=Paper=
{{Paper
|id=Vol-2727/paper13
|storemode=property
|title=Application of Artificial Neural Networks to Forecast Technological Process Parameters in Aluminum Production
|pdfUrl=https://ceur-ws.org/Vol-2727/paper13.pdf
|volume=Vol-2727
|authors=Anton Mikhalev,Nina Lugovaya,Tatiana Penkova,Anna Molyavko,Evgenia Karepova,Mikhail Sadovsky,Vladimir Shaidurov,Igor Borovikov,Roman Morozov,Margarita Favorskaya,Ivan Perevalov,Tatiana Vitova,Valery Nicheporchuk,Tatiana Penkova,Maria Senashova,Aleksey Korobko,Yulia Ponomareva,Anna Korobko,Anna Vlasenko,Natalia Zhilina,Dmitry Zhuchkov
}}
==Application of Artificial Neural Networks to Forecast Technological Process Parameters in Aluminum Production==
https://ceur-ws.org/Vol-2727/paper13.pdf
99
Application of Artificial Neural Networks
to Forecast Technological Process Parameters
in Aluminum Production*
Anton Mikhalev1[0000-0002-8986-5953], Nina Lugovaya1[0000-0002-2939-0298],
and Tatiana Penkova2[0000-0002-0057-0535]
1 Siberian Federal University, 26, Kirenskogo str., Krasnoyarsk, 660074, Russia,
2 Institute of computational modelling of the Siberian Branch
of the Russian Academy of Sciences, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russia
asmikhalev@yandex.ru
Abstract. The study is aimed at methods of machine learning as it relates to
forecasting technological process parameters. The forecasting tools are
developed in two main stages: analysis and preprocessing of input data,
elaboration of a math model and validation of the solution. Forecasting relies on
recurrent neural networks. The method of maximum accuracy was used to elicit
the neural network architecture, and calculate the metrics of MSE, MAPE, the
coefficient of determination and Theil coefficient. The results obtained in the
tests run on the suggested model of forecasting the cell voltage are deemed
acceptable in terms of predicting the technological process indicators. The
identified errors will ensure that preventive measures are taken in a timely
manner to avoid process disruptions and increase overall efficiency of
aluminum production.
Keywords: Neural Network, Forecasting, Process Disruptions, Technological
Process Parameters, Voltage, Aluminum Production.
1 Introduction
Of all non-ferrous metal industries, aluminum production has the worldβs biggest
share in manufacturing and consumption [1]. The industry develops within the lines
of enhancing productivity of the main unit, electrolysis cell, therefore one of the key
tasks is to control low-duty cells. Some of such cells are easily identifiable (shutdown
cells, those under localized repairs), so they are controlled based on the current
technical condition. Other are harder to identify, as deterioration in technology does
not manifest itself directly and can only be determined through indirect parameters.
Their number varies depending on supplied raw materials, occurring troubles,
operational activities, etc., which may cumulatively lead to a greater number of cells
* Copyright c 2020 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0).
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operating at lower capacities and consequently to a considerable decrease in technical
and economic indexes [2, 3]. Timely detection of errors in the technological process
can be ensured in case the performance parameters of the complex of aluminum
production are analyzed using modern intelligent technologies.
The technical condition of cells is controlled across a number of parameters that
are continuously measured and stored in the data base of the computer-aided process
control system: cell voltage, anode current, modes of automatic alumina consumption,
adjustable anode block position. Making sure that these parameters are properly
controlled and identified is critical in timely detection of process disruptions in the
course of cell operation.
Values of parameters that need to be predicted are predominantly described as time
series, that is, in sequences of values taken at certain instants of time. Forecasting
time series normally entails using regression and autoregression methods, exponential
smoothing, neural networks, etc. [4-5]. The forecasting model in this study is
represented by artificial neural networks [6]. This technology has the following key
strengths: solving problems with unknown patterns, resistance to noises in input data,
and potential high-speed response. Neural network topologies are selected depending
on the input data and type of tasks to be solved. This study looks at the application of
artificial neural networks to forecast one of the most crucial among the controllable
parameters β cell voltage. Recurrent neural networks (RNNs) were chosen for the
purpose. The elements in RNNs form a directed graph which allows for processing
series of events in time or consecutive spatial sequences. Unlike multilayer
perceptrons, RNNs can use their internal memory to process variable length
sequences of inputs.
The predictive tools are developed in two stages: 1) analysis and preprocessing of
input data; 2) elaboration of a math model and validation of the solutions. The main
body of the article is structured based on this logic. Section 2 spells out the objectives
for time series forecasting. Section 3 describes the inputs. Section 4 elaborates on the
applied methods of preprocessing of input data. Section 5 presents the result of
selecting an optimal neural network architecture. Section 6 gives the results of voltage
forecasting.
2 Research Objective
The aim of the time series forecasting is set as follows. Let us assume that the values
of the time series are the following:
π = {π₯(π‘), π‘ β π, π₯(π‘) β π
}, π = {1,2, β¦ , π} (4)
where π₯(π‘) is the value of the analyzed parameter registered at a given instant in time.
