Machine Learning-based Forecasting of Sensor Data for Enhanced

Environmental Sensing

MARTA NARIGINA, ARTURS KEMPELIS, ANDREJS ROMANOVS

Department of Modeling and Simulation,

Riga Technical University,

Riga,

LATVIA

Abstract: - This article presents a study that explores forecasting methods for multivariate time series data,

which was collected from sensors monitoring CO2, temperature, and humidity. The article covers the

preprocessing stages, such as dealing with missing values, data normalization, and organizing the time-series

data into a suitable format for the model. This study aimed to evaluate Long Short-Term Memory (LSTM)

networks, Convolutional Neural Networks (CNNs), Vector Autoregressive (VAR) models, Artificial Neural

Networks (ANNs), and Random Forest performance in terms of forecasting different environmental dataset

parameters. After implementing and testing fifteen different sensor forecast model combinations, it was

concluded that the Long Short-Term Memory and Vector Autoregression models produced the most accurate

results. The highest accuracy for all models was achieved when forecasting temperature data with CO2 and

humidity as inputs. The least accurate models forecasted CO2 levels based on temperature and humidity.

Key-Words: - Forecasting, Sensor Data, Machine Learning, Deep Learning, Neural Networks

Received: August 26, 2022. Revised: April 15, 2023. Accepted: May 3, 2023. Published: May 29, 2023.

1 Introduction

Various environments, such as medical facilities or

agricultural settings, necessitate monitoring,

typically accomplished using different sensor

devices, [16]. However, deploying these sensor

devices in each environment is often impractical. In

situations where only a limited number of sensor

devices are available, machine learning-based

models can be employed to estimate other sensor

values with a certain level of accuracy, thereby

potentially serving as substitutes for physical

devices.

This article explores a range of sensor

forecasting techniques, explicitly addressing the

assessment of multivariate time series forecast

methods in environmental sensing. In this analysis,

the forecasting capabilities were evaluated by

comparing forecasted sensor values to actual sensor

readings to measure the accuracy of the data

forecasts. The method of developing forecasting

models was used to forecast one of the three dataset

parameters. This method was used not only to

experimentally determine which of the chosen

models had the highest accuracy but also to

determine which parameter or sensor has the

potential to be substituted with a forecast from

sensor data trained machine learning model.

The dataset that was used for training the models

contains 20560 entries that were gathered from CO2

(ppm), Temperature (°C), and Humidity (%RH)

sensors for one month, [1]. The results of the model

experiments and data processing are discussed in

this article.

Long Short-Term Memory (LSTM) networks,

along with Convolutional Neural Networks (CNNs),

Vector Autoregressive (VAR) model forecast,

Artificial Neural Networks (ANN), and Random

Forest, were used to test the forecast accuracy. To

use the data, the following preprocessing steps of

raw sensor data were included:

 Measures to address missing values.

 Ensuring temperature, humidity, and CO2

readings were normalized.

 Presenting time-series data in the correct

model format.

An initial model structure utilized CNN,

incorporating a single convolutional layer and an

assortment of pooled and fully established layers.

Using 1D convolutions, the CNN model was

effective in detecting localized patterns in the input

data, while the pooling layers worked to decrease

spatial proportions and computational complexity.

Patterns were learned by utilizing post-

convolutional and fully connected layers with ReLU

activation, facilitating the introduction of

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nonlinearity. The sensor measurements' mean

squared error was predicted and compared for the

CNN and LSTM.

The initial steps to prepare the VAR model

included handling missing values and assessing

stationarity. Determining the optimal lag order,

which dictates how many previous time steps should

be factored into predictions, was accomplished via

the Akaike Information Criterion (AIC). After

monitoring residuals, any signs of non-stationarity

were handled by implementing diverse

transformations or differencing techniques.

