DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER EQUIPMENT
The paper deals with the development of an artificial neural network for compensating for nonkinematic errors of an information and measurement system (IMS) based on a coordinate measuring arm (CMA). After compensating for kinematic errors using a mathematical model, the proposed back-propagation ne...
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General Energy Institute of the National Academy of Sciences of Ukraine
2025
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Репозитарії
System Research in Energy| _version_ | 1871104400729047040 |
|---|---|
| author | Kacprzyk, Janusz Zaporozhets, Artur Kataiev, Denys |
| author_facet | Kacprzyk, Janusz Zaporozhets, Artur Kataiev, Denys |
| author_institution_txt_mv | [
{
"author": "Janusz Kacprzyk",
"institution": null
},
{
"author": "Artur Zaporozhets",
"institution": null
},
{
"author": "Denys Kataiev",
"institution": null
}
] |
| author_sort | Kacprzyk, Janusz |
| baseUrl_str | https://systemre.org/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T12:57:49Z |
| description | The paper deals with the development of an artificial neural network for compensating for nonkinematic errors of an information and measurement system (IMS) based on a coordinate measuring arm (CMA). After compensating for kinematic errors using a mathematical model, the proposed back-propagation neural network corrects non-kinematic errors arising from thermal deformations, noise, and element deformation inaccuracies. Experimental studies conducted on synthetic data demonstrated a significant reduction in the mean square error (MSE) of the coordinates of the measured points and a decrease in measurement uncertainty. The model exhibited high accuracy and stability, which confirms its effectiveness for controlling the geometric parameters of energy equipment. |
| doi_str_mv | 10.15407/srenergy2025.01.074 |
| first_indexed | 2026-03-24T02:03:30Z |
| format | Article |
| fulltext |
Системні дослідження в енергетиці. 2025. 1(81) 74
ІНФОРМАЦІЙНО-ВИМІРЮВАЛЬНІ ТЕХНОЛОГІЇ,
МОНІТОРИНГ ТА ДІАГНОСТИКА В ЕНЕРГЕТИЦІ
_____________________________________________________________________________
ISSN 2786-7102 (Online), ISSN 2786-7633 (Print)
https://doi.org/10.15407/srenergy2025.01.074
UDC 531.7:62-2:629.7 (043.3)
Janusz Kacprzyk1, Dr. Sci. (Engin.), Professor, https://orcid.org/0000-0003-4187-5877
Artur Zaporozhets2, Dr. Sci. (Engin.), Senior Researcher, https://orcid.org/0000-0002-0704-4116
Denys Kataiev2*, https://orcid.org/0000-0002-2383-3123
1Systems Research Institute, Polish Academy of Sciences, 6, Newelska St., Warsaw, 01-447,
Poland;
2General Energy Institute of NAS of Ukraine, 172, Antonovycha St., Kyiv, 03150, Ukraine
*Corresponding author: kataev_d.a@ukr.net
_______________________________________________________________________________________
DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND
MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER
EQUIPMENT
Abstract. The paper deals with the development of an artificial neural network for compensating for
nonkinematic errors of an information and measurement system (IMS) based on a coordinate measuring arm
(CMA). After compensating for kinematic errors using a mathematical model, the proposed back-propagation
neural network corrects non-kinematic errors arising from thermal deformations, noise, and element
deformation inaccuracies. Experimental studies conducted on synthetic data demonstrated a significant
reduction in the mean square error (MSE) of the coordinates of the measured points and a decrease in
measurement uncertainty. The model exhibited high accuracy and stability, which confirms its effectiveness for
controlling the geometric parameters of energy equipment.
Keywords: artificial neural network, error back propagation, error compensation, information and
measurement system, coordinate measuring arm, geometric parameters, modeling.
1. Introduction
Information and measurement systems (IMS) based on the coordinate measuring arm (CMA) allow for
complex three-dimensional measurements with high accuracy, which is especially important in critical industries
such as the production and maintenance of turbines, generators, pumps and other components for nuclear power
plants (NPPs), thermal power plants (TPPs) and hydroelectric power plants (HPPs). IMS are used at all stages of
the equipment life cycle, providing quality control, part reproduction, and the development of new solutions.
