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A set of models of feed-forward neural networks has been created to obtain operational forecasts of the quality of mechanical engineering processes. It is established that the use of the Back Propagation of Error machine learning algorithm allows for obtaining forecasted estimates for the controlled...
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| author | Fedin, Serhii Romaniuk, Oksana Trishch, Roman |
| author_facet | Fedin, Serhii Romaniuk, Oksana Trishch, Roman |
| author_institution_txt_mv | [
{
"author": "Serhii Fedin",
"institution": "National Transport University, Kyiv"
},
{
"author": "Oksana Romaniuk",
"institution": "Open International University of Human Development “Ukraine”, Kyiv"
},
{
"author": "Roman Trishch",
"institution": "National Aerospace University \"Kharkiv Aviation Institute\", Kharkiv"
}
] |
| author_sort | Fedin, Serhii |
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| datestamp_date | 2025-11-09T00:01:30Z |
| description | A set of models of feed-forward neural networks has been created to obtain operational forecasts of the quality of mechanical engineering processes. It is established that the use of the Back Propagation of Error machine learning algorithm allows for obtaining forecasted estimates for the controlled parameter of the metalworking process with significantly smaller ranges of the mean absolute percentage error, mean square error, relative approximation error, and variance ratio criterion compared to the BFGS algorithm. It is shown that the proposed MLP neural network models can be recommended for practical applications in controlling the accuracy of the machining process of shaft-type parts. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2025.3.09 |
| first_indexed | 2025-11-09T02:11:03Z |
| format | Article |
| fulltext |
S.S. Fedin, O.O. Romaniuk, R.M. Trishch, 2025
Системні дослідження та інформаційні технології, 2025, № 3 113
UDC 658.562:004.855.5
DOI: 10.20535/SRIT.2308-8893.2025.3.09
FORECASTING THE QUALITY OF TECHNOLOGICAL
PROCESSES BY METHODS
OF ARTIFICIAL NEURAL NETWORKS
S.S. FEDIN, O.O. ROMANIUK, R.M. TRISHCH
Abstract. A set of models of feed-forward neural networks has been created to ob-
tain operational forecasts of the quality of mechanical engineering processes. It is
established that the use of the Back Propagation of Error machine learning algorithm
allows for obtaining forecasted estimates for the controlled parameter of the metal-
working process with significantly smaller ranges of the mean absolute percentage
error, mean square error, relative approximation error, and variance ratio criterion
compared to the BFGS algorithm. It is shown that the proposed MLP neural network
models can be recommended for practical applications in controlling the accuracy of
the machining process of shaft-type parts.
Keywords: accuracy, details, quality, forecasting, machine learning, neural network,
technological process.
INTRODUCTION
In modern conditions of information development and intellectualization of vari-
ous industries, an urgent problem is the application of management methods
based on quantitative assessment of quality indicators of technological processes.
According to DSTU 2925-94, quality is a set of characteristics of a product (proc-
ess, service) that relate to its ability to meet established and foreseeable needs [1].
In other words, it is a measure of the compliance of a certain multicriteria
process with expectations or requirements, which can be presented, for example,
in the form of functionally dependent statistics proposed in scientific publications
[2; 3] for socio-economic systems or processes in the energy sector [4–9]. At the
same time, one of the urgent problems in the modern machine-building industry is
to improve the quality and efficiency of high-precision machining, the complexity
of which is associated with the fact that the cutting process on well-established
machines is characterized by instability and a multitude of interrelated variables
[10]. Cutting conditions dynamically change randomly due to the influence of
various disturbing factors: scatter of allowances, variation in the hardness and
structure of the work piece metal, continuously changing cutting properties of the
tool, etc. [11]. In addition, quality indicators depend on the stiffness and thermal
deformation of the elements of the technological system, the nature and parame-
ters of the relative vibrations of the tool and the work piece, etc. According to
DSTU 3514-97, one of the quality indicators of technological process is accuracy,
i.e. a property that determines the proximity of actual and nominal values of
parameters according to their probability distribution [12].
In this case, the control of the process accuracy is reduced to forecasting the
machining error at a certain point in time (or during a given machining cycle) and
S.S. Fedin, O.O. Romaniuk, R.M. Trishch
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 114
introducing a corrective action (a readjustment pulse) to shift the tool by the fore-
casted value [13].
