engineering & Aeronautics, University of Patras, Rio, 26504 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-0610-5938","authenticated-orcid":false,"given":"Paolo","family":"Catti","sequence":"additional","affiliation":[{"name":"Laboratory for Manufacturing Systems & Automation (LMS), Department of Mechanical Engineering & Aeronautics, University of Patras, Rio, 26504 Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Tran, N.-H., Park, H.-S., Nguyen, Q.-V., and Hoang, T.-D. (2019). Development of a Smart Cyber-Physical Manufacturing System in the Industry 4.0 Context. Appl. Sci., 9.","DOI":"10.3390\/app9163325"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.ifacol.2020.11.029","article-title":"Enabling Predictive Analytics for Smart Manufacturing through an IIoT platform","volume":"53","author":"Cerquitelli","year":"2020","journal-title":"IFAC-PapersOnLine"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Danesh, W., Sapireddy, S.R., and Rahman, M. (2025). Understanding and Detecting Adversarial Examples in IoT Networks: A White-Box Analysis with Autoencoders. Electronics, 14.","DOI":"10.3390\/electronics14153015"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"103761","DOI":"10.1016\/j.cose.2024.103761","article-title":"False Data Injection Attack with Max-Min Optimization in Smart Grid","volume":"140","author":"Bhattar","year":"2024","journal-title":"Comput. Secur."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tambare, P., Meshram, C., Lee, C.-C., Ramteke, R.J., and Imoize, A.L. (2021). Performance Measurement System and Quality Management in Data-Driven Industry 4.0: A Review. Sensors, 22.","DOI":"10.3390\/s22010224"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"114578","DOI":"10.1016\/j.nucengdes.2025.114578","article-title":"Data Reconciliation Method for Nuclear Power Steam Turbine Unit Based on Combined Robust Function and Generalized Regression Neural Network","volume":"446","author":"Wang","year":"2026","journal-title":"Nucl. Eng. Des."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"109045","DOI":"10.1016\/j.cie.2023.109045","article-title":"Anomaly Detection for Industrial Quality Assurance: A Comparative Evaluation of Unsupervised Deep Learning Models","volume":"177","author":"Zipfel","year":"2023","journal-title":"Comput. Ind. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"103300","DOI":"10.1016\/j.compind.2020.103300","article-title":"Development of Manufacturing Execution Systems in Accordance with Industry 4.0 Requirements: A Review of Standard- and Ontology-Based Methodologies and Tools","volume":"123","author":"Skrop","year":"2020","journal-title":"Comput. Ind."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1007\/s12541-014-0532-5","article-title":"Correlation of the Holes Quality with the Force Signals in a Microdrilling Process of a Sintered Tungsten-Copper Alloy","volume":"15","author":"Beruvides","year":"2014","journal-title":"Int. J. Precis. Eng. Manuf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1016\/j.jmsy.2022.01.004","article-title":"Intelligent Manufacturing Execution Systems: A Systematic Review","volume":"62","author":"Shojaeinasab","year":"2022","journal-title":"J. Manuf. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Cerquitelli, T., Nikolakis, N., O\u2019Mahony, N., Macii, E., Ippolito, M., and Makris, S. (2021). A Hybrid Cloud-to-Edge Predictive Maintenance Platform. Predictive Maintenance in Smart Factories, Springer.","DOI":"10.1007\/978-981-16-2940-2"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"103923","DOI":"10.1016\/j.compind.2023.103923","article-title":"A Review of Reference Architectures for Digital Manufacturing: Classification, Applicability and Open Issues","volume":"149","author":"Kaiser","year":"2023","journal-title":"Comput. Ind."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"120843","DOI":"10.1016\/j.apenergy.2023.120843","article-title":"Edge-Cloud Cooperation-Driven Smart and Sustainable Production for Energy-Intensive Manufacturing Industries","volume":"337","author":"Ma","year":"2023","journal-title":"Appl. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1016\/j.jmsy.2022.01.010","article-title":"Towards Edge Computing in Intelligent Manufacturing: Past, Present and Future","volume":"62","author":"Nain","year":"2022","journal-title":"J. Manuf. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wynn, M., and Irizar, J. (2023). Digital Twin Applications in Manufacturing Industry: A Case Study from a German Multi-National. Future Internet, 15.","DOI":"10.20944\/preprints202308.0135.v1"},{"key":"ref_16","unstructured":"Thiede, S., and Lutters, E. (2024). Data Analytics and AI for Quality Assurance in Manufacturing: Challenges and Opportunities. Proceedings of the Learning Factories of the Future, Springer Nature."