title: Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¼Ð°ÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÑÐµÐ½Ð¸Ñ Ð²Ð¸ÑÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð·Ð¾Ð½Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð² Ð²Ð¸Ð±ÑÐ°ÑÐ¸Ð¸ Ð½Ð° Ð²ÑÑÐ¾ÐºÐ¾ÑÐºÐ¾ÑÐ¾ÑÑÐ½Ð¾Ð¼ Ð¾ÑÐµÐ²Ð¾Ð¼ ÐºÐ¾Ð¼Ð¿ÑÐµÑÑÐ¾ÑÐµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Comparison of different machine learning methods for virtual sensing applied to vibration sensor technology on a high-speed axial compressor
Creators: name: ÐÑÐ¾ÑÑ, Ð¯Ð½
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: ÐÐµÐ¹ÑÐ¾Ð½Ð½ÑÐµ ÑÐµÑÐ¸
ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÐÐ¾Ð¼Ð¿ÑÐµÑÑÐ¾ÑÑ Ð¾ÑÐµÐ²ÑÐµ
ÐÐ°ÑÑÐ¸ÐºÐ¸
ÐÐ¸Ð±ÑÐ°ÑÐ¸Ñ
Ð²Ð¸ÑÑÑÐ°Ð»ÑÐ½Ð¾Ðµ Ð·Ð¾Ð½Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¸Ð´ÐµÐ½ÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸
ÑÐµÐ³ÑÐµÑÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð·
ÑÐ¸ÑÑÐ¾Ð²ÑÐµ Ð´Ð²Ð¾Ð¹Ð½Ð¸ÐºÐ¸
ÑÐ¸Ð»ÑÑÑÑ ÐÐ°Ð»Ð¼Ð°Ð½Ð°
ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐ½ÐµÑÐ³Ð¸Ð¸
virtual sensing
model identification
regression analysis
digital twins
kalman filters
statistical energy analysis

description: ÐÐ¸ÑÑÑÐ°Ð»ÑÐ½Ð¾Ðµ Ð·Ð¾Ð½Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ (Virtual Sensing - VS) - Ð¼ÐµÑÐ¾Ð´ Ð·Ð°Ð¼ÐµÐ½Ñ ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¸Ñ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð² Ð½Ð° ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ¸ÑÑÐµÐ¼Ð°Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½ÑÐ¼ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¾Ð¼. ÐÐ»Ñ ÑÑÐ¾Ð³Ð¾ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼Ð¾ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°ÑÑ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÑÑ Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð´Ð°ÑÑÐ¸ÐºÐ° Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð´ÑÑÐ³Ð¸Ñ, Ð¸Ð·Ð¼ÐµÑÑÐµÐ¼ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ñ. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð¿Ð¾Ð´ÑÐ¾Ð´Ñ Ðº Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¼Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¸, ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÐµÐ½Ð½Ð¾, VS. Ð ÑÑÐ¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ðµ Ð²Ð½Ð¸Ð¼Ð°Ð½Ð¸Ðµ ÑÐ´ÐµÐ»ÑÐµÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÐ¼ Ð½Ð° Ð´Ð°Ð½Ð½ÑÑ, Ð¾Ð´Ð½Ð°ÐºÐ¾ Ð² Ð½ÐµÐ¹ ÑÐ°ÐºÐ¶Ðµ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð¸ ÑÐ¼ÐµÑÐ°Ð½Ð½ÑÐ¹ Ð¿Ð¾Ð´ÑÐ¾Ð´Ñ. ÐÐ¾ÑÐ»Ðµ ÑÐ¾Ð³Ð¾, ÐºÐ°Ðº Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ñ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ Ð¿ÐµÑÑÐ¿ÐµÐºÑÐ¸Ð²Ð½ÑÐµ Ð¿Ð¾Ð´ÑÐ¾Ð´Ñ VS, Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ Ð²ÑÑÐ¾ÐºÐ¾ÑÐºÐ¾ÑÐ¾ÑÑÐ½Ð¾Ð³Ð¾ Ð¾ÑÐµÐ²Ð¾Ð³Ð¾ ÐºÐ¾Ð¼Ð¿ÑÐµÑÑÐ¾ÑÐ° Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÑÑÑÑ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ Ð´Ð»Ñ Ð·Ð°Ð¼ÐµÐ½Ñ ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾, Ð¿ÑÐµÐ·Ð¾ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð´Ð°ÑÑÐ¸ÐºÐ° ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ. Ð¢ÐµÑÑÐ¸ÑÑÐµÐ¼ÑÐ¼Ð¸ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ VS Ð¿Ð¾Ð´ÑÐ¾Ð´Ð°Ð¼Ð¸ ÑÐ²Ð»ÑÑÑÑÑ: ÑÐµÐ³ÑÐµÑÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸, ÐºÐ¾ÑÑÐµÐ»ÑÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÐµ ÑÐµÑÐ¸ Ñ Ð¿ÑÑÐ¼Ð¾Ð¹ ÑÐ²ÑÐ·ÑÑ, ÑÐµÐºÑÑÑÐµÐ½ÑÐ½ÑÐµ Ð¸ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½ÑÐµ ÑÐµÑÐ¸ Ð´Ð¾Ð»Ð³Ð¾Ð¹ ÐºÑÐ°ÑÐºÐ¾ÑÑÐ¾ÑÐ½Ð¾Ð¹ Ð¿Ð°Ð¼ÑÑÐ¸ (Long Short Term Memory - LSTM), Ð° ÑÐ°ÐºÐ¶Ðµ Ð¼Ð¾Ð´ÐµÐ»ÑÐ½ÑÐ¹ Ð¿Ð¾Ð´ÑÐ¾Ð´, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½ÑÐ¹ Ð½Ð° ÑÑÐ°ÑÐ¸ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¼ Ð°Ð½Ð°Ð»Ð¸Ð·Ðµ ÑÐ½ÐµÑÐ³Ð¸Ð¸, ÐºÐ¾ÑÐ¾ÑÑÐ¹ ÑÐ°ÐºÐ¶Ðµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÑÑÑ Ð´Ð»Ñ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ ÑÐ¼ÐµÑÐ°Ð½Ð½ÑÑ Ð²Ð¸ÑÑÑÐ°Ð»ÑÐ½ÑÑ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð² Ð² Ð²Ð¸Ð´Ðµ ÑÐ¸Ð·Ð¸ÑÐµÑÐºÐ¸ ÑÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð½ÐµÐ¹ÑÐ¾Ð½Ð½Ð¾Ð¹ ÑÐµÑÐ¸ (Physics-Informed Neural Network - PINN). Ð Ð°Ð·Ð»Ð¸ÑÐ½ÑÐµ Ð¿Ð¾Ð´ÑÐ¾Ð´Ñ VS Ð¾ÑÐµÐ½Ð¸Ð²Ð°ÑÑÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐ° ÐºÐ°ÑÐµÑÑÐ²Ð°, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð½Ð° ÑÑÐµÐ´Ð½ÐµÐ¹ Ð°Ð±ÑÐ¾Ð»ÑÑÐ½Ð¾Ð¹ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐ¸ Ð² Ð¿ÑÐ¾ÑÐµÐ½ÑÐ°Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÑÐ³ÐºÐ¸Ñ ÑÐ°ÐºÑÐ¾ÑÐ¾Ð². ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ VS Ð´ÐµÐ¹ÑÑÐ²Ð¸ÑÐµÐ»ÑÐ½ÑÑ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ ÑÑÑÐ´Ð½Ð¾ Ð´Ð¾ÑÑÐ¸Ð¶Ð¸Ð¼Ñ Ð¸Ð·-Ð·Ð° ÑÐ¸Ð»ÑÐ½Ð¾ ÐºÐ¾Ð»ÐµÐ±Ð»ÑÑÐµÐ¹ÑÑ Ð¿ÑÐ¸ÑÐ¾Ð´Ñ ÑÐ°ÐºÐ¾Ð³Ð¾ ÑÐ¾Ð´Ð° ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð², Ð´Ð°Ð¶Ðµ ÐºÐ¾Ð³Ð´Ð° ÑÑÑÐ°Ð½Ð¾Ð²Ð»ÐµÐ½Ð° ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ°Ñ ÑÐ¾ÑÐºÐ°. ÐÐ¾ÑÑÐ¾Ð¼Ñ Ð²Ð¸ÑÑÑÐ°Ð»ÑÐ½ÑÐµ Ð´Ð°ÑÑÐ¸ÐºÐ¸ Ð¿ÑÐµÐ´Ð½Ð°Ð·Ð½Ð°ÑÐµÐ½Ñ Ð´Ð»Ñ Ð¾ÑÐµÐ½ÐºÐ¸ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ð³Ð¾ Ð¸Ð»Ð¸ ÑÑÐµÐ´Ð½ÐµÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ ÑÐ¸Ð³Ð½Ð°Ð»Ð° ÑÑÐºÐ¾ÑÐµÐ½Ð¸Ñ. Ð­ÑÐ° Ð·Ð°Ð´Ð°ÑÐ° Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ ÑÐµÑÐµÐ½Ð° Ð½ÐµÑÐºÐ¾Ð»ÑÐºÐ¸Ð¼Ð¸ Ð¸Ð· Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² VS Ñ Ð¾Ð±Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½Ð¾Ð¹ ÑÐ¾ÑÐ½Ð¾ÑÑÑÑ - ÑÑÐ¾Ð¸Ñ, Ð¾Ð´Ð½Ð°ÐºÐ¾, Ð¾ÑÐ¼ÐµÑÐ¸ÑÑ, ÑÑÐ¾ Ð±Ð¾Ð»ÐµÐµ ÑÐ»Ð¾Ð¶Ð½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð½Ðµ Ð¾Ð±ÑÐ·Ð°ÑÐµÐ»ÑÐ½Ð¾ ÑÐ»ÑÑÑÐ°ÑÑ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð²Ð¸ÑÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð´Ð°ÑÑÐ¸ÐºÐ°
description: Virtual Sensing (VS) is a method to replace physical sensors on technical systems by a software counterpart. In order to achieve this, a mathematical model of the physical sensor in dependency from other, measured parameters of the technical system has to be developed. This work reviews different approaches to mathematical modelling and therefore to VS. It is focused on data-driven modelling methods, but analytical and hybrid approaches are presented too. After the most promising VS approaches are presented, different methods are applied in a case study on a high-speed axial compressor in order to replace a physical, piezo-electric acceleration sensor. The VS approaches tested in the case study are: regression models, correlation models, feed-forward, recurrent, and LSTM neural networks as well a model-based approach based on the statistical energy analysis, which is also used in order to create a hybrid virtual sensor in form of a physics-informed neural network. The different VS approaches are assessed by the means of a mean absolute percentage error inspired quality factor, as well as by soft factors. It is shown that VS of actual acceleration signals is hard to achieve, due to the highly fluctuating nature of these kinds of signals, even when a steady operating point is set. Therefore, the virtual sensors are designed to estimate the e'ective or root-mean-square value of the acceleration signal. This task can be achieved by several of the presented VS methods with reasonable accuracy - it is worth noting however that more complex models do not necessarily improve the performance of the virtual sensor.