2 Sensor Data Forecasting Methods

Nowadays, there exist many sensor data forecasting

methods. Some standard forecasting methods are:

1. Linear regression;

2. Random Forest;

3. Artificial Neural Networks;

4. Support Vector Machines;

5. Hybrid approach.

2.1 Linear Regression

Linear regression is a widely adopted statistical

method for predicting sensor data, relying on

assuming a linear relationship between input and

output variables, [2]. This method involves

constructing a linear regression model by fitting a

linear equation to the input data, which can be used

to forecast the output variable, [3]. The model has

the form:

y = β0 + β1x1 + β2x2 + ... + βnxn + ε,

where y is the dependent variable, x1, x2, ..., xn are

independent variables, β0, β1, β2, ..., βn are the

model coefficients, and ε represents the error term.

The objective of linear regression is to determine the

optimal values of the coefficients that minimize the

sum of the squared errors between the predicted and

actual values in the training data, [2]. This process is

accomplished through the least squares method,

which seeks to obtain the values of the coefficients

that minimize the sum of squared differences

between the predicted and actual values, [2].

Once the model has been trained, it can be

utilized to make predictions on new data by

inserting the values of the independent variables

into the equation and calculating the corresponding

value of the dependent variable, [3]. However, when

using linear regression for predicting sensor data, it

is crucial to consider the presence of outliers or

nonlinear relationships between the input and output

variables. More complex models, such as random

forests or neural networks, may be more

appropriate, [4]. Additionally, the data should be

preprocessed to handle missing values, scale the

features appropriately, and handle any categorical

variables using techniques such as one-hot

encoding, [5].

2.1.1 Methodology for Implementing

Linear regression can be an efficient tool for

analyzing data sets. The following methodology

outlines how to implement it effectively.

Firstly, the dependent and independent variables

must be identified. This will allow us to determine

the correlation between them. Next, the most

suitable regression model is chosen to align with the

data. This will often depend on the relationship

between the variables being analyzed. It is important

to note that the data must be clean and outlier-free,

[6].

Once the appropriate regression model has been

identified, the regression equation coefficients can

be estimated. This can be done through manual

calculations or software such as Excel or R, [7].

After this, it is vital to check the accuracy of the

regression equation. A useful metric for doing so is

the R-squared value. This will give insight into how

much of the variation in the dependent variable is

explained by the independent variable, [2]. It is also

useful to check for autocorrelation and

heteroscedasticity, [5]. Finally, the model is tested

using the data collected. This will show how well

the model fits the dataset, [8].

To begin linear regression, one must first

pinpoint the independent variables (alternatively

referred to as predictors or features) that hold

significance in predicting the dependent variable

(alternatively referred to as the response variable or

target variable) based on the gathered environmental

sensor data, [2]. Following this, the next move is to

instruct the linear regression model with a data set,

optimizing its algorithm to triangulate the

coefficients that will best diminish the contrast

between the predicted and factual values. To

conclude, for the near-final stage, a separate test set

of data is applied to determine the model's level of

precision and accuracy in correctly forecasting the

dependent variable, [9].

2.1.2 Performance of the Algorithm in Terms of

Accuracy and Precision

In terms of accuracy and precision, the algorithm's

performance is noteworthy. To appraise the linear

regression algorithm's effectiveness, one can employ

a range of measurements, such as mean absolute

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error (MAE), mean squared error (MSE), and R-

squared (R²) coefficient, [2]. The MAE and MSE

determine the mean disparity between calculated

and actual values, whereas the R² coefficient

determines the amount of independent variable

variation that accounts for the dependent variable.

The linear regression algorithm's precision and

accuracy are hinged on the sufficiency and caliber

of the environmental sensor data, coupled with the

relevance of the independent variables adopted for

the model, [7].

2.1.3 Limitations and Challenges

There exist some challenges and limitations to

consider in this matter. In predicting environmental

sensor data, linear regression is commonly utilized,

yet various issues and constraints accompany it, [2].