Sources of errors in information and measurement systems based on a coordinate measuring arm are usually
divided into kinematic errors (such as link length errors, link twist errors, and initial zero position errors) and
nonkinematic errors (such as link deformation errors, thermal errors, and encoder rotary shaft motion errors) [1−3].
Most of the research in this area has focused on compensating for kinematic errors by calibrating parametric
models and ignored the compensation of nonkinetic errors. There are various factors that can affect the motion
uncertainty of a CGM, such as structural parameter error, deformation caused by the measuring force and gravity,
rotational error of the joints, and thermal deformation. Using classical mathematical methods, it is difficult to
model and compensate for all these factors [2−4].
Системні дослідження в енергетиці. 2025. 1(81) 75
Therefore, we propose an approach in which, after compensating for kinematic errors by mathematical
methods using the classical Denavit-Hartenberg model, a back-propagation neural network is used to compensate
for nonkinematic errors.
2. Methods and materials
The Back-Propagation Neural Network (BPNN) (Fig. 1) is one of the most widely used artificial neural
networks with a powerful ability of nonlinear mapping and self-learning. Thanks to this ability, BPNN can predict
the errors of the Information and Measurement System caused by various factors, which makes it possible to
compensate for complex errors and reduce the uncertainty of the Information and Measurement System
measurements [5−8].
Figure 1. Back-Propagation Neural Network
The neural network is implemented as a BackpropagationNN class based on the PyTorch library. The neural
network consists of three main components: an input layer, one hidden layer, and an output layer.
The input layer takes as input the coordinates of a point in three-dimensional space:
𝑥 = [𝑥𝑚, 𝑦𝑚, 𝑧𝑚], (1)
where: , ,m m mx y z − coordinates of the point obtained by the measuring system. The dimension of the input layer
corresponds to the number of coordinates.
The hidden layer performs a linear transformation of the input data using a nonlinear activation function
( )Re LU
:
( )1 1
Re ,h LU W x b= + (2)
where:
64 3
1W R − hidden layer weight matrix,
64
1b R — displacement vector, ( ) ( )Re max 0,LU z z= −
Re LU activation function that adds nonlinearity to the model. The output layer performs a linear transformation
of the hidden layer output to obtain the predicted coordinates:
2 2
ˆ ,y W h b= + (3)
Системні дослідження в енергетиці. 2025. 1(81) 76
where:
3 64
2W R − matrix of weights of the output layer, 3
2b R − displacement vector. As an output, the
network returns the corrected coordinates of the point:
ˆ ˆ ˆ ˆ, , .y x y z= (4)
The Mean Square Error (MSE) ( )MSE function is used to evaluate the accuracy of a model [9−12]. It
calculates the average difference between the true coordinate (y) and the predicted coordinates (ŷ):
( ) 2
1
1
ˆ ,
N
i ii
MSE y y
N =
= − (5)
where: , ,iy x y z= − true coordinates of the point, ˆ ˆ ˆ ˆ, ,i i i iy x y z= − predicted coordinates of the point, N −
number of points in the data set.
The loss function (MSE) is minimized during training to maximize model accuracy, and the error
backpropagation algorithm calculates gradients of the loss function to update the weights and biases in the network.
Calculating the error of the output layer
ˆ ,out y y = − (6)
where:
3
out R − error in the original layer.
Gradients of weights and offsets of the original layer
2
,
T
out
MSE
h
W
=
2
.out
MSE
b
=
(7)
Calculating the hidden layer error
( ) ( )2 Re ,T
hidden outW LU h = (8)
where: ( ) 1, 0,
Re .
0, 0
z
LU z
z
=
Gradients of weights and offsets of the hidden layer
1
,T
hidden
MSE
x
W
=
1
.hidden
MSE
b
=
(9)
Weights and offsets are updated using the Adam optimization algorithm:
1
,i i
MSE
W W
W
−
(10)
where: − learning speed.
Системні дослідження в енергетиці. 2025. 1(81) 77
Adam additionally takes into account the moments of first- and second-order gradients for faster
convergence. After training the model, the uncertainty of the corrected coordinates is estimated. For this purpose,
confidence intervals are used:
,Cl t
n
= (11)
where: t − this is the quantilic of the Student distribution, − the standard deviation of the predicted coordinates,
n − the number of points.
