Abstract
The paper is concerned with the analysis of the simultaneous effect of a random perturbation and white noise in the coefficient of the system on its response. The excitation of the system of the 1st order is described by the sum of a deterministic signal and additive white noise, which is partly correlated with a parametric noise. The random perturbation in the parameter is considered statistics in a set of realizations. It reveals that the probability density of these perturbations must be limited in the phase space, otherwise the system would lose the stochastic stability in probability, either immediately or after a certain time. The width of the permissible zone depends on the intensity of the parametric noise, the extent of correlation with the additive excitation noise, and the type of probability density. The general explanation is demonstrated on cases of normal, uniform, and truncated normal probability densities.
Highlights
The parameters of dynamic systems are usually burdened by random noises due to the imperfect function of the system’s external factors, etc
The problem concerns the investigation of response statistics of a typical system, and the probable limits within which the response will occur under these conditions
The width of the admissible zone of every phase variable is dependent on the parametric noise intensity, the extent of its correlation with the additive excitation noise, and the type of probability density of imperfections
Summary
The parameters of dynamic systems are usually burdened by random noises due to the imperfect function of the system’s external factors, etc. The problem concerns the investigation of response statistics of a typical system, and the probable limits within which the response will occur under these conditions In such a case, the coefficients have two sources of perturbations: a random noise, usually introduced as the time variable Gaussian white noise, and random imperfections, representing the statistics in the framework of realizations of systems of the same type, described by a certain density of probability. The coefficients have two sources of perturbations: a random noise, usually introduced as the time variable Gaussian white noise, and random imperfections, representing the statistics in the framework of realizations of systems of the same type, described by a certain density of probability In this respect the fact of whether the non-zero density of probability is confined onto a limited area of the phase space is of fundamental significance.
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