Anomaly Detection Optimization in Cloud Technology Metric Time Series
DOI:
https://doi.org/10.31649/1997-9266-2026-185-2-29-39Keywords:
time series decomposition, MSTL, nomaly detection, cloud IT systems, linear regressionAbstract
In modern cloud IT infrastructures, hundreds of metrics must be monitored to detect anomalies and ensure stable operation. Many of these metrics exhibit multi-seasonal characteristics, requiring decomposition into three components: trend, seasonality, and residuals. However, most known decomposition methods, including the well-known Multiple Seasonal-Trend decomposition using Locally Estimated Scatterplot Smoothing (MSTL), require significant computational resources. This article proposes an alternative, more computationally efficient approach for detecting anomalies in a large array of metrics, particularly for real-time applications. The method`s core idea is to identify linearly dependent metrics and model their trend and seasonal components using linear regression with other metrics. Anomaly detection is then performed on the residual component. This reduces the required computational power, thereby optimizing the expenses of cloud infrastructure monitoring centers. This work also demonstrates how to select a suitable subset of metrics for linear regression modeling and decomposition, calculate the optimal time series length for determining linear regression model coefficients, and establish reliable criteria for detecting anomalous metric values. To verify the effectiveness of this linear regression-based decomposition approach, the experiment was conducted on a real cloud infrastructure. The experiment involved a containerized web application with heavy traffic on the Google Cloud Platform. The results showed that the Chebyshev inequality-based approach was the most suitable anomaly detection criterion in this case. Furthermore, a connection was established between the system's architecture, which defines the nature of the metrics, and their statistical properties, which influences their selection for the proposed optimization approach.
References
I. Danylyuk, and L. Budnyk, “Technology of carryng out a comprehrnsive IT monitoring of the company,” Galician economic journal, vol. 87, no. 2, pp. 40-49, 2024, https://doi.org/10.33108/galicianvisnyk_tntu2024.02.040. Available: https://galicianvisnyk.tntu.edu.ua/index.php?art=1280. Accessed: Dec. 11, 2025.
A. Mishra, R. Sriharsha, and S. Zhong, “OnlineSTL: scaling time series decomposition by 100x,” Proc. VLDB Endow., vol. 15, no. 7, pp. 1417-1425, Mar. 2022, https://doi.org/10.14778/3523210.3523219. Available: https://dl.acm.org/doi/10.14778/3523210.3523219. Accessed: Dec. 11, 2025.
Г. Пахаренко, «Використання декомпозиції часових рядів в задачах моніторингу хмарної інфраструктури,» in Future of Work: Technological, Generational and Social Shifts. Proceedings of the 4th International Scientific and Practical Internet Conference, May 2025, pp. 160-163.
T. Mathonsi, and T. L. V. Zyl, “Multivariate anomaly detection based on prediction intervals constructed using deep learning,” Neural Comput & Applic, vol. 37, no. 2, pp. 707-721, Jan. 2025, https://doi.org/10.1007/s00521-021-06697-x. Available: https://link.springer.com/10.1007/s00521-021-06697-x. Accessed: Dec. 11, 2025.
K. Bandara, R. J. Hyndman, and C. Bergmeir, “MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with Multiple Seasonal Patterns.” arXiv, 2021. https://doi.org/10.48550/ARXIV.2107.13462. Available: https://arxiv.org/abs/2107.13462. Accessed: Dec. 11, 2025.
S. J. Taylor, and B. Letham, “Forecasting at scale.” Sept. 27, 2017. https://doi.org/10.7287/peerj.preprints.3190v2. Available: https://peerj.com/preprints/3190v2. Accessed: Dec. 11, 2025.
A. T. Williams, R. E. Sperl, and S. M. Chung, “Anomaly Detection in Multi-Seasonal Time Series Data,” IEEE Access, vol. 11, pp. 106456-106464, 2023, https://doi.org/10.1109/ACCESS.2023.3317791. Available: https://ieeexplore.ieee.org/document/10256098/. Accessed: Dec. 11, 2025.
Z. Zhang, K. Nie, and T. T. Yuan, “Moving Metric Detection and Alerting System at eBay,” arXiv, 2020. https://doi.org/10.48550/ARXIV.2004.02360. Available: https://arxiv.org/abs/2004.02360. Accessed: Dec. 11, 2025.
A. Dokumentov, and R. J. Hyndman, “STR: Seasonal-Trend Decomposition Using Regression.” arXiv, 2020. https://doi.org/10.48550/ARXIV.2009.05894. Available: https://arxiv.org/abs/2009.05894. Accessed: Dec. 11, 2025.
Q. Wen, J. Gao, X. Song, L. Sun, H. Xu, and S. Zhu, “RobustSTL: A Robust Seasonal-Trend Decomposition Algorithm for Long Time Series.” arXiv, 2018. https://doi.org/10.48550/ARXIV.1812.01767. Available: https://arxiv.org/abs/1812.01767. Accessed: Dec. 11, 2025.