The standard deviation of the projected coordinates was calculated by the formula:
( ) ( ) ( )( )
2
2 2 2
1
1
ˆ ˆ ˆ
N
i i i i i i
i
x x y y z z
N
=
= + + + + + (12)
where , ,i i ix y z , are true coordinates, ˆ ˆ ˆ, ,i i ix y z are the predicted coordinates and N is the number of points in the
data set.
To build and train a neural network, we have conducted an experimental simulation of the process of
calibration of the Information and Measurement System [13−15]. In the context of this work, uncertainty is a
characteristic of a random component after amending systematic influences that are adjusted by a neural network.
Systematic errors caused by influences, such as thermal deformations, noise, elements of deformation of the
elements, are offset by teaching the network on synthetic data and using appropriate algorithms. However, the
residual errors remaining after correction consist of unchanged components of a systematic error and a random
component. Thus, uncertainty after correction determines the distribution of these residual errors. This means that
the trust intervals that are evaluated after processing by the neural network characterize the influence of both
adjusted and non -co -entered components of errors, which causes their complex nature.
A synthetic dataset consisting of three-dimensional coordinates was used for the experiment. The data was
generated around a sphere of 30mm diameter. The data was generated using a normal distribution. To simulate
destabilizing factors that correspond to real distortions that may occur during measurement, noise was added to
the coordinates according to the Gaussian distribution (Fig. 2) [16].
Figure 2. Adding noise according to the Gaussian distribution
The generated data were divided into training and test sets in the ratio of 80 % to 20 % using the stratified
k-fold cross-validation method (Fig. 3) [17−19].
Системні дослідження в енергетиці. 2025. 1(81) 78
Figure 3. Stratified k-fold cross-validation
The training set was used to train the model, and the test set was used to evaluate its accuracy. Key
generation parameters include: number of samples = 1000; sphere diameter = 30 mm.
An experimental study was conducted to determine the impact of different activation functions on the
model's accuracy. The purpose of the experiment is to compare the effect of activation functions on model accuracy
by conducting 100 training iterations for each activation function. The results were evaluated based on the average
test losses obtained during each iteration (Fig. 4).
Figure 4. Average test losses for different activation functions
The ReLU activation function showed the best performance, achieving the lowest average loss over 100
training epochs. We also conducted a series of experiments to substantiate the selected hyperparameters [20].
To conduct the experiment, we used a combination of typical key hyperparameters that affect the
performance of a neural network (Table 1).
Системні дослідження в енергетиці. 2025. 1(81) 79
Table 1. Typical key hyperparameters
Hyperparameters Typical values
Number of neurons 32 64 128 256
Speed of learning 0.001 0.01 0.1
Number of epochs 50 100 200
Size of mini-packs 16 32 64 128
Regularization 0.0001 0.001 0.01
Thus, 432 possible combinations were formed to experimentally substantiate the choice of hyperparameters.
The neural network was trained on the coordinates of the sphere surface using 432 typical combinations of
hyperparameters, noisy data were processed by the neural network, and the predicted coordinates of 10 test points
were obtained, followed by a comparison of the predicted coordinates with the reference coordinates and
confidence intervals [21−23].
We also selected the appropriate metrics to determine how changes in hyperparameters affect the
measurement results. Train Loss - losses on training data. Validation Loss - losses on validation data. Mean Square
Error (MSE) of the predicted coordinates of the control points. Reduction of uncertainty before and after the
coordinates are processed by the neural network. Correction rate, which indicates the percentage of model
predictions that required correction after processing.
Models with zero correction rate were chosen as stable. This means that all the predicted coordinates after
processing by the neural network fell within the confidence interval, and no corrections were required [24].
Among the models with zero correction rate, uncertainty reduction was used as the main criterion for
selecting the most accurate models. Based on the comparative analysis, model No. 127 was selected (Table 2),
which has a zero correction rate, which means that the predictions are stable (all predicted coordinates fell within
the confidence interval) and which showed the greatest reduction in uncertainty, indicating the ability to provide
the highest accuracy [25].
