Combined use of two methods for analysis of nonstationary time series for solving forecasting and control problems Текст научной статьи по специальности «Физика»

Численное статистическое моделирование и методы Монте-Карло

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a size of a projection, an evacuation way. It gives a wide opportunities to state a simulation task and reproduce a real phenomena. Different approaches [3] from mathematically continuous models to pure discrete models are developed already. A discrete-continuous approach combines advantages of both approaches: people move in a continuous space, but there are only fixed number of directions where a person can move.

In the article one discrete-continuous model is considered. A validation of the SigmaEva evacuation module is given with respect to a very important case study - fundamental diagrams (flow-density dependence) under periodic boundary conditions.

References

1. Schadschneider A., Klingsch W., Kluepfel H., Kretz T., Rogsch C., Seyfried A. Evacuation Dynamics: Empirical Results, Modeling and Applications. Encyclopedia of Complexity and System Science. Springer, 2009 (3). P. 3142-3192.

2. Kirik E., Vitova T., Malyshev A., Popel E. On the Validation of Pedestrian Movement Models under Transition and Steady-state Conditions // Proceedings of the Ninth International Seminar on Fire and Explosion Hazards (21-26 April 2019 Saint Petersburg, Russia), edited by A. Snegirev, Vol. 2. P. 1271-1280.

Combined use of two methods for analysis of nonstationary time series for solving forecasting and control problems

S. I. Kolesnikova, A. D. Bogdanova

Saint-Petersburg State University of Aerospace Instrumentation

Email: skolesnikova@yandex.ru

DOI: 10.24411/9999-017A-2020-10251

Combined algorithm for time series analysis based on two following basic methods [1, 2]: the empirical mode decomposition and nuclear regression is considered. Essence of the presented algorithm is the sequential calculation of nuclear regressions and residues resulting in decomposition of the original series into an additive mixture of the number of regressions and residual series.

The paper provides a comparative review of three methods and their implementing algorithms for the analysis and forecasting of nonstationary time series, and also an algorithm is obtained on the basis of their combined application.

There are grounds for believing that the synthetic use of two popular nonparametric forecasting algorithms will lead to a more efficient forecasting algorithm, at least for solving a certain class of control problems [3, 4].

This work was (partially) supported by the Russian Foundation for Basic Research (grant 20-08-00747). References

1. Huang, H et al. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series. Analysis Proc. R. Soc. Lond. A. 1998. V. 454. P. 903-995.

2. Nadaraya E. On Estimating Regression. TV and its applications. 1964. V. 9(1). P. 141-142.

3. Kolesnikova S. Stochastic discrete nonlinear control system for minimum dispersion of the output variable n Advances in Intelligent Systems and Computing. 2019. V 986. P. 325-31.

4. Kolesnikova S. I. A multiple-control system for nonlinear discrete object under uncertainty.Optimization Methods and Software. 2019. Т. 34. № 3. P. 578-585. URL: https://doi.org/10.1080/10556788.2018.1472258.

Численные статистические алгоритмы решения обратных задач теории переноса излучения в атмосфере с учетом поляризации

А. С. Корда

Институт математики и математической геофизики СО РАН

Email: asc@osmf.sscc.ru

DOI: 10.24411/9999-017A-2020-30371

В данном докладе описывается ряд численных статистических методов, построенных авторами для решения обратных задачи теории переноса излучения в атмосфере с учетом поляризации. Рассматривается задача восстановления матрицы аэрозольного рассеяния атмосферы по наземным наблюдениям поляризационных характеристик излучения в альмукантарате Солнца, для ее решения предлагаются алгоритмы, основанные на адаптивном и комбинированном способах моделирования рассеяния в атмосфере при больших оптических толщах аэрозоля. С помощью численного статистического моделирования была исследована эффективность этих способов в ранее предложенном методе "предиктор-корректор" восстановления первых двух компонент матрицы рассеяния, позволяющем повысить точность восстановления индикатрисы рассеяния.

Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (проект № 18-01-00356)