Entropy estimation of a dynamical system via a contact interaction

V. Deeva, S. Slobodyan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Over the last several decades the problem of predicting dynamical contact has played a major role in the effort to understand the contact interaction between sliding surfaces. The opportunity for direct visual observation of surfaces interaction is limited thereby the study of contact area formed by wear particles has stayed unsatisfactory. Entropy models have become popular statistical models in surface damage and other contact problems, and can be useful tools for obtaining estimates of dynamical systems. We propose an alternative approach for the problem of entropy estimation, based on the Kolmogorov–Sinai entropy for a dynamical system. In this paper, we extend a previous spatial stochastic model of the bounded entropy for binary space with different sets. We consider the dynamical contact between two surfaces with three probabilistic sets of the surface contact caused by the existence of microscopic surface roughness (the set of direct contact, the non-contact set, the set of “third body” – by wear particles). Based on this model, using the Kolmogorov entropy, we find the lower and the upper bounds of entropy of the dynamical system for these three probabilistic sets. Furthermore, we make sure that the value of entropy would be within the bounds of a range of ln 2; ln 3; 2⋅ln 2 depending on the surface states.

Original languageEnglish
Title of host publicationSafety and Reliability – Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017
EditorsMarko Cepin, Radim Briš
PublisherCRC Press/Balkema
Pages2577-2584
Number of pages8
ISBN (Print)9781138629370
DOIs
Publication statusPublished - 1 Jan 2017
Event27th European Safety and Reliability Conference, ESREL 2017 - Portorož, Slovenia
Duration: 18 Jun 201722 Jun 2017

Publication series

NameSafety and Reliability - Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017

Conference

Conference27th European Safety and Reliability Conference, ESREL 2017
CountrySlovenia
CityPortorož
Period18.6.1722.6.17

Fingerprint

Dynamical systems
Entropy
Wear of materials
Surface states
Stochastic models
Surface roughness

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality

Cite this

Deeva, V., & Slobodyan, S. (2017). Entropy estimation of a dynamical system via a contact interaction. In M. Cepin, & R. Briš (Eds.), Safety and Reliability – Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017 (pp. 2577-2584). (Safety and Reliability - Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017). CRC Press/Balkema. https://doi.org/10.1201/9781315210469-327

Entropy estimation of a dynamical system via a contact interaction. / Deeva, V.; Slobodyan, S.

Safety and Reliability – Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017. ed. / Marko Cepin; Radim Briš. CRC Press/Balkema, 2017. p. 2577-2584 (Safety and Reliability - Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Deeva, V & Slobodyan, S 2017, Entropy estimation of a dynamical system via a contact interaction. in M Cepin & R Briš (eds), Safety and Reliability – Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017. Safety and Reliability - Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017, CRC Press/Balkema, pp. 2577-2584, 27th European Safety and Reliability Conference, ESREL 2017, Portorož, Slovenia, 18.6.17. https://doi.org/10.1201/9781315210469-327
Deeva V, Slobodyan S. Entropy estimation of a dynamical system via a contact interaction. In Cepin M, Briš R, editors, Safety and Reliability – Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017. CRC Press/Balkema. 2017. p. 2577-2584. (Safety and Reliability - Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017). https://doi.org/10.1201/9781315210469-327
Deeva, V. ; Slobodyan, S. / Entropy estimation of a dynamical system via a contact interaction. Safety and Reliability – Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017. editor / Marko Cepin ; Radim Briš. CRC Press/Balkema, 2017. pp. 2577-2584 (Safety and Reliability - Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017).
@inproceedings{8357daeb89d3422e9ecfefeea2817af8,
title = "Entropy estimation of a dynamical system via a contact interaction",
abstract = "Over the last several decades the problem of predicting dynamical contact has played a major role in the effort to understand the contact interaction between sliding surfaces. The opportunity for direct visual observation of surfaces interaction is limited thereby the study of contact area formed by wear particles has stayed unsatisfactory. Entropy models have become popular statistical models in surface damage and other contact problems, and can be useful tools for obtaining estimates of dynamical systems. We propose an alternative approach for the problem of entropy estimation, based on the Kolmogorov–Sinai entropy for a dynamical system. In this paper, we extend a previous spatial stochastic model of the bounded entropy for binary space with different sets. We consider the dynamical contact between two surfaces with three probabilistic sets of the surface contact caused by the existence of microscopic surface roughness (the set of direct contact, the non-contact set, the set of “third body” – by wear particles). Based on this model, using the Kolmogorov entropy, we find the lower and the upper bounds of entropy of the dynamical system for these three probabilistic sets. Furthermore, we make sure that the value of entropy would be within the bounds of a range of ln 2; ln 3; 2⋅ln 2 depending on the surface states.",
author = "V. Deeva and S. Slobodyan",
year = "2017",
month = "1",
day = "1",
doi = "10.1201/9781315210469-327",
language = "English",
isbn = "9781138629370",
series = "Safety and Reliability - Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017",
publisher = "CRC Press/Balkema",
pages = "2577--2584",
editor = "Marko Cepin and Radim Briš",
booktitle = "Safety and Reliability – Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017",