Real-world environmental sensing applications may

not always present a linear correlation between

independent and dependent variables, which is an

understandable limitation. Furthermore, it may not

be competent in detecting intricate, nonlinear

relationships within variables. Therefore, more

advanced techniques, such as decision trees or

neural networks, must be implemented, [3]. Lastly,

the model's effectiveness is strongly influenced by

the precision and soundness of the environmental

sensor data used during the training process, [8].

2.2 Random Forest

Random Forest is a machine learning model that has

gained popularity in predicting sensor data, [4]. An

ensemble learning method combines multiple

decision trees to make forecasts. Each decision tree

is trained on a random subset of the input features

and a random subset of the training data, and the

final prediction is made by averaging the predictions

of all the trees. Random Forest is particularly useful

for handling complex interactions between input

variables and can handle both continuous and

categorical input variables and can be used for both

regression and classification problems, [6].

To use Random Forest for sensor data

forecasting, the data is first collected and

preprocessed, which may include cleaning,

normalization, and feature engineering, [3]. Then,

the sensor data is divided into training and testing

sets. The Random Forest model is trained on the

training set using the input features and output

variables, [5]. The model's performance is evaluated

using the testing set, and metrics such as mean

squared error (MSE) and R-squared are calculated,

[4]. The model can be optimized by tuning the

hyperparameters, such as the number of trees in the

forest, the maximum depth of the trees, and the size

of the random subsets, [3].

Random Forest has several advantages for

predicting sensor data, including high accuracy,

robustness, and the ability to provide information on

the importance of each input feature, [10]. This

information can help understand the underlying

patterns in the data, [7]. It is important to note that

Random Forest may not be suitable for all cases,

and the presence of outliers or nonlinear

relationships may require more complex models,

such as neural networks or support vector machines,

[11]. Additionally, data preprocessing techniques,

such as handling missing values, scaling features

appropriately, and one-hot encoding categorical

variables, should be applied to improve the model's

performance, [2].

2.2.1 Methodology for Implementing

Random Forest provides superior results by

improving prediction precision and consistency

using multiple decision trees in an ensemble

learning algorithm, [4]. This environmental sensor

data prediction tactic yields quantifiable gains in

accurately forecasting air or water quality based on

sensor outputs, [12].

To put the Random Forest model into practice,

one must start by choosing the appropriate

independent and dependent variables according to

the data given by the environmental sensor, [4].

Next, the training phase of the model begins by

taking a subset of the features and data points and

using them to set up multiple decision trees, [4]. The

impurity of these trees is evaluated to optimize the

selection of thresholds and features used to split the

data. The model is estimated using a different

testing set to analyze and measure its precision and

accuracy in predicting the dependent variable.

2.2.2 Performance of the Algorithm in Terms of

Accuracy and Precision

Depending on the data being used, there are

different ways to evaluate the Random Forest

algorithm. Three standard metrics include the mean

absolute error (MAE), mean squared error (MSE),

and R-squared (R²) coefficient, [4]. For this

algorithm to be effective, it relies on accurate and

plentiful data that can be measured by

environmental sensors, [3]. Additionally, the choice

of independent variables partially influences the

model's success. If there are nonlinear correlations

between the independent and dependent variables,

Random Forest tends to be a better choice than

linear regression, [4].

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2.2.3 Limitations and Challenges

Several limitations and challenges exist for the

Random Forest machine learning algorithm. One of

these challenges is the potential for overfitting the

training data resulting in poor generalization

performance on the test data. It can also be

computationally expensive when there is a

significant number of features or data points,

leading to limited scalability in some applications,

[9]. Lastly, environmental sensor data quality and

accuracy significantly affect the algorithm's

performance, [6].

2.3 Artificial Neural Networks

Artificial Neural Networks (ANNs) are a popular

machine learning technique for predicting sensor

data inspired by the structure and function of the

human brain. ANNs consist of interconnected

nodes, or neurons, arranged in layers, which process

information and make predictions. ANNs are

particularly useful for handling complex and

nonlinear relationships between input and output

variables and can handle continuous and categorical

input variables.

