{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T04:59:35Z","timestamp":1780549175093,"version":"3.54.1"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T00:00:00Z","timestamp":1718582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"publisher","award":["92270117"],"award-info":[{"award-number":["92270117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"publisher","award":["62376214"],"award-info":[{"award-number":["62376214"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"publisher","award":["2024JC-YBQN-0697"],"award-info":[{"award-number":["2024JC-YBQN-0697"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"publisher","award":["2023-JC-YB-533"],"award-info":[{"award-number":["2023-JC-YB-533"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China (NSFC)","doi-asserted-by":"publisher","award":["103-451123015"],"award-info":[{"award-number":["103-451123015"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["92270117"],"award-info":[{"award-number":["92270117"]}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["62376214"],"award-info":[{"award-number":["62376214"]}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["2024JC-YBQN-0697"],"award-info":[{"award-number":["2024JC-YBQN-0697"]}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["2023-JC-YB-533"],"award-info":[{"award-number":["2023-JC-YB-533"]}]},{"name":"Natural Science Basic Research Program of Shaanxi","award":["103-451123015"],"award-info":[{"award-number":["103-451123015"]}]},{"name":"Doctoral Scientific Research Startup Foundation of Xi\u2019an University of Technology","award":["92270117"],"award-info":[{"award-number":["92270117"]}]},{"name":"Doctoral Scientific Research Startup Foundation of Xi\u2019an University of Technology","award":["62376214"],"award-info":[{"award-number":["62376214"]}]},{"name":"Doctoral Scientific Research Startup Foundation of Xi\u2019an University of Technology","award":["2024JC-YBQN-0697"],"award-info":[{"award-number":["2024JC-YBQN-0697"]}]},{"name":"Doctoral Scientific Research Startup Foundation of Xi\u2019an University of Technology","award":["2023-JC-YB-533"],"award-info":[{"award-number":["2023-JC-YB-533"]}]},{"name":"Doctoral Scientific Research Startup Foundation of Xi\u2019an University of Technology","award":["103-451123015"],"award-info":[{"award-number":["103-451123015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Despite their high prediction accuracy, deep learning-based soft sensor (DLSS) models face challenges related to adversarial robustness against malicious adversarial attacks, which hinder their widespread deployment and safe application. Although adversarial training is the primary method for enhancing adversarial robustness, existing adversarial-training-based defense methods often struggle with accurately estimating transfer gradients and avoiding adversarial robust overfitting. To address these issues, we propose a novel adversarial training approach, namely domain-adaptive adversarial training (DAAT). DAAT comprises two stages: historical gradient-based adversarial attack (HGAA) and domain-adaptive training. In the first stage, HGAA incorporates historical gradient information into the iterative process of generating adversarial samples. It considers gradient similarity between iterative steps to stabilize the updating direction, resulting in improved transfer gradient estimation and stronger adversarial samples. In the second stage, a soft sensor domain-adaptive training model is developed to learn common features from adversarial and original samples through domain-adaptive training, thereby avoiding excessive leaning toward either side and enhancing the adversarial robustness of DLSS without robust overfitting. To demonstrate the effectiveness of DAAT, a DLSS model for crystal quality variables in silicon single-crystal growth manufacturing processes is used as a case study. Through DAAT, the DLSS achieves a balance between defense against adversarial samples and prediction accuracy on normal samples to some extent, offering an effective approach for enhancing the adversarial robustness of DLSS.<\/jats:p>","DOI":"10.3390\/s24123909","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T06:29:43Z","timestamp":1718605783000},"page":"3909","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Adversarial Robustness Enhancement for Deep Learning-Based Soft Sensors: An Adversarial Training Strategy Using Historical Gradients and Domain Adaptation"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7426-3212","authenticated-orcid":false,"given":"Runyuan","family":"Guo","sequence":"first","affiliation":[{"name":"School of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingyuan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6618-1380","authenticated-orcid":false,"given":"Han","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3318-8137","authenticated-orcid":false,"given":"Wenqing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation and Information Engineering, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6859","DOI":"10.1109\/TII.2022.3181692","article-title":"A Self-Interpretable Soft Sensor Based on Deep Learning and Multiple Attention Mechanism: From Data Selection to Sensor Modeling","volume":"19","author":"Guo","year":"2023","journal-title":"IEEE Trans. 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