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Nowadays advanced sensing technology enables high-resolution in-process data collection in various systems, known as profile data. These data facilitate in-process monitoring and anomaly detection, which have been extensively studied in recent years. This paper conducts a comprehensive survey on the recent literature for profile modeling and monitoring, including linear profiles, nonlinear profiles, spatial profiles, multi-stage profiles, profile network data, and partially observable profiles, covering techniques such as functional data analysis, tensor analysis, deep learning, etc. By summarizing the developments and challenges associated with the reviewed papers, this paper aims to provide researchers and practitioners with a valuable resource for understanding the latest research advances.
Liu et al. (2024) studied this question.