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3083","DOI":"10.1016\/j.procs.2024.02.124","article-title":"A Hybrid Digital Twin Approach for Proactive Quality Control in Manufacturing","volume":"232","author":"Catti","year":"2024","journal-title":"Procedia Comput. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"103888","DOI":"10.1016\/j.jnca.2024.103888","article-title":"Digital Twin-Driven Secured Edge-Private Cloud Industrial Internet of Things (IIoT) Framework","volume":"226","author":"Hossain","year":"2024","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Harbi, Y., Medani, K., Gherbi, C., Aliouat, Z., and Harous, S. (2024). Roadmap of Adversarial Machine Learning in Internet of Things-Enabled Security Systems. Sensors, 24.","DOI":"10.3390\/s24165150"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"111972","DOI":"10.1016\/j.jcp.2023.111972","article-title":"A Physics-Informed Diffusion Model for High-Fidelity Flow Field Reconstruction","volume":"478","author":"Shu","year":"2023","journal-title":"J. Comput. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Amato, F., Cirillo, E., Fonisto, M., and Moccardi, A. (2024). Detecting Adversarial Attacks in IoT-Enabled Predictive Maintenance with Time-Series Data Augmentation. Information, 15.","DOI":"10.3390\/info15110740"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"100721","DOI":"10.1016\/j.ijcip.2024.100721","article-title":"Digital Twin-Assisted Anomaly Detection for Industrial Scenarios","volume":"47","author":"Alcaraz","year":"2024","journal-title":"Int. J. Crit. Infrastruct. Prot."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sayghe, A. (2025). Digital Twin-Driven Intrusion Detection for Industrial SCADA: A Cyber-Physical Case Study. Sensors, 25.","DOI":"10.20944\/preprints202507.0172.v1"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"108158","DOI":"10.1016\/j.comcom.2025.108158","article-title":"A Survey on Security Enhancing Digital Twins: Models, Applications and Tools","volume":"238","author":"Qureshi","year":"2025","journal-title":"Comput. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"107877","DOI":"10.1016\/j.neunet.2025.107877","article-title":"Adversarial Purification with One-Step Guided Diffusion Model","volume":"192","author":"Li","year":"2025","journal-title":"Neural Netw."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Cai, M., Wang, X., Sohel, F., and Lei, H. (2024). Diffusion Models-Based Purification for Common Corruptions on Robust 3D Object Detection. Sensors, 24.","DOI":"10.3390\/s24165440"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ye, X., Zhang, Q., Cui, S., Ying, Z., Sun, J., and Du, X. (2024). Mitigating Adversarial Attacks in Object Detection through Conditional Diffusion Models. Mathematics, 12.","DOI":"10.3390\/math12193093"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s10462-025-11110-3","article-title":"Comprehensive Exploration of Diffusion Models in Image Generation: A Survey","volume":"58","author":"Chen","year":"2025","journal-title":"Artif. Intell. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Koo, I., Chae, D.-K., and Lee, S.-C. (2023). Improving Adversarial Robustness via Distillation-Based Purification. Appl. Sci., 13.","DOI":"10.20944\/preprints202309.1733.v1"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ye, H., Zhang, Y., and Zhao, X. (2023). Robust and Refined Salient Object Detection Based on Diffusion Model. Electronics, 12.","DOI":"10.3390\/electronics12244962"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"129041","DOI":"10.1016\/j.eswa.2025.129041","article-title":"BoostCount: Diffusion-Based Position-Sensitive Adversarial Purification for Crowd Counting","volume":"296","author":"Du","year":"2026","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"110249","DOI":"10.1016\/j.sigpro.2025.110249","article-title":"APDMs: Adversarial Purification Diffusion Models for Automatic Modulation Classification","volume":"239","author":"Zhang","year":"2026","journal-title":"Signal Process."},{"key":"ref_33","unstructured":"Nie, W., Guo, B., Huang, Y., Xiao, C., Vahdat, A., and Anandkumar, A. (2022). Diffusion Models for Adversarial Purification. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"106693","DOI":"10.1016\/j.bspc.2024.106693","article-title":"Diffusion Based Comprehensive Approach for Highly Contaminated Electrocardiogram Segmentation","volume":"97","author":"Zhu","year":"2024","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"101047","DOI":"10.1016\/j.patter.2024.101047","article-title":"Generating Realistic Neurophysiological Time Series with Denoising Diffusion Probabilistic Models","volume":"5","author":"Vetter","year":"2024","journal-title":"Patterns"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1631\/FITEE.2300310","article-title":"Diffusion Models for Time-Series Applications: A Survey","volume":"25","author":"Lin","year":"2024","journal-title":"Front. Inform. Technol. Electron. