Speakers
Description
The presentation we will describe the mathematical model of an oscillator with damping, whose vibrations were forced by a random series of impulses. Under appropriate assumptions regarding random variables, in the model, the vibrations of the system become a process which, in the limit as time tends to infinity, is stationary and ergodic. For value of the impulses, which are independent discrete random variables, for the time intervals between impulses, which are independent continuous random variables for which the function of probability density assumes the form of exponential distribution, the probabilities are computed from the system of equations. In the presentation we indicate the errors in computing of distributions of impulses, which issue from the fact that we apply the model for analysis of vibrations of the system within several minutes. In this case the mathematical model of an oscillator is understood in accord with the terminology used for defining statistical models as a formalized description of a certain theory or causal situations that are assumed to generate the observed data. Simulation studies aimed at detecting distributions of impulses involve an analysis of data recorded in the form of spatial-temporal matrices. Analyzing hundreds of courses we check when it is possible to apply a mathematical model, and when we have to use artificial intelligence algorithms in order to solve an inverse problem.