The steps for using ANNs to predict sensor data

are as follows:

 Data preparation: This involves collecting

and preprocessing the sensor data, including

cleaning, normalization, and feature

engineering.

 Splitting the data: The sensor data is divided

into training and testing sets.

 Model training: The ANN model is trained

on the training set using backpropagation,

which updates the weights between the

neurons to minimize the error between the

predicted and actual output.

 Model evaluation: The model's performance

is evaluated using the testing set, and metrics

such as mean squared error (MSE) and R-

squared are calculated.

 Model optimization: The model can be

optimized by tuning the hyperparameters,

such as the number of hidden layers, the

number of neurons per layer, and the

learning rate, [5].

ANNs offer several advantages for predicting

sensor data, including their ability to model

nonlinear relationships between input and output

variables, their robustness to noise and missing data,

and their adaptability to changing environments.

Additionally, ANNs can be used for regression and

classification problems, [7].

2.3.1 Methodology for Implementing

ANNs find frequent use in predicting environmental

information, such as air quality, [13], and water

quality, [12], using sensor data.

Selecting the relevant independent and

dependent variables based on environmental sensor

data is the initial step in implementing ANNs. A

training set of data is utilized to create and train the

ANN model, requiring adjustments to the neural

network's weights and biases to reduce the

discrepancy between actual and predicted values of

the dependent variable. Utilizing backpropagation,

the algorithm updates the weights and biases of the

neural network in response to the error gradient

during the training process. A distinct test set of data

is assessed to examine the ANN model's accuracy

and precision in anticipating the dependent variable.

2.3.2 Performance of the Algorithm in Terms of

Accuracy and Precision

Using metrics like the R-squared (R²) coefficient

and mean absolute error (MAE), the effectiveness of

the ANN algorithm is assessed, [7]. The accuracy

and precision of this algorithm are contingent on the

quality and quantity of environmental sensor data, in

addition to proper independent variable selection,

[7], [12]. When there are nonlinear connections

between independent and dependent variables,

ANNs can outperform the Random Forest and linear

regression algorithms, [7], [9]. Mean squared error

(MSE) is another metric used to evaluate the

performance of the ANN algorithm.

2.3.3 Limitations and Challenges

ANNs, while a productive machine learning

algorithm, come with certain limitations and

obstacles. Despite their strength, they can lead to a

lack of generalizability when overfitted to the

training data. They also require much training data

and computational resources, limiting their

applicability, [9]. Lastly, a daunting task lies in

expertly selecting architecture and hyperparameters

for the ANN model through experimentation, [5].

2.4 Support Vector Machines

Support Vector Machines (SVMs) are a popular

machine learning model for predicting sensor data,

capable of handling regression and classification

problems, [9]. SVMs work by identifying a

hyperplane in the input space that separates the data

into two classes for classification or that best fits the

data for regression. This hyperplane is chosen to

maximize the margin between the two classes or the

distance between the hyperplane and the data points,

[11].

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SVMs are particularly useful for handling high-

dimensional data, including continuous and

categorical input variables. The general steps for

using SVMs to predict sensor data involve data

preparation, splitting the data into a training and

testing set, model training, evaluation, and

optimization, [3]. During model training, the SVM

model finds the hyperplane that best separates the

data into two classes or best fits the data. The

model's performance is evaluated using mean

squared error (MSE) and R-squared, [11].

SVMs have several advantages for predicting

sensor data, including high accuracy due to the

optimal hyperplane and the ability to handle linear

and nonlinear relationships between input variables

and output variables using different kernel

functions, [9], [11]. Additionally, SVMs are robust

to overfitting, which can occur when a model is too

complex and captures noise in the data. SVMs are

also versatile, making them popular for various

machine learning applications, [13].

2.4.1 Methodology for Implementing

Predictive algorithms known as Support Vector

Machines (SVMs) have their place in classification

and regression. Often, they are implemented in

determining environmental factors, like air and

water quality, concerning sensor data, [14].

