Responses of first-order dynamical systems to Matérn, Cauchy, and Dagum excitationsReport as inadecuate




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1 Capital Normal University Beijing 2 Department of Mechanical Science and Engineering Urbana 3 UTFSM - Universidad Tecnica Federico Santa Maria Valparaiso

Abstract : The responses of dynamical systems under random forcings is a well-understood area of research. The main tool in this area, as it has evolved over a century, falls under the heading of stochastic differential equations. Most works in the literature are related to random forcings with a known parametric spectral density. This paper considers a new framework: the Cauchy and Dagum covariance functions indexing the random forcings, do not have a closed form for the associated spectral density, while allowing decoupling of the fractal dimension and Hurst effect. On the basis of a first-order stochastic differential equation, we calculate the transient second-order characteristics of the response under these two covariances and make comparisons to responses under white, Ornstein–Uhlenbeck, and Matérn noises.





Author: Lihua Shen - Martin Ostoja-Starzewski - Emilio Porcu -

Source: https://hal.archives-ouvertes.fr/



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