{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:39Z","timestamp":1760145759247,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2024,8,21]],"date-time":"2024-08-21T00:00:00Z","timestamp":1724198400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Fund of Sichuan Science and Technology Program","award":["2023NSFSC1429","2024NSFSC1425","2024NSFSC0868","2023YFG0196","2023YFN0077","WRXT2022-005","KYTZ202139"],"award-info":[{"award-number":["2023NSFSC1429","2024NSFSC1425","2024NSFSC0868","2023YFG0196","2023YFN0077","WRXT2022-005","KYTZ202139"]}]},{"name":"Key R&amp;D project of Science and Technology Department of Sichuan Province","award":["2023NSFSC1429","2024NSFSC1425","2024NSFSC0868","2023YFG0196","2023YFN0077","WRXT2022-005","KYTZ202139"],"award-info":[{"award-number":["2023NSFSC1429","2024NSFSC1425","2024NSFSC0868","2023YFG0196","2023YFN0077","WRXT2022-005","KYTZ202139"]}]},{"name":"Sichuan unmanned system and intelligent perception Engineering Laboratory Open Fund","award":["2023NSFSC1429","2024NSFSC1425","2024NSFSC0868","2023YFG0196","2023YFN0077","WRXT2022-005","KYTZ202139"],"award-info":[{"award-number":["2023NSFSC1429","2024NSFSC1425","2024NSFSC0868","2023YFG0196","2023YFN0077","WRXT2022-005","KYTZ202139"]}]},{"name":"Research Fund of Chengdu University of Information Technology","award":["2023NSFSC1429","2024NSFSC1425","2024NSFSC0868","2023YFG0196","2023YFN0077","WRXT2022-005","KYTZ202139"],"award-info":[{"award-number":["2023NSFSC1429","2024NSFSC1425","2024NSFSC0868","2023YFG0196","2023YFN0077","WRXT2022-005","KYTZ202139"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Data-driven fault diagnosis, identifying abnormality causes using collected industrial data, is one of the challenging tasks for intelligent industry safety management. It is worth noting that practical industrial data are usually related to a mixture of several physical attributes, such as the operating environment, product quality and working conditions. However, the traditional models may not be sufficient to leverage the coherent information for diagnostic performance enhancement, due to their shallow architecture. This paper presents a hierarchical matrix factorization (HMF) that relies on a succession of matrix factoring to find an efficient representation of industrial data for fault diagnosis. Specifically, HMF consecutively decomposes data into several hierarchies. The intermediate hierarchies play the role of analysis operators which automatically learn implicit characteristics of industrial data; the final hierarchy outputs high-level and discriminative features. Furthermore, HMF is also extended in a nonlinear manner by introducing activation functions, referred as NHMF, to deal with nonlinearities in practical industrial processes. The applications of HMF and NHMF to fault diagnosis are evaluated by the multiple-phase flow process. The experimental results show that our models achieve competitive performance against the considered shallow and deep models, consuming less computing time than deep models.<\/jats:p>","DOI":"10.3390\/s24165408","type":"journal-article","created":{"date-parts":[[2024,8,23]],"date-time":"2024-08-23T12:58:07Z","timestamp":1724417887000},"page":"5408","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Hierarchical Matrix Factorization-Based Method for Intelligent Industrial Fault Diagnosis"],"prefix":"10.3390","volume":"24","author":[{"given":"Yanxia","family":"Li","sequence":"first","affiliation":[{"name":"School of Automation, Chengdu University of Information Technology, Chengdu 610225, China"}]},{"given":"Han","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Automation, Chongqing University, Chongqing 400044, China"}]},{"given":"Jiajia","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Automation, Chengdu University of Information Technology, Chengdu 610225, China"}]},{"given":"Xuemin","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Automation, Chengdu University of Information Technology, Chengdu 610225, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yang, Z., Chai, Y., Yin, H., and Tao, S. 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