Based on the values of the analyzed parameter at preceding moments in time
π₯(π‘), π₯(π‘ β 1), π₯(π‘ β 2), β¦ π₯(π‘ β π + 1), π β€ π we must predict (assess the values
with highest precision) the analyzed parameter as it should appear at points in time
π‘ + 1, π‘ + 2, β¦ , π‘ + π, i.e. build a sequence of forecasted values:
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π = {π₯ (π‘ + 1), π₯ (π‘ + 2), β¦ , π₯ (π‘ + π)} (5)
To calculate the values in the time series at future moments in time, we must
determine the functional relationship that shows the connection between the past and
future values of this time:
π₯ (π‘ + π) = π π₯(π‘ β π + 1), π₯(π‘ β π + 2), β¦ , π₯(π‘ + π β 1) (6)
The presented functional relationship (3) represents the prediction model.
Therefore, the task of time series forecasting is fulfilled through creating a
forecasting model that will satisfy the relevant criteria of forecasting quality control.
Figure 1 illustrates the idea behind the objective of time series forecasting.
Fig. 1. Illustrated objective of time series forecasting.
Currently the accuracy of time series modelling is commonly estimated using the
following two indicators:
β mean squared error, MSE:
πππΈ = β π₯(π) β π₯ (π) (7)
β mean absolute percentage error, MAPE, mean average percentage deviation (mean
relative forecast error):
| () ( )|
ππ΄ππΈ = π β β 100% (8)
()
In addition, apart from the given evaluation characteristics, this study estimates the
accuracy of forecasts made to the elaborated prediction model using the coefficient of
determination and Theil inequality coefficient:
β the coefficient of determination:
β ( () )
π
= (9)
β ( ( ) )
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The coefficient of determination characterizes the strength of association of inputs
and forecasts, so the closer it gets to 1, the better is the quality of the prediction
model.
β Theil inequality coefficient:
β () ()
π£= (10)
β () β ()
The Theil index shows the strength of association in time series, so the closer it is to
zero, the more strongly associated the series are that are compared.
3 Description of Inputs
The basic time series presents the data on the cell voltage registered by system
detectors in the experimental area of the Khakas aluminum smelter. The voltage time
series contain three-minute values of voltage for the period from January 3, 2020 to
January 31, 2020. The time series parameters are demonstrated in Table 1.
Table 1. Parameters of voltage time series.
Cell Series length Mean value Min value Max value Standard
error
No.1 14320 3.737383 3.192000 4.023000 0.067460
No.2 14320 3.737383 3.192000 4.023000 0.067460
No.3 14320 3.692608 2.959000 4.198000 0.062725
No.4 14320 3.712393 0.000000 4.123000 0.107927
No.5 14320 3.702826 2.367000 4.469000 0.061439
No.6 14320 3.739327 3.483000 4.201000 0.081022
No.7 14320 3.701671 0.000000 4.224000 0.090101
No.8 14320 3.716235 0.000000 4.450000 0.083461
The overall sample volume contains about 115,000 entries. To set up the prediction
model and evaluate the quality of the model itself, the sample volume was broken
down into three parts: training (voltage at cells No.1-6), validating (voltage at cell No.
7), and testing (voltage at cell No.7).
4 Preprocessing of Inputs
The stage of building a prediction model is preceded by the stage of analysis and
preprocessing of the time series. The preprocessing of the time series entails
identifying outliers and smoothing the series. Certain discrepancies in the quality of
measurements occur in various time series of data characterizing the production
process. The outliers may be caused by technical errors in data collection, processing,
and transfer.
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Sifting out the outliers from the rest of data is a specific mechanism to identify
and delete obvious discrepancies and other possible errors in inputs and make sure
further forecasts are accurate. In the study, outliers were isolated by the isolation
forest algorithm [7]. The isolation forest is a method to detect outliers that is mainly
centered around constructing a forest of decision trees during training and forecast
output. When it comes to detecting outliers, this method relies on the fact that outliers
have values that are decidedly different from the norm and only make up a small
proportion of the whole set of data. The results of detected outliers for voltage in cell
No. 1 are presented in Figure 2.
Fig. 2. Example of the isolation forest algorithm as it is applied to inputs.
Detected outliers are removed from the set and the resulting gaps in the data are
recovered by the interpolation technique [8]. The view after the removal of outliers
for the cell voltage can be seen in Figure 3.
Fig. 3. Example of cleaned inputs for retention cell No. 1.
5 Selection of Neural Network Architecture
The efficiency of solving time series forecasting tasks that feature artificial neural
networks is defined by their hyperparameters. The main hyperparameters underlying
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an artificial neural network are the number of layers and the number of neurons in
each of the layers.
The neural network architecture was selected by iterating over the values of the
number of layers/neurons. The number of LSTM-layers ranged from 1 to 3, whereas
the number of neurons in each layer varied from 50 to 100 with the step size of 10.