Machining errors have systematic and random components and are essentially
random variables, for the forecasting of which it is necessary to know the probable
estimates of the distribution and stability characteristics over time, fixing the value of
the controlled parameter of each details that is consistently manufactured [14]. These
fixed values are the basis for building analytical models and control charts that
can be used to estimate the components of the total machining error:
a systematic component — to eliminate the scattering centers of the con-
trolled parameter of the details (setting level);
a random component — for the displacement of the dimensions of details
from the centers of scattering (according to the instantaneous distribution of di-
mensional deviations under the constant action of external factors within con-
trolled limits) [13].
It should be noted that the principle of using control charts and analytical
models to synthesize algorithms of existing systems for controlling the accuracy
of metalworking processes has some drawbacks, namely:
the estimation of the distribution parameters should be based on the as-
sumption that the machine setup level remains unchanged, but the center of the
details size dispersion is shifted randomly;
the use of control cards allows you to adjust the parameters of the ma-
chining equipment (machine) after evaluating the results of the previous detail
before the start of production of the next detail and, thus, control is carried out
off-line.
One of the ways to technologically ensure the accuracy of machining proc-
esses is to introduce corrective actions in automated machine control systems
based on the results of forecasting deviations of the controlled parameters of de-
tails based on adaptive artificial intelligence models [15].
The modern approach to adaptive management requires the model to be able
to automatically change its structure or algorithm of functioning. However, the
effective practical application of control algorithms depends on their flexibility
and learning ability [16]. Therefore, an urgent task is to improve the accuracy of
the adaptation process when changing on-line technological parameters using
self-tuning models. Such information models can be more adaptive due to recon-
figuration (retraining) on the basis of retrospective statistical information when
the parameters of the details machining process change in order to determine or
adjust the control law and, as a consequence, to ensure the quality of the metal-
working process. Taking into account the conditions of nonlinear dynamics of
technological parameters, the efficiency of adaptive control of metalworking pro-
cesses can be significantly increased by using models of rectilinear artificial neu-
ral networks (Multilayer Perceptron – MLP). At the same time, the joint use of
MLP models and control cards will allow to realize the principle of information
support for the accuracy of technological processes.
PROBLEM DEFINITION
The choice of the neural network modeling methodology for operational forecasting
of the quality of technological processes is due to the following properties [17; 18]:
Forecasting the quality of technological processes by methods of artificial neural networks
Системні дослідження та інформаційні технології, 2025, № 3 115
first, neural networks are among the best methods for classifying patterns,
approximating and extrapolating nonlinear functions, including non-stationary
time series;
secondly, the presence of nonlinear activation functions in a multilayer
neural network ensures the effective implementation of any nonlinear mappings
X→Y with a given accuracy for the identification and control of complex nonlin-
ear technical objects;
thirdly, the parallelism of neural networks is a prerequisite for the ef-
fective implementation of software and hardware support for neural network
controllers, which allow, on the basis of quantitative retrospective informa-
tion, to provide on-line control of the metalworking process based on the fore-
casted discrete values of the controlled parameter of the details that are se-
quentially manufactured.
Consider a discrete process with one input )(ty , for which each subsequent
output value )1( ty depends only on the previous value
)](..., ),1( ),([)1( qtytytyfty p , (1)
where y is an input/output, t is a discrete integer time, q is a nonnegative integer,
and )(pf a function.
The task is to control an object that is described by expression (1) based on
learning. The control must be performed in such a way that the output signal cor-
responds to a reference signal )(tr , subject of minimizing a certain norm
)()()( tytrte . In this case, the a priori quantitative information about the con-
trol object is the value q, which is an estimate of the value q of expression (1).
This task can be solved on the basis of MLP models, the adaptive properties of
which allow us to consider their various architectures and configurations in the
structure of a neurocontroller or neuroemulator [19].
Given a given estimate of q, an MLP-type neural network model with
1 qn inputs and one output 1m can be used to model the function )(pf of
expression (1). Denoting the mapping performed by the neuroemulator of the con-
trol object as )(E and its output as 1y , we obtain
)(1 EE xy ,
where nxE is an n-dimensional vector.
