{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T17:16:15Z","timestamp":1778001375728,"version":"3.51.4"},"reference-count":26,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,22]],"date-time":"2021-08-22T00:00:00Z","timestamp":1629590400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["61922072, 61876169"],"award-info":[{"award-number":["61922072, 61876169"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Trend anomaly detection is the practice of comparing and analyzing current and historical data trends to detect real-time abnormalities in online industrial data-streams. It has the advantages of tracking a concept drift automatically and predicting trend changes in the shortest time, making it important both for algorithmic research and industry. However, industrial data streams contain considerable noise that interferes with detecting weak anomalies. In this paper, the fastest detection algorithm \u201csliding nesting\u201d is adopted. It is based on calculating the data weight in each window by applying variable weights, while maintaining the method of trend-effective integration accumulation. The new algorithm changes the traditional calculation method of the trend anomaly detection score, which calculates the score in a short window. This algorithm, SNWFD\u2013DS, can detect weak trend abnormalities in the presence of noise interference. Compared with other methods, it has significant advantages. An on-site oil drilling data test shows that this method can significantly reduce delays compared with other methods and can improve the detection accuracy of weak trend anomalies under noise interference.<\/jats:p>","DOI":"10.3390\/e23081093","type":"journal-article","created":{"date-parts":[[2021,8,22]],"date-time":"2021-08-22T21:47:52Z","timestamp":1629668872000},"page":"1093","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Research on the Fastest Detection Method for Weak Trends under Noise Interference"],"prefix":"10.3390","volume":"23","author":[{"given":"Guang","family":"Li","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Automation, Henan Institute of Technology, Xinxiang 453003, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0811-0223","authenticated-orcid":false,"given":"Jing","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Zhengzhou University, Zhengzhou 450001, China"}]},{"given":"Caitong","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Zhengzhou University, Zhengzhou 450001, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,22]]},"reference":[{"key":"ref_1","unstructured":"Wu, W., He, L., and Lin, W. 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