O. Yunkova, and P. Kucher, “Modeling and forecasting of commodity markets based on the decomposition method,” MISE, no. 101, pp. 182-191, Dec. 2021, https://doi.org/10.33111/mise.101.15. Available:
https://mise.kneu.ua/archive/2021/101.15. Accessed: Dec. 11, 2025.
O. P. Gozhy, I. O. Kalinina, V. O. Gozhy, and V. V. Dymo, “System approach to forecasting electricity demand based on machine learning,” System technologies, vol. 3, no. 158, pp. 36-47, Apr. 2025, https://doi.org/10.34185/1562-9945-3-158-2025-05. Available: https://journals.nmetau.edu.ua/index.php/st/article/view/1994. Accessed: Dec. 11, 2025.
I. Kalinina, P. Bidyuk, A. Gozhyj, and P. Malchenko, “Combining Forecasts Based on Time Series Models in Machine Learning Tasks,” MoMLeT+DS 2023, Lviv, June 2023. Available: https://ceur-ws.org/Vol-3426/paper3.pdf
I. Koblianska, L. Kalachevska, S. Minta, N. Strochenko, and S. Lukash, “Modelling and forecasting of potato sales prices in Ukraine,” Agric. resour. econ., vol. 7, no. 4, pp. 160-179, Dec. 2021, https://doi.org/10.51599/are.2021.07.04.09. Available: https://are-journal.com/are/article/view/483. Accessed: Dec. 11, 2025.
T. Marynych, “Comparative Analysis of Univariate Time Series Modeling and Forecasting Techniques for Short-Term Unstable Data,” Математичне моделювання в техніці та технологіях. Вісник НТУ «ХПІ», vol. 6, no. 1128, pp. 63-69, 2017.
Шмундяк Д. О., Мокін В. Б. «Метод ідентифікації параметрів гармонік та аномалій періодичного часового ряду на основі адаптивної декомпозиції,» Вісник Вінницького політехнічного інституту, № 6, с. 46-56, 2023, https://doi.org/10.31649/1997-9266-2023-171-6-46-56.
Лосенко А. В., «Інформаційна технологія прогнозування часового ряду кількості хворих на коронавірус на основі моделі Facebook Prophet,» Вісник Вінницького політехнічного інституту, № 5, с. 50-59, 2023. https://doi.org/10.31649/1997-9266-2023-170-5-50-59. Дата звернення: груд., 11, 2025.
A. Anwar, A. Sailer, A. Kochut, and A. R. Butt, “Anatomy of Cloud Monitoring and Metering: A case study and open problems,” in Proceedings of the 6th Asia-Pacific Workshop on Systems, Tokyo Japan: ACM, July 2015, pp. 1-7. https://doi.org/10.1145/2797022.2797039. Available: https://dl.acm.org/doi/10.1145/2797022.2797039. Accessed: Dec. 11, 2025.
L. Yang, Q. Wen, B. Yang, and L. Sun, “A Robust and Efficient Multi-Scale Seasonal-Trend Decomposition,” 2021, https://doi.org/10.48550/ARXIV.2109.08800. Available: https://arxiv.org/abs/2109.08800. Accessed: Dec. 11, 2025.
A. Singal, D. Pathak, K. Ray, F. George, M. Verma, and P. Moogi, “Metric Criticality Identification for Cloud Microservices.” arXiv, 2025. https://doi.org/10.48550/ARXIV.2501.03547. Available: https://arxiv.org/abs/2501.03547. Accessed: Dec. 11, 2025.
R. M. Karp, “Reducibility Among Combinatorial Problems,” in 50 Years of Integer Programming 1958-2008, M. Jünger, T. M. Liebling, D. Naddef, G. L. Nemhauser, W. R. Pulleyblank, G. Reinelt, G. Rinaldi, and L. A. Wolsey, Eds., Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, pp. 219-241. https://doi.org/10.1007/978-3-540-68279-0_8. Available:
http://link.springer.com/10.1007/978-3-540-68279-0_8. Accessed: Dec. 11, 2025.
R. Kohavi, and G. H. John, “Wrappers for feature subset selection,” Artificial Intelligence, vol. 97, no. 1-2, pp. 273-324, Dec. 1997, https://doi.org/10.1016/S0004-3702(97)00043-X. Available: https://linkinghub.elsevier.com/retrieve/pii/S000437029700043X. Accessed: Dec. 11, 2025.
R. Cleveland, STL: A Seasonal-Trend Decomposition Procedure Based on Loess, 1990.
W. Cleveland, “Robust Locally Weighted Regression and Smoothing Scatterplots,” J. Am. Stat. Assoc, vol. 74, no. 368, pp. 829-836, 1979.
