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Localization and classification of anomalies in one-dimensional signals based on wavelet analysis and mathematical optimization methods
N.D. Sakovich1,2, D.A. Aksenov1,2, E.S. Pleshakova3, S.T. Gataullin4

1 Financial University under the Government of the Russian Federation, 125167, Moscow, Leningradsky Prospekt, 49/2;
2 The Scientific Research Institute of Goznak, 115162, Moscow, Mytnaya st., 19;
3 MIREA -- Russian Technological University, 119454, Moscow, Vernadsky Ave., 78;
4 CEMI RAS, 117418, Moscow, Nakhimovsky pr., 47

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DOI: 10.18287/COJ1683

Article ID: 1683

Language: English

Abstract:
A method for classifying types of non-stationarities in time series based on wavelet analysis for localization and detection of non-stationarity boundaries; mathematical algorithms for comparing types of non-stationarities based on templates of reference signals and classifying anomalies using non-gradient optimization methods; with the possibility of further application for developing automated information systems for comprehensive monitoring of the state of the power grid and its individual components is presented in this study. The code base is located in the open project repository and available to reproduce computational experiments. The suggested approach has a wide range of applications, but special attention should be paid to the possible integration in order to improve the reliability of diagnostic systems with Internet of Things (IoT) technologies, the digital twins construction, agent-based modeling (ABM) for complex socio-economic processes, and cloud high-performance computing (HPC) that allows real time big data analytics.

Keywords:
digital signal processing, wavelet analysis, numerical methods, algorithms.

Acknowledgements:
This research was funded by the Ministry of Science and Higher Education of the Russian Federation grant no. 075-15-2024-525.

Citation:
Sakovich ND, Aksenov DA, Pleshakova ES, Gataullin ST. Localization and classification of anomalies in one-dimensional signals based on wavelet analysis and mathematical optimization methods. Computer Optics 2026; 50(1): 1683. DOI: 10.18287/COJ1683.

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