Open AccessInvestigation of error in evaluation of spectral statistical characteristics of numerical solution of stochastic dynamic system
Author(s) -
Yaroslav Beskrovnii,
Олексій Ларін
Publication year - 2021
Publication title -
vestnik nacionalʹnogo tehničeskogo universiteta "hpi". dinamika i pročnostʹ mašin
Language(s) - English
Resource type - Journals
ISSN - 2078-9130
DOI - 10.20998/2078-9130.2021.1.232387
Subject(s) - numerical integration , algorithm , mathematics , numerical analysis , approximation error , order of accuracy , interval (graph theory) , differential equation , signal (programming language) , computer science , numerical stability , mathematical analysis , combinatorics , programming language
In this paper, an algorithm for numerical simulations is developed for calculating a discrete dynamic system with a stochastic perturbation and an analysis of the quality of numerical solutions is carried out. For this, an algorithm for the numerical solution of a second-order differential equation with a stochastic right-hand side was developed and this algorithm was implemented as a program. The next step was to carry out a set of computational studies by varying the parameters of numerical integration with the subsequent assessment of their impact on the error and accuracy of simulations. To estimate the spectral density, the Welch periodogram method was used. To check the quality of simulations and assess the accuracy of solutions, it is proposed to compare the results of numerical integration and subsequent digital processing with analytical solutions that are known for the linear problem, given by the equation. As a result of the work, a comparative analysis of the dispersion of displacements relative to the lengths of signals from a different number of blocks was carried out, into which the signal is divided for the Welch method; the confidence interval of the error at different signal lengths and the confidence interval of the error with a different number of blocks at a certain signal length. Comparison of the variance with a different number of blocks showed that with a signal length of 30 s and from 90 s, there is a slight scatter of the variance values within an error of ± 5%.