}

TY - GEN

T1 - Entropy estimation of a dynamical system via a contact interaction

AU - Deeva, V.

AU - Slobodyan, S.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Over the last several decades the problem of predicting dynamical contact has played a major role in the effort to understand the contact interaction between sliding surfaces. The opportunity for direct visual observation of surfaces interaction is limited thereby the study of contact area formed by wear particles has stayed unsatisfactory. Entropy models have become popular statistical models in surface damage and other contact problems, and can be useful tools for obtaining estimates of dynamical systems. We propose an alternative approach for the problem of entropy estimation, based on the Kolmogorov–Sinai entropy for a dynamical system. In this paper, we extend a previous spatial stochastic model of the bounded entropy for binary space with different sets. We consider the dynamical contact between two surfaces with three probabilistic sets of the surface contact caused by the existence of microscopic surface roughness (the set of direct contact, the non-contact set, the set of “third body” – by wear particles). Based on this model, using the Kolmogorov entropy, we find the lower and the upper bounds of entropy of the dynamical system for these three probabilistic sets. Furthermore, we make sure that the value of entropy would be within the bounds of a range of ln 2; ln 3; 2⋅ln 2 depending on the surface states.

AB - Over the last several decades the problem of predicting dynamical contact has played a major role in the effort to understand the contact interaction between sliding surfaces. The opportunity for direct visual observation of surfaces interaction is limited thereby the study of contact area formed by wear particles has stayed unsatisfactory. Entropy models have become popular statistical models in surface damage and other contact problems, and can be useful tools for obtaining estimates of dynamical systems. We propose an alternative approach for the problem of entropy estimation, based on the Kolmogorov–Sinai entropy for a dynamical system. In this paper, we extend a previous spatial stochastic model of the bounded entropy for binary space with different sets. We consider the dynamical contact between two surfaces with three probabilistic sets of the surface contact caused by the existence of microscopic surface roughness (the set of direct contact, the non-contact set, the set of “third body” – by wear particles). Based on this model, using the Kolmogorov entropy, we find the lower and the upper bounds of entropy of the dynamical system for these three probabilistic sets. Furthermore, we make sure that the value of entropy would be within the bounds of a range of ln 2; ln 3; 2⋅ln 2 depending on the surface states.

UR - http://www.scopus.com/inward/record.url?scp=85061381217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061381217&partnerID=8YFLogxK

U2 - 10.1201/9781315210469-327

DO - 10.1201/9781315210469-327

M3 - Conference contribution

AN - SCOPUS:85061381217

SN - 9781138629370

T3 - Safety and Reliability - Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017

SP - 2577

EP - 2584

BT - Safety and Reliability – Theory and Applications - Proceedings of the 27th European Safety and Reliability Conference, ESREL 2017

A2 - Cepin, Marko

A2 - Briš, Radim

PB - CRC Press/Balkema

ER -