title: Ð¡Ð¾Ð·Ð´Ð°Ð½Ð¸Ðµ ÑÐ¸ÑÑÐ¾Ð²Ð¾Ð³Ð¾ Ð´Ð²Ð¾Ð¹Ð½Ð¸ÐºÐ° Ð¾Ð±ÑÐµÐºÑÐ° ÑÐµÐ¿Ð»Ð¾ÑÐ½Ð°Ð±Ð¶ÐµÐ½Ð¸Ñ Ð´Ð»Ñ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð½ÐµÑÑÐ°ÑÐ½ÑÑ Ð¸ Ð°Ð²Ð°ÑÐ¸Ð¹Ð½ÑÑ ÑÐ¸ÑÑÐ°ÑÐ¸Ð¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of a digital twin of a heat supply facility for emergency forecasting system
Creators: name: ÐÐ°Ð²ÑÐ¸Ð»Ð¾Ð²Ð°, ÐÐ°Ð»ÐµÑÐ¸Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: ÑÐ¸ÑÑÐ¾Ð²Ð¾Ð¹ Ð´Ð²Ð¾Ð¹Ð½Ð¸Ðº
Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð²
Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ ÑÐµÐ³ÑÐµÑÑÐ¸Ñ
SARIMA
Ð¸ÑÐºÑÑÑÑÐ²ÐµÐ½Ð½Ð°Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð°Ñ ÑÐµÑÑ
LSTM
digital twin
time series forecasting
linear regression
artificial neural network

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð² Ð´Ð»Ñ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ ÑÐ¸ÑÑÐ¾Ð²Ð¾Ð³Ð¾ Ð´Ð²Ð¾Ð¹Ð½Ð¸ÐºÐ° Ð¾Ð±ÑÐµÐºÑÐ° ÑÐµÐ¿Ð»Ð¾ÑÐ½Ð°Ð±Ð¶ÐµÐ½Ð¸Ñ. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ:
1. ÐÐ·ÑÑÐµÐ½Ð¸Ðµ Ð¾Ð±ÑÐµÐºÑÐ° ÑÐµÐ¿Ð»Ð¾ÑÐ½Ð°Ð±Ð¶ÐµÐ½Ð¸Ñ.
2. ÐÐ·ÑÑÐµÐ½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð².
3. ÐÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸, ÑÐµÐ·Ð¾Ð½Ð½Ð¾Ð¹ Ð°Ð²ÑÐ¾ÑÐµÐ³ÑÐµÑÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ ÑÐºÐ¾Ð»ÑÐ·ÑÑÐµÐ¹ ÑÑÐµÐ´Ð½ÐµÐ¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸ Ð¸ÑÐºÑÑÑÑÐ²ÐµÐ½Ð½Ð¾Ð¹ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÑÐ¸ LSTM.
4. ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ ÑÐ¸ÑÑÐ¾Ð²Ð¾Ð³Ð¾ Ð´Ð²Ð¾Ð¹Ð½Ð¸ÐºÐ° Ð¾Ð±ÑÐµÐºÑÐ° ÑÐµÐ¿Ð»Ð¾ÑÐ½Ð°Ð±Ð¶ÐµÐ½Ð¸Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¸ÑÐºÑÑÑÑÐ²ÐµÐ½Ð½Ð¾Ð¹ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÑÐ¸.
Ð Ð°Ð±Ð¾ÑÐ° Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° Ð½Ð° Ð±Ð°Ð·Ðµ Ð¾Ð±ÑÐµÐºÑÐ° ÑÐµÐ¿Ð»Ð¾ÑÐ½Ð°Ð±Ð¶ÐµÐ½Ð¸Ñ, Ð³Ð´Ðµ ÑÐ¾Ð±Ð¸ÑÐ°Ð»Ð¸ÑÑ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¸Ñ Ñ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð² ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð¸ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ. ÐÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð² Ð¸ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ñ Ð¼ÐµÑÐ¾Ð´Ñ Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð¸ Ð³Ð»ÑÐ±Ð¾ÐºÐ¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ. ÐÐ»Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð´Ð°Ð½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð±ÑÐ»Ð¸ Ð½Ð°Ð¿Ð¸ÑÐ°Ð½Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð½Ð° ÑÐ·ÑÐºÐµ Python.
Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ» Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÑÐµÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¸ ÑÐ´ÐµÐ»Ð°Ð½ Ð²ÑÐ²Ð¾Ð´, ÑÑÐ¾ Ð¼Ð¾Ð´ÐµÐ»Ñ LSTM Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÐµÑ Ð»ÑÑÑÐ¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÑÐ¸ Ð±ÑÐ» Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½ ÑÐ¸ÑÑÐ¾Ð²Ð¾Ð¹ Ð´Ð²Ð¾Ð¹Ð½Ð¸Ðº Ð¾Ð±ÑÐµÐºÑÐ° ÑÐµÐ¿Ð»Ð¾ÑÐ½Ð°Ð±Ð¶ÐµÐ½Ð¸Ñ.
description: This work is devoted to research in the field of time series forecasting for developing a digital twin of a heat supply facility. The research set the following goals:
1. Exploring the heat supply facility.
2. Studying time series forecasting methods.
3. Practical implementation of linear regression, seasonal autoregressive integrated moving average models and artificial neural network LSTM.
4. Building a digital twin of a heat supply facility based on an artificial neural network.
The work was performed based on a heat supply facility, where readings from temperature and pressure sensors were collected. Research has been conducted in the field of time series forecasting and machine learning and deep learning methods have been applied. Python programs were written to implement these methods.
As a result, three forecasting methods were analysed, and it was concluded that the LSTM model shows the best results. A digital double of the heat supply facility was built based on a neural network.