Table 2. Parameters of model No. 127
Model № 127
Number of neurons 64
Learning speed 0,001
Number of learning epochs 100
The size of mini-batches 64
Regularization 0,0001
Train Loss 0,027
Validation Loss 0,026
Uncertainty X before processing (mm) 8,91
Uncertainty X after processing (mm) 8,38
Uncertainty Y before processing (mm) 8,76
Uncertainty Y after processing (mm) 8,02
Uncertainty Z before processing (mm) 8,2
Uncertainty Z after processing (mm) 7,95
MSE 0,009
Frequency of correction 0
Системні дослідження в енергетиці. 2025. 1(81) 80
Thus, it has been experimentally determined that the best model performance in terms of stability and
reduction of uncertainty is provided by the following hyperparameters: number of neurons: 64; learning rate:
0.001; number of epochs: 100; mini-packet size: 64; regularization: 0.001.
A synthetic data set was generated for the training of the neural network, which simulates the process of
measuring on the surface of the sphere with a diameter of 30 mm (coordinate range: from -15 mm to 15 mm). To
model random errors to the coordinates, a noise with a normal distribution was added, the average value of which
was -0.1 mm, and the average square deviation was 0.1 mm. Thus, the ratio between the average quadratic
deviation of noise and the maximum coordinate is approximately 0.67 %. This ensures the realism of the model,
allowing to evaluate the effect of small random errors on the accuracy of projected coordinates. For each coordinate
of the measured points, confidence intervals were calculated with a confidence level of 95 % [26]. The real and
predicted coordinates were compared according to the criterion of finding the predicted coordinates within the
confidence interval (Fig. 5).
To prevent overtraining, the model used an early stopping technique with the parameter `patience' = 20.
This means that training was stopped if there was no improvement in the loss function on the validation data within
20 epochs. The model was trained on 80 % of the total generated data, while 20 % of the data was used for
validation.
Figure 5. Correspondence of the predicted coordinates to the confidence interval
The criterion for stopping the training was the stabilization of the loss function on the validation data within
20 epochs, which allowed to avoid overtraining.
3. Results
After training, the model was evaluated on a test dataset that was not used for training and validation
(Table 3).
Системні дослідження в енергетиці. 2025. 1(81) 81
Table 3. Measurement result
The distance of the point from the center of the reference sphere (r) is determined:
2 2 2r x y z= + + , (13)
where: , ,x y z − point coordinates, r − distance from the point to the center.
If the diameter of the sphere 30d мм= , then:
15 .
2
d
R мм= = (14)
Determine how far the point deviates from the surface of the reference sphere:
r r R = − , (15)
where: r − calculated distance of the point, 15 .R мм=
If ,after beforer r then the point has approached the surface of the sphere (+), otherwise it has moved
away (-) (Table 4).
Table 4. The result of the calculations
Point rbefore (mm) rafter (mm Deviations before processing (mm) Deviations after processing (mm) Result
1 13.97 14.89 1.03 0.11 +
2 14.04 14.82 0.96 0.18 +
3 14.14 15.12 0.86 -0.12 +
4 14.68 15.07 0.32 -0.07 +
5 12.65 14.95 2.35 0.05 +
6 15.58 15.26 -0.58 -0.26 +
7 14.91 15.14 0.09 -0.14 -
8 14.41 14.70 0.59 0.30 +
9 14.75 14.95 0.25 0.05 +
10 14.00 14.94 1.00 0.06 +
Point
X before
processing
(mm)
X after
processing
(mm)
Y before
processing
(mm)
Y after
processing
(mm)
Z before
processing
(mm)
Z after
processing
(mm)
Distance to the
sphere surface
before
processing
Distance to
the sphere
surface after
processing
1 4,09 5,11 -13,32 -13,98 -1,02 0,15 1,03 0,12
2 1,38 1,36 0,56 1,31 13,96 14,7 0,96 0,18
3 -4,4 -3,36 -12,95 -14 3,59 4,63 0,86 -0,12
4 5,5 5,93 -9,03 -8,89 -10,19 -10,62 0,32 -0,07
5 5,68 6,03 -5,42 -7,15 9,92 11,66 2,35 0,05
6 -2,3 -1,99 9,55 9,24 -12,09 -11,98 -0,59 -0,26
7 0,98 0,83 -13,64 -14,09 -5,93 -5,49 0,09 -0,15
8 11,68 11,43 7,66 8,97 3,53 2,21 0,59 0,30
9 -5,94 -6,31 7,24 6,86 -11,4 -11,69 0,25 0,05
10 -5,26 -5,05 -7,6 -8,14 10,51 11,46 1,00 0,06
Системні дослідження в енергетиці. 2025. 1(81) 82
After processing with the neural network, the coordinates for most of the predicted points (9 out of 10)
became closer to the reference surface of the sphere (Fig. 6).
