Process Modeling for Energy Usage in “Smart House” System with a Help of Markov Discrete Chain

<- Back to II. Mechanical Engineering & Physics Vol. 7

Cite the paper

Victor Kravets, Vladimir Kravets, Olexiy Burov (2016). Process Modeling for Energy Usage in “Smart House” System with a Help of Markov Discrete Chain. Mechanics, Materials Science & Engineering, Vol 7, pp. 85-96, doi:10.13140/RG.2.2.34948.32643

Authors: Victor Kravets, Vladimir Kravets, Olexiy Burov

ABSTRACT. Method for evaluating economic efficiency of technical systems using discrete Markov chains modelling illustrated by the system of “Smart house”, consisting, for example, of the three independently functioning elements. Dynamic model of a random power consumption process in the form of a symmetrical state graph of heterogeneous discrete Markov chain is built. The corresponding mathematical model of a random Markov process of power consumption in the “smart house” system in recurrent matrix form is being developed. Technique of statistical determination of probability of random transition elements of the system and the corresponding to the transition probability matrix of the discrete inhomogeneous Markov chain are developed. Statistically determined random transitions of system elements power consumption and the corresponding distribution laws are introduced.

The matrix of transition prices, expectations for the possible states of a system price transition and, eventually, the cost of Markov process of power consumption throughout the day.

Keywords: smart house, Markov discrete chains, possible states, transition probabilities matrix, transition costs matrix, mathematical expectations of transitions costs, cost of Markov random process

DOI 10.13140/RG.2.2.34948.32643

References

[1] G. W. Hart, Nonintrusive appliance load monitoring, Proceedings of the IEEE, vol. 80, no. 12, Dec. 1992, pp. 1870-1891.

[2] M. Weiss, A. Helfenstein, F. Mattern, T. Staake, Leveraging smart meter data to recognize home appliances, Proceedings of the IEEE International Conference on Pervasive Computing and Communications (PerCom 2012), Lugano, Switzerland, March 2012, pp. 190-197.

[3] Alan P. Rossiter (Editor), Beth P. Jones (Editor), Energy management and efficiency for the process industries, AICHE Inc., John&Sons Inc., Hoboken, New Jersey, 2015, 400 p., ISBN: 978-1-118-83825-9.

[4] B. Ayyub, R. Mccuen, Probability, statistics & reliability for engineers, CRC Press, New York, 1997, 663 p.

[5] A. Birolini, Quality and Reliability of Technical Systems: Theory, Practice, Management, Edition Springer, 2004. DOI: 10.1007/978-3-642-97983-5.

[6] V. Kravets, Vl. Kravets, O. Burov, Reliability of Systems. Part 1. Statics of Failures. Lap Lambert Academic Publishing, Omni Scriptum GmbH & Co. KG., 2016.

[7] E.S. Ventcel’, Issledovanie operacij [Operations research], Moscow, Sovetskoe radio Publ., 1972, 552 p. [in Russian].

[8] E.S. Ventcel’, L.A. Ovcharov, Theory of random processes and its engineering application, Moscow, Nauka Publ., 1991, 384 p.

[9] V. Kravets, Vl. Kravets, O. Burov, Reliability of Systems. Part 2. Dynamics of Failures. Lap Lambert Academic Publishing, Omni Scriptum GmbH & Co. KG., 2016.

[10] V.A. Kotelnikov, R.A. Silverman, Theory of optimum noise immunity, New York, Dover Publ., 1968, 140 p.

[11] Victor Kravets, Vladimir Kravets & Olexiy Burov (2016). Matrix Method for Assessing Economic Efficiency of Systems Simulated with Asymmetric Markov Discrete Chains, Automation, Software Development & Engineering Journal, ISSN 2415-6531

 

Creative Commons Licence
Mechanics, Materials Science & Engineering Journal by Magnolithe GmbH is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at www.mmse.xyz.