Determination of the trend component of a time series by real-time means in technical operation of complex energy facilities

Volodymyr Myrhorod, Iryna Hvozdeva

Abstract


This study proposes an approach to determine the trend component of the time series of technical condition registration during the long-term operation of complex energy facilities by real-time means. The relevance of solving the specified scientific and applied problem is due to the need for a current analysis of the technical condition of the specified facilities to establish the possibility of their operation according to the established resource. An analysis and comparison of methods for assessing the trend component of time series regarding the possibility of their implementation by real-time means is conducted using analytical justification and solution of a test case, and analysis of real data during technical operation of a complex energy facility built on the basis of a gas turbine engine.The proposed methods for estimating the trend component of time series by real-time means, namely, the considered methods of exponential smoothing, Kalman filtering, and singular spectral analysis, differ significantly in terms of accuracy and speed. The methods of exponential smoothing and Kalman filtering and the corresponding recursive algorithms, which are implemented in the form of filters with an infinite impulse characteristic, provide the most achievable speed. However, such processing time series methods have a methodological speed error. For the first time, a new modification of the singular spectral analysis method for time series is proposed, enabling the development of high-precision, real-time algorithms. The speed of such a method for determining the trend component of the time series is limited only by the dimension of the analysis window. This study proposes a two-stage approach to the analysis of time series of technical condition registration during long-term operation of complex energy facilities. The first of these stages involves determining a trend using known trend statistics. The next stage is to determine the trend component using known and proposed methods.


Keywords


technical condition; mathematical modeling; complex energy facilities; gas turbine engine; time series; statistical model; trend assessment

References


Anderson, O. D. Time series analysis and forecasting. Butterworths, London, 1976. 182 p.

Kendall, M., & Stuart, A. The advanced theory of statistics. Hafner, New York, 1979, Vol. 2. 748 p.

Box, G. E. P., & Jenkins, G. M. Time series analysis: Forecasting and control. Holden Day, San Francisco, 1976. 575 p.

Montgomery, D. C., Johnson, L. A., & Gardiner, J. S., Forecasting and time series analysis. McGraw-Hill, New York, 1990. 300 р.

Shumway, R. H. Applied statistical time series analysis. Prentice Hall, New York, 1988, 384 p.

Wei, W. W. Time series analysis: Univariate and multivariate methods. Addison-Wesley, New York, 1989, 640 p.

Hvozdeva, I., Myrhorod, V., & Derenh, Y. The Method of Trend Analysis of Parameters Time Series of Gas-turbine Engine State. In AMiTaNS’17, AIP Conf. Proc., vol. 1895, edited by M. D. Todorov (American Institute of Physics, Melville, NY, 2017), pp. 030002-1-030002-9. doi: 10.1063/1.5007361.

Myrhorod, V., Hvozdeva, I., & Demirov, V. Some Interval and Trend Statistics with Non-Gaussian Initial Data Distribution. In AMiTaNS’18, AIP Conf. Proc., vol. 2025, edited by M. D. Todorov (American Institute of Physics, Melville, NY, 2018), pp. 040011-1-040011-12, doi: 10.1063/1.5064895

Myrhorod, V., Hvozdeva, I., & Derenh, Y. Two-dimensional trend analysis of time series of complex technical objects diagnostic parameters. 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19, AIP Conference Proceedings, 2019, vol. 2164, no. 1, pp. 040011-1-040011-12. doi: 10.1063/1.5130815.

Wald, A., &Wolfowitz, J. An exact test for randomness in the non-parametric case based on serial correlation. AMS, 1943, vol. 14, pp. 378-388.

Bartels, R. The rank version of von Neumann’s ratio test for randomness. JASA, 1982, vol. 77, no. 377. pp. 40-46.

Korn, G. A., & Korn, T. M. Mathematical Handbook. McGraw-Hill Book, 1968. 832 p.

Dorf, R. C., & Bishop., R. H. Modern Control Systems. Prentice Hall, 2004. 832 p.

Van Loan, Ch. F. Generalizing the singular value decomposition. SIAM J. Numer., Anal., 1976, no. 13, pp. 76–83.

Ed. Danilova, D. L., & Zhiglyavskii, A. A. The main components of the time series: the method of "Caterpillar, C.-P. Univ, 1997.

Marple, S. L. Digital Spectral Analysis: With Application. Prentice-Hall, N.Y., 1987. 232 p.




DOI: https://doi.org/10.32620/aktt.2025.4sup1.23