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On the Poisson XLindley process

Sakri Amine, Seghier Fatma-Zohra, Vinoth Raman, Zeghdoudi Halim

Mathematica Applicanda

2023

Vol. 51, no. 2

273--289

Due to their advantages, non-homogeneous Poisson processes have so far been used extensively in a variety of practical applications. They do, however, also have important application-related limits. A novel counting process model named the Poisson–XLindley Process was created to get around these restrictions. We shall demonstrate that this new model lacks such constraints. These fundamental stochastic properties of the process are derived. Additionally, the dependence structure is examined along with the new idea of positively dependent increments. Generic versions of several of the features derived in this article will be offered. This is an innovative concept related to counting processes, which allows the probability function to be described explicitly. It is one of its major contributions

Niejednorodne procesy Poissona są szeroko stosowane w modelowaniu chociaż mają istotne ograniczenia jesli chcemy uzyskać wysoką zgodność modelu z zjawiskiem. W celu usunięcia tych problemów wprowadzamy zmodyfikowany opis procesu liczącego, nazwany Procesem Poissona XLindleya. W pracy pokazujemy przełamanie istotnych ograniczeń niejednorodnego procesu Poissona przez nowy model. Wyprowadzono podstawowe właściwości probabilistyczne tego procesu, badana jest równiez struktura zależności przyrostów z wykorzystaniem idei przyrostów dodatnio zależnych. W pracy pokazano ogólną wersję funkcjonałów od tego procesu. Ta innowacyjna koncepcja procesu liczącego, pozwalająca na jawny formuły opisujące rozkłady prawdopodobieństwa, jest jednym z jej głównych walorów pracy.

Optimisation of the parameters of a vibration damper installed on a historic bridge

Podwórna Monika, Grosel Jacek

Architecture Civil Engineering Environment

2023

Vol. 16, no. 4

93--101

The paper presents theoretical analyses of renovating a historical bridge in order to decrease stresses. The installation of additional equipment, including a vibration absorber, is relatively easy to perform if such a need is indicated by the current bridge diagnostics or the monitoring of the structure’s vibrations. Moreover, absorbers could be mounted in such a way as not to alter the appearance of the historic structure. The authors focused on the problem of optimising the cooperation between a dynamic vibration absorber (DVA) and a structure under dynamic load moving with constant velocity. A simple degree of freedom (SDOF) system – as a model of the absorber and a multi-degree of freedom (MDOF) system – as the primary structure, were adopted in the calculations. Every force is regarded as a random variable, as well as interarrivals of moving forces. Two different situations and solutions were presented. The first case is when the stream of moving forces with a constant velocity is modelled as the filtered Poisson process. The second one when one of the forces is located in the point of the beam in which the response of the beam has the maximum value.