Figure 6. Distance to the surface of the sphere
The average deviation of the coordinates after neural network processing decreased from 0.8 mm to
0.14 mm.
Thus, on the basis of experimental studies, the effectiveness of using a neural network to control the
geometric dimensions of power equipment was confirmed.
The proposed neural network, integrated into the TDF software system, allows correcting non-kinematic
measurement errors in real time.
4. Conclusions
Experimental studies were conducted to evaluate the effectiveness of the proposed information and
measurement system (IMS) based on a coordinate measuring arm (CMA) and an artificial neural network.
The architecture of the neural network for compensation of measurement errors is proposed, which allows
to improve the results of controlling the geometric parameters of equipment.
The influence of various neural network training parameters on measurement accuracy and data processing
speed is investigated.
Comparison of the results before and after neural network processing showed a significant increase in the
accuracy of predicting the measured parameters.
Author Contributions. Methodology and ideology of the research, data analysis, manuscript preparation –
Artur Zaporozhets; methodology and ideology of the research – Janusz Kacprzyk; data collection and analysis,
preparation of the initial manuscript – Denys Kataiev.
Funding. The paper was supported by the departmental scientific program of the NAS of Ukraine
"Development of methods and means of monitoring the state of the environment of energy facilities based on
wireless sensor networks" (0123U100127).
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РОЗРОБКА ШТУЧНОЇ НЕЙРОННОЇ МЕРЕЖІ ДЛЯ ІНФОРМАЦІЙНО-
ВИМІРЮВАЛЬНОЇ СИСТЕМИ КОНТРОЛЮ ГЕОМЕТРИЧНИХ РОЗМІРІВ
ЕНЕРГЕТИЧНОГО ОБЛАДНАННЯ
Януш Кацпжик1, д-р техн. наук, професор, https://orcid.org/0000-0003-4187-5877
Артур Запорожець2, д-р техн. наук, ст. досл., https://orcid.org/0000-0002-0704-4116
Денис Катаєв2*, https://orcid.org/0000-0002-2383-3123
1Інститут системних досліджень, Польська академія наук, вул. Невельська, 6, Варшава, 01-
447, Польща;
2Інститут загальної енергетики НАН України, вул. Антоновича, 172, Київ, 03150, Україна
*Автор-кореспондент: kataev_d.a@ukr.net
Анотація. У статті розглядається розробка штучної нейронної мережі для компенсації
некінематичних похибок інформаційно-вимірювальної системи (ІВС) на базі координатно-
вимірювальної руки (КВР). Після компенсації кінематичних похибок за допомогою математичної
моделі, запропонована нейронна мережа зі зворотним поширенням помилки забезпечує корекцію
некінематичних похибок, що виникають через термічні деформації, шум і похибки деформації
елементів. Експериментальні дослідження, проведені на основі синтетичних даних, показали значне
зниження середньоквадратичної похибки (MSE) координат вимірюваних точок та зменшення
невизначеності вимірювань. Модель продемонструвала високу точність і стабільність, що
підтверджує її ефективність для контролю геометричних параметрів енергетичного обладнання.
Keywords: штучна нейронна мережа, зворотне поширення помилки, компенсація похибок,
інформаційно-вимірювальна система, координатно-вимірювальна рука, геометричні параметри,
моделювання.