Contrastingly, they first choose which parameters

and environmental indicators are relevant before

continuing by using a kernel function that raises the

information to a higher level of complexity. The

algorithm then proceeds by using a linear

hyperplane to differentiate the classes. Training the

SVM model on a data set maximizes the margin

between the classes. Then, the SVM model’s

accuracy and precision in predicting the dependent

variable are evaluated using a separate test set of

data, [15].

2.4.2 Performance of the Algorithm in Terms of

Accuracy and Precision

Various metrics are available to evaluate the SVM

algorithm’s performance, including mean absolute

error (MAE), mean squared error (MSE), and R-

squared (R²) coefficient, [9]. The performance of the

SVM algorithm depends on the proper selection of

the kernel function and the quality and quantity of

environmental sensor data, [9]. When working with

high-dimensional data or nonlinear relationships

between dependent and independent variables,

SVMs can outperform linear regression and

Random Forest, [2].

2.4.3 Limitations and Challenges

For SVMs, there are a few hindrances and obstacles

to be aware of. One issue is that their performance

can be affected by the selection of kernel functions

and hyperparameters – this is something to keep in

mind. Training and optimizing SVMs can also be

computationally demanding and may hinder their

scalability in certain situations. Lastly, grappling

with interpreting the SVM model is a task because it

relies on a multifaceted objective function, [9].

2.5 SARIMA

2.5.1 Methodology for Implementing

The order of seasonal differencing (D) and seasonal

orders for autoregressive (p), integrated (q), and

moving average (P and Q) components must be

selected after identifying the seasonal pattern in the

data when implementing SARIMA. The augmented

Dickey-Fuller test, [6], and visual inspection are

methods for choosing appropriate values.

Using maximum likelihood estimation, one must

fit the SARIMA model to the data, but before that,

one needs to establish the values for D, p, q, P, and

Q. The idea is to determine the model parameters

that would optimize the likelihood of observing the

data based on the values established, [12].

2.5.2 Performance of the Algorithm in Terms of

Accuracy and Precision

The accuracy and precision of the SARIMA

algorithm are contingent upon both the quality of

data and its intended use. A strong seasonal pattern

with stationary data post-seasonal differencing

provides the ideal circumstances for SARIMA to

perform well – especially regarding seasonal time

series data predictions. For data lacking a well-

defined seasonal pattern, SARIMA was deemed

unsuitable according to a study of various time

series forecasting approaches. In cases where data

displayed a distinct monthly trend, SARIMA

surpasses other techniques.

2.5.3 Limitations and Challenges

Challenges and limitations are present in this

scenario, causing difficulty in achieving objectives.

In the realm of time series forecasting, SARIMA

comes with its fair share of challenges and

limitations, [17]. One of its challenges involves the

data’s stationarity, which must be achieved via

seasonal differencing. However, this task can prove

to be difficult, especially if the data isn’t stationary

to begin with.

In practice, a linear process generating the data is

not always assumed by SARIMA, presenting

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another challenge. It is also sensitive and may not

function effectively when the data contains

significant anomalies or outliers.

Interpreting the model parameters and grasping

the dynamics behind time series data is a

complicated feat with SARIMA, which is a notable

drawback. This poses a challenge when trying to

utilize SARIMA for causal inference or to seek

comprehension of the underlying mechanisms

producing the data. Ultimately, SARIMA falls short

in providing easy-to-understand explanations or

insights.

2.6 Hybrid Approach

In machine learning, a hybrid model for predicting

sensor data involves combining multiple models to

enhance predictions’ accuracy or address individual

models’ limitations. For instance, one approach for

predicting temperature sensor data is using a hybrid

model that combines a linear regression model and a

random forest model.

The sensor data is first prepared by cleaning,

normalizing, and engineering features to create this

hybrid model. The data is then split into training and

testing sets, and two models are trained on the

training set: a linear regression model that uses

previous temperature readings to predict the next

reading and a random forest model that incorporates

additional features like time of day, day of the week,

and season.

