Analysis of the trajectories of non-differentiable random processes
Authors: Gusev A.S., Naydenov S.O. | Published: 08.09.2014 |
Published in issue: #9(654)/2014 | |
Category: Calculation and Design of Machinery | |
Keywords: path, extremum, maximum, random process, white noise, spectrum |
The calculations based on the analysis of random processes in mechanical systems are currently being increasingly used. This is especially true when the behavior of such systems is analyzed over time. The article deals with the analysis of the trajectories of differentiable and non-differentiable random processes. The objective of this analysis is to define the expected number of zeros, extrema, inflection points of the trajectory, and the probability distribution of the maxima and absolute maxima of random processes. The spectral densities of nondifferentiable random processes are represented as a product of two complex conjugate functions (quasi-spectra), with white noises being excluded. This makes it possible to solve all problems stated for simple processes. The spectra of complex processes running in systems with two or more degrees of freedom are represented in the form of delta-functions of their natural frequencies. Simple formulas are obtained for determining the parameters of the trajectories. A beam loaded by white noise forces is considered as an example.
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