For case T)](..., ),1( ),([)( qtytytytxE — the goal of neurosimulator
machine learning is to minimise a norm of error )(txE
T)](..., ),1( ),([ qtytyty .
RESEARCH OBJECTIVE
The aim of the work is to create adaptive models of feed-forward neural networks
for operational forecasting of the quality of mechanical engineering processes by
the accuracy parameter of cylindrical details of the “shaft” type.
S.S. Fedin, O.O. Romaniuk, R.M. Trishch
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 116
Literature review. One of the ways to solve the problem of quality assur-
ance by increasing the accuracy and productivity of machining details is to use
on-line tracking automatic control systems in machine tools. In particular, the
fundamental research conducted by B.S. Balakshin made it possible to establish
links between the factors acting in the process of machining details and to formal-
ize the mechanisms of error formation [20].
In modern industrial production, technological process control is based on
the use of methods and means of active control of the quality of manufactured
products. In the studies of by S.S. Volosov [21] and M.S. Nevelson [22] show that
the most effective means of active control are automatic or combined systems that
implement the principle of adaptive control. Studies [23; 24] note that the current
level of development and improvement of methods and means of active control
requires the introduction of adaptive systems for monitoring technological proc-
esses based on artificial intelligence technologies, in particular, neural network
modeling. For example, S.V. Bilenko [23] developed methods for identifying the
state and intelligent control of the machining process, aimed at determining the
optimal cutting mode with a minimum amount of a priori information for con-
tinuous correction of this mode in the face of disturbances in the dynamic system
of the machine tool. In the paper A.P. Nikishechkin [24] proposed the principles
of constructing neural network adaptive control systems for metalworking proc-
esses and created a method for synthesizing neural network components of an
adaptive control system directly in the process of its operation. The work of P.D.
Wasserman [25] shows that when choosing a neural network architecture for
forecasting, several configurations with different numbers of hidden neurons are
usually tested. At the same time, an effective solution to the problem of time se-
ries forecasting based on the use of MLP models is shown. An adaptive MLP
model was proposed in [26] to determine the structure of the time series of devia-
tions of the diameter of shaft-type details from the nominal size and to forecast
the accuracy of the technological process of machining details by a controlled
parameter. It is shown that the use of such a model under the condition of non-
stationarity of the controlled parameters of product quality allows obtaining reli-
able information about the future state of the technological process and increasing
the efficiency of quality management in real time. Paper [27] shows that for qual-
ity management at a separate stage of the technological process in the conditions
of noisy input information, one of the effective methods is the use of two-layer
MLPs with the Back Propagation of Error learning algorithm.
Paper [28] proposes a model of a feed-forward neural network for forecast-
ing and controlling production, the practical application of which is aimed at im-
plementing a mechanism for controlling continuous multi-stage production proc-
esses without intermediate outputs. Study [29] proposes a method of using neural
networks to identify product defects and make corrective changes to the techno-
logical process in order to manage its quality.
It should be noted that the construction of neurocontrollers is an important
area of application of neurocontrol in metalworking to ensure the quality of tech-
nological processes. Thus, in [30], a method was formalized for creating neural-
index models designed to plan the process of machining rotating details based on
typical examples. Study [31] proposes a controller for optimizing the milling pro-
cess, in which modeling based on artificial neural networks is used to learn the
correspondence between the inputs and outputs of the technological process.
Tianjin University (China) has developed a milling process control technology
based on the use of a three-layer neural network with the Back Propagation of
Forecasting the quality of technological processes by methods of artificial neural networks
Системні дослідження та інформаційні технології, 2025, № 3 117
Error machine learning algorithm and performed simulations for different proc-
essing modes with experimental confirmation of the effectiveness of the proposed
control technology [32].
Thus, the literature review shows the relevance of scientific and practical re-
search aimed at managing the quality of technological processes of machining
sequentially machined details based on methods for forecasting the accuracy of
their manufacture using adaptive neural networks.
MATERIALS AND METHODS
The controlled parameter of sequentially machined details is the accuracy of the
cylindrical surface diameter of the shaft detail, namely the deviation of the actual
surface size from its nominal value within the tolerance field. The tolerance field
and the nominal value are determined by the requirements of the relevant stan-
dards and design documentation.
