Mathematical modeling of the duration and frequency of water consumption by water collection devices of a residential building

About the authors:

Dmitrii E. Polivanov, Postgraduate Student, Department of Information Systems and Technologies, Faculty of Environmental Engineering and Municipal Services, Saint Petersburg State University of Architecture and Civil Engineering, Saint Petersburg, Russia; dmitry_polivanov@mail.ru, https://orcid.org/0000-0002-4215-1208

Alexey A. Semenov, Cand. Sci. (Tech.), Associate Professor, Department of Information Systems and Technologies, Faculty of Environmental Engineering and Municipal Services, Saint Petersburg State University of Architecture and Civil Engineering, Saint Petersburg, Russia; sw.semenov@gmail.com, https://orcid.org/0000-0001-9490-7364

Liya V. Movsesova, Cand. Sci. (Phys.-Math.), Associate Professor, Department of Informatics, Faculty of Environmental Engineering and Municipal Services, Saint Petersburg State University of Architecture and Civil Engineering, Saint Petersburg, Russia; movse@lan.spbgasu.ru, https://orcid.org/0000-0002-0776-0374

Abstract:

The actual operating modes of water supply systems cannot be characterized in sufficient detail and accurately by several values obtained during calculations using traditional deterministic methods and models. Nevertheless, the task of obtaining comprehensive information about the modes of operation of water supply systems can be solved using simulation modeling, which allows detailed analysis of the variability of water consumption over time. At the same time, the most important components of this process, which should be taken into account when modeling, are the intensity, duration and frequency of water consumption.
This article discusses the mathematical description of the variability of the duration and frequency of water consumption by the most common types of water collection devices (kitchen sink and bathtub faucets / shower cubicle, toilet bowl with flush tank, washing machine and dishwasher) using water from the water supply system of a residential building.
The aim of the work is to evaluate and substantiate the theoretical laws of the distribution of the duration of water consumption by the most common types of water collection devices, as well as the frequency (probability) of their use during the most characteristic period of water consumption (day).
The paper presents the results of a study of the duration and frequency of water consumption by the most common types of water collection devices. The analysis of histograms and graphs based on the obtained statistical data, as well as estimates of the main numerical characteristics, is presented. The evaluation and substantiation of the theoretical laws of the distribution of duration and frequency (probability) of water consumption has been carried out.
As a result of the performed research, a variant of the mathematical description of the nature of variability in the duration of periods of continuous water consumption by the most common types of water collection devices, as well as the frequency (probability) of their use during the day, is proposed.

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