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Yang, Y., Jin, M., Wen, H., Zhang, C., Liang, Y., Ma, L., Wang, Y., Liu, C., Yang, B., and Xu, Z. (2025). A Survey on Diffusion Models for Time Series and Spatio-Temporal Data 2024. arXiv.","DOI":"10.1145\/3783986"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Xu, Y., Huang, L., Zhang, L., Qian, L., and Yang, X. (2024). Diffusion-Based Radio Signal Augmentation for Automatic Modulation Classification. Electronics, 13.","DOI":"10.3390\/electronics13112063"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Zhou, H.A., Wolfschl\u00e4ger, D., Florides, C., Werheid, J., Behnen, H., Woltersmann, J.-H., Pinto, T.C., Kemmerling, M., Abdelrazeq, A., and Schmitt, R.H. (2025). Generative AI in Industrial Machine Vision: A Review. J. Intell. Manuf., 1\u201324.","DOI":"10.1007\/s10845-025-02604-6"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Bagazinski, N.J., and Ahmed, F. (2023). ShipGen: A Diffusion Model for Parametric Ship Hull Generation with Multiple Objectives and Constraints. J. Mar. Sci. Eng., 11.","DOI":"10.3390\/jmse11122215"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Christiand, C., Kiswanto, G., Baskoro, A.S., Hasymi, Z., and Ko, T.J. (2024). Tool Wear Monitoring in Micro-Milling Based on Digital Twin Technology with an Extended Kalman Filter. J. Manuf. Mater. Process., 8.","DOI":"10.3390\/jmmp8030108"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Liu, J., Yang, F., Peng, S., Huang, X., Tang, X., and Qiao, X. (2025). Physics-Guided Conditional Diffusion Model for GPR Denoising and Signal Recovery in Complex Mining Environments. Remote Sens., 17.","DOI":"10.3390\/rs17233837"},{"key":"ref_43","unstructured":"Kassis, A., Hengartner, U., and Yu, Y. (2025). DiffBreak: Is Diffusion-Based Purification Robust?. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Giorgetti, G., and Pau, D.P. (2025). Transitioning from TinyML to Edge GenAI: A Review. Big Data Cogn. Comput., 9.","DOI":"10.20944\/preprints202502.0265.v1"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"113874","DOI":"10.1016\/j.asoc.2025.113874","article-title":"Fortifying Vision Models: A Comprehensive Survey of Defences against Adversarial Examples","volume":"185","author":"Kumar","year":"2025","journal-title":"Appl. Soft Comput."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"127998","DOI":"10.1016\/j.eswa.2025.127998","article-title":"Towards Robust and Generalizable Adversarial Purification for Deep Image Classification under Unknown Attacks","volume":"286","author":"Chen","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Xu, Y., Sun, H., Chen, J., Lei, L., Ji, K., and Kuang, G. (2021). Adversarial Self-Supervised Learning for Robust SAR Target Recognition. Remote Sens., 13.","DOI":"10.3390\/rs13204158"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"111481","DOI":"10.1016\/j.ymssp.2024.111481","article-title":"Time Series Diffusion Method: A Denoising Diffusion Probabilistic Model for Vibration Signal Generation","volume":"216","author":"Yi","year":"2024","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"103983","DOI":"10.1016\/j.jvcir.2023.103983","article-title":"Unsupervised Industrial Anomaly Detection with Diffusion Models","volume":"97","author":"Xu","year":"2023","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Wang, C., Huang, C., Zhang, L., Xiang, Z., Xiao, Y., Qian, T., and Liu, J. (2024). Denoising Diffusion Implicit Model Combined with TransNet for Rolling Bearing Fault Diagnosis Under Imbalanced Data. Sensors, 24.","DOI":"10.3390\/s24248009"},{"key":"ref_51","first-page":"1","article-title":"Digital Twin-Based Anomaly Detection with Curriculum Learning in Cyber-Physical Systems","volume":"32","author":"Xu","year":"2023","journal-title":"ACM Trans. Softw. Eng. Methodol."},{"key":"ref_52","unstructured":"Kang, M., Song, D., and Li, B. (2023). DiffAttack: Evasion Attacks Against Diffusion-Based Adversarial Purification. arXiv."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"107705","DOI":"10.1016\/j.neunet.2025.107705","article-title":"Adversarial Guided Diffusion Models for Adversarial Purification","volume":"191","author":"Lin","year":"2025","journal-title":"Neural Netw."}],"container-title":["Future Internet"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-5903\/18\/1\/23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T05:20:08Z","timestamp":1767417608000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-5903\/18\/1\/23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,1]]},"references-count":53,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["fi18010023"],"URL":"https:\/\/doi.org\/10.3390\/fi18010023","relation":{},"ISSN":["1999-5903"],"issn-type":[{"type":"electronic","value":"1999-5903"}],"subject":[],"published":{"date-parts":[[2026,1,1]]}}}