The data for creating neural network models are presented in the form of di-
ameter deviations of 50 consecutively machined details of the shaft type 50h11
made of St45 steel within the tolerance field of a controlled size of 200 μm [26].
Thus, the time series of diameter deviations contains 25 values for each of the 2
realizations of the machining process obtained between machine tool adjustments
under the same roughing modes (Table 1).
T a b l e 1 . Deviation of the controlled size of details of the type shaft 50h11
from the nominal value of y, μm [33]
Detail number Implementation No. 1 Implementation No. 2
1 24 38
2 36 49
3 35 55
4 44 61
5 50 76
6 55 80
7 76 71
8 75 88
9 63 93
10 84 85
11 88 105
12 80 90
13 103 101
14 90 110
15 100 92
16 105 133
17 91 125
18 129 128
19 125 152
20 115 143
21 142 166
22 149 167
23 158 165
24 183 169
25 185 173
S.S. Fedin, O.O. Romaniuk, R.M. Trishch
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 118
To build neural network forecasted models, examples of the training sample
were obtained using the sliding window method ix and 1ix , which moves along
the time sequence of retrospective data of deviations of the controlled parameter
(Table 1) with a step equal to one processing cycle (one detail). In this case, the
data in the window xi are the inputs of the neural network, and the data of the sec-
ond window nix are the outputs.
Thus, training samples are instantaneous samples of values of the controlled
parameter of sequentially machined details, represented as a time series shifted
relative to the initial values ix with a lag of one machining cycle, which corre-
sponds to the process (1).
When forming examples of training sample, it is advisable to divide the time
series of the forecasted indicator by ix into 20,,5n values, as this range
characterizes the volume of instantaneous sampling of deviations of details di-
mensions from nominal values, accepted in mechanical engineering [13; 34]. Tak-
ing into account this range and the total volume of realizations No. 1 and No. 2,
which is equal to 25 values of deviations of details dimensions, a training set with
6n inputs corresponding to the values of a sequentially shifted (by five levels)
time series of deviations of details dimensions was created. In this case, the output
1m determines the “reference” value of the deviation of the size of each subse-
quent detail – y. Thus, the number of examples (facts) of the training sample from
implementation No. 1 is 19625 (Table 2).
T a b l e 2 . Training sample based on data from implementation No. 1
Example number x1 x2 x3 x4 x5 x6 y
1 24 36 35 44 50 55 76
2 36 35 44 50 55 76 75
3 35 44 50 55 76 75 63
4 44 50 55 76 75 63 84
5 50 55 76 75 63 84 88
6 55 76 75 63 84 88 80
7 76 75 63 84 88 80 103
8 75 63 84 88 80 103 90
9 63 84 88 80 103 90 100
10 84 88 80 103 90 100 105
11 88 80 103 90 100 105 91
12 80 103 90 100 105 91 129
13 103 90 100 105 91 129 125
14 90 100 105 91 129 125 115
15 100 105 91 129 125 115 142
16 105 91 129 125 115 142 149
17 91 129 125 115 142 149 158
18 129 125 115 142 149 158 183
19 125 115 142 149 158 183 185
To obtain forecaster estimates of the accuracy of the technological process, a
second sample of 19 examples was prepared, characterizing the values of devia-
tions in the shaft diameter of each consecutively manufactured detail from im-
plementation No. 2 (Table 3).
Forecasting the quality of technological processes by methods of artificial neural networks
Системні дослідження та інформаційні технології, 2025, № 3 119
T a b l e 3 . Forecasted sample based on the data from implementation No. 2
Example number x1 x2 x3 x4 x5 x6 y
1 38 49 55 61 76 80 71
2 49 55 61 76 80 71 88
3 55 61 76 80 71 88 93
4 61 76 80 71 88 93 85
5 76 80 71 88 93 85 105
6 80 71 88 93 85 105 90
7 71 88 93 85 105 90 101
8 88 93 85 105 90 101 110
9 93 85 105 90 101 110 92
10 85 105 90 101 110 92 133
11 105 90 101 110 92 133 125
12 90 101 110 92 133 125 128
13 101 110 92 133 125 128 152
14 110 92 133 125 128 152 143
15 92 133 125 128 152 143 166
16 133 125 128 152 143 166 167
17 125 128 152 143 166 167 165
18 128 152 143 166 167 165 169
19 152 143 166 167 165 169 173
Given the fact that multilayer neural networks with only one hidden layer
and a sigmoidal activation function can perform any nonlinear mapping between
two finite-dimensional spaces with a given accuracy, we will determine a suffi-
cient number of hidden neurons [35]. At the same time, we note that in the on-line
mode, during the sequential manufacture of each detail, the training sample size
increases by one example. Thus, when training MLP models to obtain a forecaster
estimate of the controlled indicator of detail No. 25 from implementation No. 2
(Table 1), the training sample size will be equal to 371819 K . Using the
values of nK , , and m , we will determine the minimum minL and maximum maxL
number of neurons in the hidden layer based on the dependencies presented in [36]
.2)(5.0,2 maxmin KmnLmnL (2)
In accordance with dependencies (2), the total number of neurons in the hid-
den layer was calculated as the arithmetic mean between 9.4(min) L and
7.15(max) L . Thus, computational experiments are performed using MLP models
with a 6:10:1 architecture and sigmoidal neuronal activation functions.
