title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ¾Ð²Ð½ÐµÐ¹ Ð²Ð¾Ð´Ñ Ð² Ð¿ÑÐµÐ·Ð¾Ð¼ÐµÑÑÐ°Ñ Ð½Ð° Ð³Ð¸Ð´ÑÐ¾ÑÐµÑ Ð½Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¾Ð¾ÑÑÐ¶ÐµÐ½Ð¸ÑÑ
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: Research of methods for predicting water levels in piezometers at hydraulic structures
Creators: name: ÐÐµÑÑ, ÐÐ½Ð´ÑÐµÐ¹
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: 2024
Subjects: Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÑÐ¾Ð²ÐµÐ½Ñ Ð²Ð¾Ð´Ñ Ð² Ð¿ÑÐµÐ·Ð¾Ð¼ÐµÑÑÐµ
Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÐµ ÑÐµÑÐ¸
forecasting
the water level in the piezometer
neural networks

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ¾Ð²Ð½ÐµÐ¹ Ð²Ð¾Ð´Ñ Ð² Ð¿ÑÐµÐ·Ð¾Ð¼ÐµÑÑÐ°Ñ Ð½Ð° Ð³Ð¸Ð´ÑÐ¾ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¾Ð¾ÑÑÐ¶ÐµÐ½Ð¸ÑÑÂ». 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) ÑÐ±Ð¾Ñ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¸ÑÑÐ¾Ð´Ð½ÑÑ Ð´Ð°Ð½Ð½ÑÑ; 2) ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð°ÑÑÐ¸ÑÐµÐºÑÑÑÑ Ð¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ¸ÑÑÐµÐ¼Ñ; 3) ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÑÐ»Ñ; 4) Ð¾ÑÐµÐ½ÐºÐ° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð², Ð²ÑÐ²Ð¾Ð´Ñ. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¾ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð´Ð°Ð½Ð½ÑÑ ÑÑÐ¾Ð²Ð½ÐµÐ¹ Ð²Ð¾Ð´Ñ Ð² Ð¿ÑÐµÐ·Ð¾Ð¼ÐµÑÑÐ°Ñ Ð¸ ÑÑÐ¾Ð²Ð½Ðµ Ð²ÐµÑÑÐ½ÐµÐ³Ð¾ Ð±ÑÐµÑÐ°. ÐÑÐ»Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ñ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾-Ð´Ð¸Ð°Ð³Ð½Ð¾ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ð¾Ð¹ Â«ÐÐµÐ´Ð°Ð» 2.0Â» ÐÐ Â«ÐÐÐÐÐ Ð¸Ð¼. Ð. Ð. ÐÐµÐ´ÐµÐ½ÐµÐµÐ²Ð°Â». ÐÑÐ»Ð¸ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ: - Ð¼ÐµÑÐ¾Ð´ ÑÐºÐ¾Ð»ÑÐ·ÑÑÐµÐ³Ð¾ ÑÑÐµÐ´Ð½ÐµÐ³Ð¾; - Ð¿ÑÐ¾ÑÑÐ¾Ðµ ÑÐºÑÐ¿Ð¾Ð½ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ðµ ÑÐ³Ð»Ð°Ð¶Ð¸Ð²Ð°Ð½Ð¸Ðµ; - ÑÑÐ¾Ð¹Ð½Ð¾Ðµ ÑÐºÑÐ¿Ð¾Ð½ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ðµ ÑÐ³Ð»Ð°Ð¶Ð¸Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð¾ Ð¼ÐµÑÐ¾Ð´Ñ Ð¥Ð¾Ð»ÑÑÐ°-ÐÐ¸Ð½ÑÐµÑÑÐ°; - ÑÐµÐºÑÑÑÐµÐ½ÑÐ½Ð°Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð°Ñ ÑÐµÑÑ LSTM. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð¼ÐµÑÑÐ¸ÐºÐ¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»ÑÑ ÐºÐ¾ÑÐµÐ½Ñ Ð¸Ð· ÑÑÐµÐ´Ð½ÐµÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¾ÑÐ¸Ð±ÐºÐ¸. ÐÐµÐ¹ÑÐ¾Ð½Ð½Ð°Ñ ÑÐµÑÑ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° Ð² Jupyter Notebook Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÑÐµÐ¹Ð¼Ð²Ð¾ÑÐºÐ° Keras Ð½Ð° ÑÐ·ÑÐºÐµ Python. ÐÐ»Ñ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ ÑÐµÑÐ¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð¸ÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð²Ð°ÑÐ¸Ð°ÑÐ¸Ð¸ Ð´Ð°Ð½Ð½ÑÑ, Ð²ÐºÐ»ÑÑÐ°Ñ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½ÑÐµ, Ð¼Ð½Ð¾Ð³Ð¾Ð¼ÐµÑÐ½ÑÐµ Ð¸ Ð¼Ð½Ð¾Ð³Ð¾Ð¼ÐµÑÐ½ÑÐµ Ñ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸ÐµÐ¹. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð½Ð° Ð´Ð°Ð½Ð½ÑÑ, Ð½Ðµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼ÑÑ Ð´Ð»Ñ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ ÐºÐ¾ÑÐ½Ñ Ð¸Ð· ÑÑÐµÐ´Ð½ÐµÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¾ÑÐ¸Ð±ÐºÐ¸: - Ð¼ÐµÑÐ¾Ð´ ÑÐºÐ¾Ð»ÑÐ·ÑÑÐµÐ³Ð¾ ÑÑÐµÐ´Ð½ÐµÐ³Ð¾ â 0.404; - Ð¿ÑÐ¾ÑÑÐ¾Ðµ ÑÐºÑÐ¿Ð¾Ð½ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ðµ ÑÐ³Ð»Ð°Ð¶Ð¸Ð²Ð°Ð½Ð¸Ðµ â 0.395; - ÑÑÐ¾Ð¹Ð½Ð¾Ðµ ÑÐºÑÐ¿Ð¾Ð½ÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ðµ ÑÐ³Ð»Ð°Ð¶Ð¸Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð¾ Ð¼ÐµÑÐ¾Ð´Ñ Ð¥Ð¾Ð»ÑÑÐ°-ÐÐ¸Ð½ÑÐµÑÑÐ° â 0.287; - ÑÐµÐºÑÑÑÐµÐ½ÑÐ½Ð°Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð°Ñ ÑÐµÑÑ LSTM (Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ) â 0.286; - ÑÐµÐºÑÑÑÐµÐ½ÑÐ½Ð°Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð°Ñ ÑÐµÑÑ LSTM (Ð¼Ð½Ð¾Ð³Ð¾Ð¼ÐµÑÐ½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ) â 0.477; - ÑÐµÐºÑÑÑÐµÐ½ÑÐ½Ð°Ñ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð°Ñ ÑÐµÑÑ LSTM (Ð¼Ð½Ð¾Ð³Ð¾Ð¼ÐµÑÐ½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ Ñ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸ÐµÐ¹) â 0.083. ÐÐ¾ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ°Ð¼ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐºÐ¾ÑÑÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ñ ÐÐÐ¡ Â«ÐÐµÐ´Ð°Ð» 2.0Â», ÑÐ´ÐµÐ»Ð°Ð½Ñ Ð²ÑÐ²Ð¾Ð´Ñ Ð¾ Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐ¼ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¸ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ð¸ ÑÐ¾Ð·Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸.
description: The topic of the final qualifying work is âResearch of methods for predicting water levels in piezometers at hydraulic structuresâ. Tasks that were solved during the research: 1) collection and analysis of initial data; 2) development of the architecture and model of the system; 3) development of a software module; 4) evaluation of the obtained results, conclusions. The study was performed on the basis of data on water levels in piezometers and the upstream level. A model of interaction with the information and diagnostic system âDedal 2.0â of JSC VNIIG B. E. Vedeneev was developed. The following forecasting models were considered: - the moving average method; - simple exponential smoothing; - triple exponential smoothing using the Holt-Winters method; - recurrent neural network LSTM. The root of the standard error was used as a metric. The neural network was developed in Jupyter Notebook using the Keras framework in Python. Different variations of data were used to train the network, including one-dimensional, multidimensional, and multidimensional with approximation. A study was conducted on data not used for training. As a result of the simulation, the following mean values of the root mean square error were obtained: - moving average method â 0.404; - simple exponential smoothing â 0.395; - triple exponential smoothing using the Holt-Winters method â 0.287; - recurrent neural network LSTM (one-dimensional data) â 0.286; - recurrent neural network LSTM (multidimensional data) â 0.477; - recurrent neural network LSTM (multidimensional data with approximation) â 0.083. Based on the simulation results, the model of interaction with the information and diagnostic âDedal 2.0â was adjusted, conclusions were drawn about the further use and development of the created model.