The article proposes a model of a seismic signal based on the use of the theory of random functions. To study the characteristics of any system by mathematical methods, including machine methods, it is necessary to formalize this process, that is, a mathematical model is built. The central place is given to a mathematical description of the motion of soil particles in the real process of their oscillations. To this end, probabilistic methods are used to represent random functions in the form of harmonic series, a spectral decomposition of the dispersion of a random process. This approach to modeling a seismic signal is controversial, since it is known that the structure of a seismic signal is determined by the source mechanism and the laws of the process of propagation of seismic wave signals in an elastic half-space. The main thing in the article is the development of a method for estimating the motion parameters of soil particles that determine the force effect on a building structure based on an irregular wave process model. At the same time, the background of mechanical noise always complicates the seismic signal, which is a random process. Subject. Mathematical description of the motion of soil particles in the real process of their oscillations. Materials and methods. General wave process theory for ground motion modeling. Probabilistic methods for representing random functions as harmonic series, spectral decomposition of the variance of a random process. Results. The developed methodology for calculating the parameters of irregular wave processes was tested when studying the effect of sea waves on moving objects. Conclusions. The development of the method of estimating the motion parameters of soil particles that determine the force impact on a building structure based on the irregular wave process model makes it possible to obtain an objective assessment of physical phenomena and processes at the stage of assessing the strength characteristics of objects during their operation.
stationarity of random processes, correlation function, spectral density, normalized spectral density, spectrum of random process, reliability of building structures
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