To verify the obtained results of neural network forecasting, the following
statistical criteria are used: mean absolute percentage error MAPE (3); root mean
square error RMSE (4); minimum and maximum relative approximation error (5);
coefficient of determination )6(D ; correlation coefficient )7(R ; variance ratio )8(S :
n
i i
ii
y
yy
N
MAPE
1
out
100
, (3)
where yout, y are respectively the forecasted and actual values of the i-th example,
ni ,,1 , 19N ;
S.S. Fedin, O.O. Romaniuk, R.M. Trishch
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 120
N
yy
RMSE
N
i
ii
1
2out )(
; (4)
100δ ,100δ
min
max
max
min
y
RMSE
y
RMSE
; (5)
2
1
out
1
2out
2
11
2
2
1 1 1
outout )(
N
i
i
N
i
i
N
i
i
N
i
i
N
i
N
i
N
i
iiii
yyNyyN
yyyyN
D ; (6)
DR ; (7)
y
S
σ
σ , (8)
– standard deviation of the forecast error; )( outyy – forecast error; yσ –
standard deviation of the forecasted indicator.
CONDUCTING COMPUTATIONAL EXPERIMENTS USING NEURAL
NETWORK MODELING METHODS
When creating MLP models, we used STATISTICA 10, a system for statistical
data analysis and forecasting, as well as BrainMaker Professional 3.52, a system
for modeling neural networks. The use of different software during computational
experiments is due to the need to ensure the reproducibility of the forecasting re-
sults. To ensure the convergence of the forecasting results and their verification
assessment, two series of computational experiments were performed in
STATISTICA and BrainMaker Professional. Thus, the training of neural network
models was repeated twice for each sequentially manufactured detail from im-
plementation No. 2 (Table 3). In this case, the BFGS (Broyden-Fletcher-
Goldfarb-Shanno) algorithm was used in the STATISTICA system, and the Back
Propagation of Error algorithm was used in the BrainMaker Professional system.
It should be noted that these machine learning algorithms are iterative gradient
methods of numerical optimization designed to find local extrema of a nonlinear
transformation function by minimizing the MLP error and obtaining the desired
output — y.
Using the BFGS algorithm in the Automated Neural Networks module of the
STATISTICA 10 system, one neural network model out of 50 MLP models was
automatically selected for each detail from implementation No. 2 according to the
criterion of minimum training and testing error. An example of the interface of
the created forecasted MLP-model for the first forecasted example (Table 3), i.e.
the 7th detail from realisation No. 2 (Table 1) in the STATISTICA system is
shown in Fig. 1.
When using the Back Propagation of Error algorithm in the BrainMaker sys-
tem, the accuracy tolerance parameter for training neural network models was set
to 1.0TOL . Analysis of the results of training the MLP model at the number of
Forecasting the quality of technological processes by methods of artificial neural networks
Системні дослідження та інформаційні технології, 2025, № 3 121
epochs 163Run for the 7th detail from implementation No. 2 (Table 1) and the
value of 070.0RMS indicates high accuracy of neural network training (Fig. 2).
An example of the interface of the trained and tested MLP model for the
7th detail from implementation No. 2, which shows the absence of unrecog-
nized facts (Bad=0) in the BrainMaker system, is shown in Fig. 3.