Надійшла до редколегії: 25.12.2024
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| id | systemreorg-article-887 |
| institution | System Research in Energy |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:23:30Z |
| publishDate | 2025 |
| publisher | General Energy Institute of the National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | systemreorg/a9/775d6b7d0a5bc50152538a3bc82d24a9.pdf |
| spelling | systemreorg-article-8872026-07-18T12:57:49Z DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER EQUIPMENT Розробка штучної нейронної мережі для інформаційно-вимірювальної системи контролю геометричних розмірів енергетичного обладнання Kacprzyk, Janusz Zaporozhets, Artur Kataiev, Denys штучна нейронна мережа, зворотне поширення помилки, компенсація похибок, інформаційно-вимірювальна система, координатно-вимірювальна рука, геометричні параметри, моделювання. artificial neural network, error back propagation, error compensation, information and measurement system, coordinate measuring arm, geometric parameters, modeling. The paper deals with the development of an artificial neural network for compensating for nonkinematic errors of an information and measurement system (IMS) based on a coordinate measuring arm (CMA). After compensating for kinematic errors using a mathematical model, the proposed back-propagation neural network corrects non-kinematic errors arising from thermal deformations, noise, and element deformation inaccuracies. Experimental studies conducted on synthetic data demonstrated a significant reduction in the mean square error (MSE) of the coordinates of the measured points and a decrease in measurement uncertainty. The model exhibited high accuracy and stability, which confirms its effectiveness for controlling the geometric parameters of energy equipment. У статті розглядається розробка штучної нейронної мережі для компенсації некінематичних похибок інформаційно-вимірювальної системи (ІВС) на базі координатно-вимірювальної руки (КВР). Після компенсації кінематичних похибок за допомогою математичної моделі, запропонована нейронна мережа зі зворотним поширенням помилки забезпечує корекцію некінематичних похибок, що виникають через термічні деформації, шум і похибки деформації елементів. Експериментальні дослідження, проведені на основі синтетичних даних, показали значне зниження середньоквадратичної похибки (MSE) координат вимірюваних точок та зменшення невизначеності вимірювань. Модель продемонструвала високу точність і стабільність, що підтверджує її ефективність для контролю геометричних параметрів енергетичного обладнання. General Energy Institute of the National Academy of Sciences of Ukraine 2025-02-27 Article Article application/pdf https://systemre.org/index.php/journal/article/view/887 10.15407/srenergy2025.01.074 System Research in Energy; No. 1 (81) (2025): System Research in Energy; 74-84 Системні дослідження в енергетиці; № 1 (81) (2025): Системні дослідження в енергетиці; 74-84 2786-7102 2786-7633 en https://systemre.org/index.php/journal/article/view/887/795 Copyright (c) 2025 Janusz Kacprzyk, Artur Zaporozhets, Denys Kataiev https://creativecommons.org/publicdomain/zero/1.0 |
| spellingShingle | штучна нейронна мережа зворотне поширення помилки компенсація похибок інформаційно-вимірювальна система координатно-вимірювальна рука геометричні параметри моделювання. Kacprzyk, Janusz Zaporozhets, Artur Kataiev, Denys DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER EQUIPMENT |
| title | DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER EQUIPMENT |
| title_alt | Розробка штучної нейронної мережі для інформаційно-вимірювальної системи контролю геометричних розмірів енергетичного обладнання |
| title_full | DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER EQUIPMENT |
| title_fullStr | DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER EQUIPMENT |
| title_full_unstemmed | DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER EQUIPMENT |
| title_short | DEVELOPMENT OF AN ARTIFICIAL NEURAL NETWORK FOR INFORMATION AND MEASUREMENT SYSTEM FOR CONTROLLING THE GEOMETRIC DIMENSIONS OF POWER EQUIPMENT |
| title_sort | development of an artificial neural network for information and measurement system for controlling the geometric dimensions of power equipment |
| topic | штучна нейронна мережа зворотне поширення помилки компенсація похибок інформаційно-вимірювальна система координатно-вимірювальна рука геометричні параметри моделювання. |
| topic_facet | штучна нейронна мережа зворотне поширення помилки компенсація похибок інформаційно-вимірювальна система координатно-вимірювальна рука геометричні параметри моделювання. artificial neural network error back propagation error compensation information and measurement system coordinate measuring arm geometric parameters modeling. |
| url | https://systemre.org/index.php/journal/article/view/887 |
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