The Dropout technique was used to combat overfitting.
The results of the neural network architecture selection are presented in Table 2.
Table 2. Values of the forecast model quality evaluation characteristics
for various neural network architectures.
Number of 1 2 3
neurons/Number of
layers
50 MSE 0.0003195597 MSE 0.000321653 MSE 0.0003247026
MAPE 0.231096479 MAPE 0.23555911 MAPE 0.253191952
π£ 0.0034003583981 π£ 0.003410919610 π£ 0.0034285759926
π
0.891027504246 π
0.89031356842 π
0.88927375558
60 MSE 0.0003215470 MSE 0.000335930 MSE 0.0003606315
MAPE 0.228269917 MAPE 0.25498155 MAPE 0.300183535
π£ 0.0034105846637 π£ 0.0034843430721 π£ 0.0036151698427
π
0.890349819008 π
0.885444884519 π
0.877021687371
70 MSE 0.0003359085 MSE 0.0003257920 MSE 0.0003255863
MAPE 0.261688514 MAPE 0.239746288 MAPE 0.237674537
π£ 0.0034879700818 π£ 0.0034340883833 π£ 0.0034330130443
π
0.885452433313 π
0.888902250687 π
0.888972387867
80 MSE 0.0003399340 MSE 0.0003398388 MSE 0.0003229711
MAPE 0.265887808 MAPE 0.256396719 MAPE 0.234390351
π£ 0.0035089207105 π£ 0.0035081461294 π£ 0.0034188288637
π
0.884079714165 π
0.884112165713 π
0.889864189599
90 MSE 0.0003275380 MSE 0.0003216582 MSE 0.0003421464
MAPE 0.238560829 MAPE 0.248235352 MAPE 0.263077962
π£ 0.0034412220481 π£ 0.0034113558002 π£ 0.0035161051010
π
0.888306851186 π
0.890311907914 π
0.883325278229
100 MSE 0.0003231217 MSE 0.0003437367 MSE 0.0003504917
MAPE 0.241065737 MAPE 0.277972490 MAPE 0.278388048
π£ 0.0034181660805 π£ 0.0035288340033 π£ 0.0035634811089
π
0.889812833874 π
0.882782972649 π
0.880479436508
The training data showed a similar result for all possible architectures. The eventually
selected architecture consisted of 1 LSTM-layers with 50 neurons and one fully
connected layer.
Other hyperparameters of the model were set using the random-walk method with
cross-validation. The parameters for model construction were selected based on the
principle of maximum accuracy (Table 3).
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Table 3. Setting the hyperparameters of the model.
Parameter name Description Value
Optimizer Parameter that shows how the model is adam
updated based on inputs and the loss
function
Loss function Parameter that measures the model mean_absolute_error
accuracy during training
Metrics Parameter that is used to monitor training accuracy
and testing of the model
Number of epochs Number of training algorithm runs across 50
the entire set of training data
Mini-batch size Number of sets that must be processed 50
before the model parameters are updated
6 Forecasting Voltage
Process disruptions in the retention cell operation build up over time and undetected
errors may spiral into serious accidents. Timely detection of deviation will entail
long-term forecasting.
The long-term voltage forecasting is carried out through the iterative approach.
The iterative approach in forecasting involves a few forecasting runs performed one
step ahead, though using the values in the preceding stage. The general diagram of
long-term forecasting is given in Figure 4.
Fig. 4. Diagram of long-term forecasting.
The forecasting sequence is chosen to have a length of 10. The forecasts were fulfilled
10 steps ahead, which translates into 30 minutes. The forecasting results for the test
sets are presented in Figure 5.
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Fig. 1. Results of voltage forecasting.
It can be derived from the resulting graph that long-term forecasting performed with
the iterative approach entails a value in every step that will differ from the real one,
i.e. there will always be a certain error that will be growing with every new step. In its
turn, the resulting prediction model makes it possible to reveal a tendency in how the
controlled parameter is changing and identify the process disruptions in a timely
manner.
7 Conclusion
The paper presents the results of artificial neural networks as they were applied to
forecast the values of the technological process parameters in aluminum production. It
looks at the mechanics of the prediction model construction aimed at one of the key
controllable process parameters, namely the retention cell voltage. The elaboration of
the forecasting tools is carried out in two main stages: analysis and preprocessing of
inputs, construction of a math model and validation of the solution. Forecasting was
chosen to be performed using recurrent neural networks. The method of maximum
accuracy was used in the selection of an optimal neural network architecture,
calculation of MSE, MAPE metrics, determination coefficient, and Theil coefficient.
As it can be derived from the values of the selected metrics, the accuracy of the
suggested model may be deemed appropriate.
The results obtained in the testing process are acceptable in terms of forecasting
values of the process parameters. Timely detection of deviations in the forecasted
parameter will allow for a quick response to prevent any process disruptions and thus
increase aluminum production efficiency.
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