To forecast the controlled parameter of the machining process of the 8th detail
from implementation No. 2, the MLP model was trained using sample examples (Ta-
ble 2) with the first fact from Table 3 added to it. Using this fact in the training sample
allows us to implement the principle of simulation of the neurocontroller's function-
ing and continue the process of training the neural network model on-line.
Thus, by the method of sequentially adding facts to the training set, 19 MLP
models with a 6:10:1 architecture were created in two series of computational ex-
periments using the gradient learning algorithms BFGS and Back Propagation of
Fig. 1. Interface of the MLP model with 6:10:1 architecture created in STATISTICA 10
for the 7th detail of implementation No. 2
Fig. 2. Graph of changes in the RMS Error of training the MLP model in BrainMaker
Professional 3.52 for the 7th detail from implementation No. 2 of the first series of com-
putational experiments
S.S. Fedin, O.O. Romaniuk, R.M. Trishch
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 122
Error for all — from the 7th to the 25th consecutively manufactured details from
implementation No. 2 (Table 3).
RESULTS OF COMPUTATIONAL EXPERIMENTS
The results of forecasting the value of the controlled parameter for the 7th detail from
implementation No. 2, obtained MLP models trained in two series of computational
experiments using the BFGS algorithm are shown in Fig. 4 and Fig. 5, respectively.
The results of the forecasting in two series of computational experiments us-
ing the Back Propagation of Error algorithm for the 7th detail from implementa-
tion No. 2 are shown in Fig. 6 and Fig. 7, respectively.
Fig. 3. The interface of the MLP model with 6:10:1 architecture created in BrainMaker
Professional 3.52 for the 7th detail of the implementation No. 2 of the first series of com-
putational experiments
Fig. 5 The result of forecasting the controlled parameter of the 7th detail from implementation
No. 2, obtained in STATISTICA 10 for the second series of computational experiments
Fig. 4. The result of forecasting the controlled parameter of the 7th detail from implementa-
tion No. 2, obtained in STATISTICA 10 for the first series of computational experiments
Forecasting the quality of technological processes by methods of artificial neural networks
Системні дослідження та інформаційні технології, 2025, № 3 123
The obtained forecaster estimates of the deviation of the controlled size of
shaft type details 50h11 from the nominal value for all sequentially manufac-
tured details from the 7th to the 25th in two series of computational experiments
conducted using MLP models with 6:10:1 architecture and trained by BFGS and
Back Propagation of Error algorithms are shown in Table 4.
T a b l e 4 . The results of forecasting the controlled size of details of the type
shaft 50h11 from the nominal value of yout, μm
Algorithm BFGS Algorithm Back Propagation of Error Example
number Series 1 Series 2 Series 1 Series 2
1 70 69 71 74
2 80 83 79 77
3 84 90 81 87
4 88 90 88 88
5 103 102 104 101
6 92 86 98 96
7 100 103 99 108
8 121 118 115 111
9 96 103 109 109
10 133 123 128 121
11 145 151 125 128
12 112 118 126 129
13 152 152 155 158
14 168 172 146 145
15 166 166 172 172
16 180 183 173 173
17 168 173 172 169
18 173 174 179 175
19 173 179 177 176
Fig. 6. The result of forecasting the controlled parameter of the 7th detail from imple-
mentation No. 2, obtained in BrainMaker Professional 3.52 for the first series of compu-
tational experiments
Fig. 7. The result of forecasting the controlled parameter of the 7th detail from imple-
mentation No. 2, obtained in BrainMaker Professional 3.52 for the second series of com-
putational experiments
S.S. Fedin, O.O. Romaniuk, R.M. Trishch
ISSN 1681–6048 System Research & Information Technologies, 2025, № 3 124
DISCUSSION OF THE OBTAINED RESULTS
The reproducibility of the obtained forecasting results is confirmed by testing the
statistical hypothesis that there is no significant difference between the forecast-
ing results using different machine learning algorithms for two series of experi-
ments (Table 4), which was performed on the basis of a t-test for independent var-
iables, since the condition 05.0p is met (Fig. 8).
The convergence of the two series of neural network forecasting results
based on the machine learning algorithms BFGS and Back Propagation of Error
(Table 4) is confirmed by the significant pairwise correlation coefficients
993.0BFGS R and 995.0nPropagatioBack R , respectively.