Z. Ouyang, M. Jabloun, and P. Ravier, “STLformer: Exploit STL Decomposition and Rank Correlation for Time Series Forecasting,” in 2023 31st European Signal Processing Conference (EUSIPCO), Helsinki, Finland: IEEE, Sept. 2023, pp. 1405-1409. https://doi.org/10.23919/EUSIPCO58844.2023.10290126. Available: https://ieeexplore.ieee.org/document/10290126/. Accessed: Dec. 11, 2025.
M. Braverman, “The Gradient Complexity of Linear Regression” Proceedings of Thirty Third Conference on Learning Theory, PLMR, 2020, pp. 627-647.
A. Frank, D. Fabregat-Traver, and P. Bientinesi, “Large-scale linear regression: Development of high-performance routines,” Applied Mathematics and Computation, vol. 275, pp. 411-421, Feb. 2016, https://doi.org/10.1016/j.amc.2015.11.078. Available: https://linkinghub.elsevier.com/retrieve/pii/S0096300315015805. Accessed: Dec. 11, 2025.
R. P. Hafen, et al., “Syndromic surveillance: STL for modeling, visualizing, and monitoring disease counts,” BMC Med Inform Decis Mak, vol. 9, no. 1, p. 21, Dec. 2009, https://doi.org/10.1186/1472-6947-9-21. Available: https://bmcmedinformdecismak.biomedcentral.com/articles/10.1186/1472-6947-9-21. Accessed: Dec. 11, 2025.
F. E. Grubbs, “Procedures for Detecting Outlying Observations in Samples,” Technometrics, vol. 11, no. 1, pp. 1-21, Feb. 1969, https://doi.org/10.1080/00401706.1969.10490657. Available: http://www.tandfonline.com/doi/abs/10.1080/00401706.1969.10490657. Accessed: Dec. 11, 2025.
М. Бешлей, А. Прислупський, М. Медвецький, і Г. Бешлей, «Інтелектуальна система моніторингу та аналізу трафіку для виявлення атак в програмно-конфігурованих мережах,» ICTEE, т. 2, № 1, с. 1-11, 2022, https://doi.org/10.23939/ictee2022.01.001. Available: http://ictee.arleons.com/?journal=ictee&page=issue&op=view&path%5B%5D=ictee-2-1-22&path%5B%5D=ictee-2-1-22-st1. Accessed: Dec. 11, 2025.
A. Senyk, Y. Pyrih, and O. Shpur, “Study of the Intelligent Monitoring Algorithm of Qos in the Mass Service Systems,” ICTEE, vol. 4, no. 2, pp. 103-112, Oct. 2024, https://doi.org/10.23939/ictee2024.02.103. Available:
https://science.lpnu.ua/ictee/all-volumes-and-issues/volume-4-number-2-2024/study-intelligent-monitoring-algorithm-qos-mass. Accessed: Dec. 11, 2025.
А. Гребенник, «Виявлення та прогнозування рівня загроз для корпоративної комп’ютерної мережі,» Технічні науки та технології, т. 2, № 20, с. 175-185, 2020.
O. M. Shopskyi, and R. R. Golovatiy, “Application of machine learning models for early detection of emergency situations based on streaming big data,” NMetAU Journals, vol. 4, no. 159, pp. 85-98, May 2025, https://doi.org/10.34185/1562-9945-4-159-2025-09. Available: https://journals.nmetau.edu.ua/index.php/st/article/view/2043. Accessed: Dec. 11, 2025.
O. Yu. Tarnovetska, K. P. Hazdiuk, S. M. Balen, and K. M. Dmytrashchuk, “Study of Internet System Connection to Monitoring Using Modern Devops TechnologieS,” Scientific notes of Taurida National V.I. Vernadsky University. Series: Technical Sciences, vol. 1, no. 1, pp. 295-302, 2024, https://doi.org/10.32782/2663-5941/2024.1.1/44. Available: https://www.tech.vernadskyjournals.in.ua/journals/2024/1_2024/part_1/46.pdf. Accessed: Dec. 11, 2025.
X. He, Y. Li, J. Tan, B. Wu, and F. Li, “OneShotSTL: One-Shot Seasonal-Trend Decomposition for Online Time Series Anomaly Detection And Forecasting,” Proc. VLDB Endow., vol. 16, no. 6, pp. 1399-1412, Feb. 2023, https://doi.org/10.14778/3583140.3583155. Available: https://dl.acm.org/doi/10.14778/3583140.3583155. Accessed: Dec. 11, 2025.
H. Wang, H. Guo, Z. Zhu, Y. Zhang, Y. Zhou, and X. Zheng, “BacktrackSTL: Ultra-Fast Online Seasonal-Trend Decomposition with Backtrack Technique,” in Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, Barcelona Spain: ACM, Aug. 2024, pp. 5848-5859. https://doi.org/10.1145/3637528.3671510. Available: https://dl.acm.org/doi/10.1145/3637528.3671510. Accessed: Dec. 11, 2025.
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