Verification of the obtained results of neural network forecasting of the ac-
curacy of the technological process of details machining was carried out using
statistical criteria (3)–(8) (Table 5).
T a b l e 5 . Estimates of statistical criteria for forecast verification
Criterion
Algorithm
MAPE, % RMSE, μm min, % max, % R D S
Series 1 5.322 9.668 5.589 13.617 0.969 0.939 0.282
BFGS
Series 2 6.494 11.180 6.463 15.747 0.964 0.929 0.314
Series 1 4.767 6.886 3.981 9.699 0.984 0.969 0.198 Back Propagation
of Error Series 2 5.051 6.856 3.963 9.656 0.983 0.966 0.197
Based on the values of the coefficient of determination D (Table 5), we cal-
culated the correlation coefficients (7), the value of which allowed us to classify
all the results obtained by R (Table 5) as “Strong” – a qualitative measure of sta-
tistical relationship according to the Chaddock scale (Table 6).
T a b l e 6 . Correlation between quantitative and qualitative estimates of the
correlation coefficient according to the Chaddock scale [37]
Quantitative measure
statistical connection
Qualitative measure
statistical connection
0<R<0.1 None
0.1<R<0.3 Weak
0.3 <R<0.5 Moderate
0.5<R<0.7 Noticeable
0.7<R<0.9 Close
0.9<R<0.99 Strong
0.99<R<1 Functional
Fig. 8. Screenshot of the result of testing the statistical hypothesis that there is no signifi-
cant difference between the forecasting results for two series of experiments in
STATISTICA 10
Forecasting the quality of technological processes by methods of artificial neural networks
Системні дослідження та інформаційні технології, 2025, № 3 125
Thus, the analysis of the values of all statistical criteria (Table 5) allows us
to recommend the use of the Back Propagation of Error algorithm when creating
neural network models to forecast the quality of machining processes for details
by the parameter of shaft diameter deviation from the nominal value. It should be
noted that since the proposed methods of neural network forecasting are based on
the use of machine learning algorithms that allow finding local minima in the
nonlinear mapping YX , the prospect of further research may be the joint ap-
plication of neural network methods and evolutionary modelling, which include
genetic algorithms [38; 40].
CONCLUSIONS
1. To obtain an operational forecasting of the quality of mechanical engi-
neering technological processes by the parameter of accuracy of machining of
shaft-type details, MLP neural network models with the BFGS and Back Propaga-
tion of Error training algorithms were developed using STATISTICA 10 and
BrainMaker Professional 3.52 systems, respectively.
2. As a result of two series of computational experiments, it was found that
the use of the Back Propagation of Error algorithm allows to obtain forecasted
estimates of the controlled process parameter with significantly smaller ranges of
the mean absolute percentage error, mean square error, relative approximation
error and variance ratio criterion compared to the BFGS algorithm. At the same
time, sufficiently large values of the coefficient of determination and significant
estimates of the correlation coefficient were obtained for both algorithms.
3. It has been established that the use of the developed adaptive MLP-models
with the Back Propagation of Error algorithm allows to obtain forecasted estima-
tions of accuracy indicators of technological processes of shaft-type details ma-
chining with 90-96 % reliability, which is confirmed by the range of values of
relative approximation error (5). Thus, the created MLP-models can be recom-
mended for application in neurocontrollers or neuroemulators for formation of
control actions and prevention of discrepancies of parameters of details at control
of accuracy of process of their machining in a mode on-line.
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Received 07.05.2025
INFORMATION ON THE ARTICLE
Serhii S. Fedin, ORCID: 0000-0001-9732-632X, National Transport University, Ukraine,
e-mail: sergey.fedin1975@gmail.com
Oksana O. Romaniuk, ORCID: 0000-0001-9774-9875, Open International University of
Human Development “Ukraine”, Ukraine, e-mail: knutdromanuk@gmail.com
Roman M. Trishch, ORCID: 0000-0002-9503-8428, Ukraine National Aerospace Uni-
versity “Kharkiv Aviation Institute”, Ukraine, e-mail: trich_@ukr.net
ПРОГНОЗУВАННЯ ЯКОСТІ ТЕХНОЛОГІЧНИХ ПРОЦЕСІВ МЕТОДАМИ
ШТУЧНИХ НЕЙРОННИХ МЕРЕЖ / С.С. Федін, О.О. Романюк, Р.М. Тріщ
Анотація. Створено комплекс моделей прямошарових нейронних мереж для
отримання оперативних прогнозів якості технологічних процесів машинобу-
дування. Установлено, що використання алгоритму машинного навчання Back
Propagation of Error дає змогу отримати прогнозні оцінки контрольованого па-
раметра процесу металообробки зі значно меншими діапазонами середньої аб-
солютної відсоткової похибки, середньої квадратичної похибки, відносної по-
хибки апроксимації та критерію дисперсійного відношення порівняно з
алгоритмом BFGS. Показано, що запропоновані моделі нейронних мереж типу
MLP можуть бути рекомендовані для практичного застосування під час управ-
ління точністю процесу механічної обробки деталей типу вал.
Ключові слова: деталі, машинне навчання, нейронна мережа, прогнозування,
технологічний процес, точність, якість.
|
| id | journaliasakpiua-article-343080 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-11-09T02:11:03Z |
| publishDate | 2025 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/ad/bf9c41af822518c0684c5f2a1eba42ad.pdf |
| spelling | journaliasakpiua-article-3430802025-11-09T00:01:30Z Forecasting the quality of technological processes by methods of artificial neural networks Прогнозування якості технологічних процесів методами штучних нейронних мереж Fedin, Serhii Romaniuk, Oksana Trishch, Roman деталі машинне навчання нейронна мережа прогнозування технологічний процес точність якість accuracy details quality forecasting machine learning neural network technological process A set of models of feed-forward neural networks has been created to obtain operational forecasts of the quality of mechanical engineering processes. It is established that the use of the Back Propagation of Error machine learning algorithm allows for obtaining forecasted estimates for the controlled parameter of the metalworking process with significantly smaller ranges of the mean absolute percentage error, mean square error, relative approximation error, and variance ratio criterion compared to the BFGS algorithm. It is shown that the proposed MLP neural network models can be recommended for practical applications in controlling the accuracy of the machining process of shaft-type parts. Створено комплекс моделей прямошарових нейронних мереж для отримання оперативних прогнозів якості технологічних процесів машинобудування. Установлено, що використання алгоритму машинного навчання Back Propagation of Error дає змогу отримати прогнозні оцінки контрольованого параметра процесу металообробки зі значно меншими діапазонами середньої абсолютної відсоткової похибки, середньої квадратичної похибки, відносної похибки апроксимації та критерію дисперсійного відношення порівняно з алгоритмом BFGS. Показано, що запропоновані моделі нейронних мереж типу MLP можуть бути рекомендовані для практичного застосування під час управління точністю процесу механічної обробки деталей типу вал. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2025-09-29 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/343080 10.20535/SRIT.2308-8893.2025.3.09 System research and information technologies; No. 3 (2025); 113-127 Системные исследования и информационные технологии; № 3 (2025); 113-127 Системні дослідження та інформаційні технології; № 3 (2025); 113-127 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/343080/331016 |
| spellingShingle | деталі машинне навчання нейронна мережа прогнозування технологічний процес точність якість Fedin, Serhii Romaniuk, Oksana Trishch, Roman Прогнозування якості технологічних процесів методами штучних нейронних мереж |
| title | Прогнозування якості технологічних процесів методами штучних нейронних мереж |
| title_alt | Forecasting the quality of technological processes by methods of artificial neural networks |
| title_full | Прогнозування якості технологічних процесів методами штучних нейронних мереж |
| title_fullStr | Прогнозування якості технологічних процесів методами штучних нейронних мереж |
| title_full_unstemmed | Прогнозування якості технологічних процесів методами штучних нейронних мереж |
| title_short | Прогнозування якості технологічних процесів методами штучних нейронних мереж |
| title_sort | прогнозування якості технологічних процесів методами штучних нейронних мереж |
| topic | деталі машинне навчання нейронна мережа прогнозування технологічний процес точність якість |
| topic_facet | деталі машинне навчання нейронна мережа прогнозування технологічний процес точність якість accuracy details quality forecasting machine learning neural network technological process |
| url | https://journal.iasa.kpi.ua/article/view/343080 |
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