The predicted values from both models are then

combined using a weighted average, with weights

determined based on each model’s performance on

the training set. Finally, the performance of the

hybrid model is evaluated using the testing set, with

metrics like mean squared error and R-squared

calculated.

Another example of a hybrid approach for

predicting sensor data is the combination of

Random Forest and Artificial Neural Network

models for predicting air quality using

environmental sensor data, [13]. The Random Forest

model was used to select essential features from the

sensor data, which were then used as inputs to the

Artificial Neural Network model for air quality

prediction. The hybrid approach outperformed both

individual models in terms of prediction accuracy.

The advantages of using a hybrid model for

sensor data prediction include the ability to capture

both linear and nonlinear relationships between

input and output variables, as well as the ability to

incorporate additional features that can improve

prediction accuracy. Moreover, combining multiple

models can help reduce the risk of overfitting and

improve prediction robustness. However, the

specific hybrid model that is most appropriate will

depend on the nature of the data and the problem

being addressed.

2.6.1 Methodology for Implementing

To enhance the precision and accuracy of

environmental sensor data forecasts, a hybrid

strategy fuses numerous machine learning

algorithms, including artificial neural networks,

support vector machines, Random Forest, and linear

regression. A hybrid approach selection process

requires evaluating the specific combination of

algorithms best suited for the type of data and

prediction issue at hand. A widely adopted hybrid

approach merges the strengths of Random Forest

and linear regression for improved efficacy. To

assess the accuracy and precision of the hybrid

model’s prediction of the dependent variable, it

must first undergo training with a data set and then

evaluation through an alternative test set.

2.6.2 Performance of the Algorithm in Terms of

Accuracy and Precision

By considering the strengths of different algorithms,

hybrid models can achieve greater accuracy and

precision compared to individual algorithms, which

can be assessed through various metrics such as

mean absolute error (MAE), mean squared error

(MSE), and the R-squared (R²) coefficient. The

success of the hybrid approach is primarily

determined by the quality and quantity of the

environmental sensor data, the relevance of the

chosen algorithms for the hybrid model, and the

techniques utilized to integrate the results of various

algorithms.

2.6.3 Limitations and Challenges

Optimal algorithm combinations can be complicated

when implementing a hybrid approach for

forecasting. The cost of computing during hybrid

model training and optimization can also prove

pricier than with solo algorithms. Furthermore,

hybrid models can intensify model complexity, thus

rendering result interpretation and revision a bit

trickier.

3 Comparison of Methods

This study compared five methods for forecasting

sensor data: random forest, artificial neural

networks, convolutional neural networks, and

autoregression. Each method has its strengths and

weaknesses, which we summarize below:

Random forest is an ensemble method that

combines multiple decision trees to improve

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accuracy and reduce overfitting. It can handle

continuous and categorical input variables and

capture nonlinear relationships between input and

output variables, [18]. However, training can be

slow and requires more computational resources.

Artificial neural networks can handle complex

nonlinear relationships between input and output

variables and can handle both continuous and

categorical input variables. However, they can be

prone to overfitting if the model is too complex and

requires a large amount of data for training.

Artificial neural networks can also be trained slowly

and require more computational resources.

Convolutional Neural Networks (CNNs) are

highly effective for tasks involving spatial patterns

and hierarchical features in data, such as image and

time-series analysis. They can handle both

continuous and categorical input variables and

manage complex relationships between inputs and

outputs. CNNs consist of convolutional layers that

detect local patterns, pooling layers that reduce

spatial dimensions, and fully connected layers that

integrate learned features. These networks are adept

at capturing intricate structures in data and can

generalize well, although careful architecture design

and hyperparameter tuning are required to optimize

performance and prevent overfitting.

Ultimately, the choice of method for predicting

sensor data will depend on the nature of the data and

the specific problem at hand. For simple problems

with linear relationships, linear regression may be a

good choice, while more complex issues may

require methods like random forests or artificial

neural networks. Therefore, this study aims to

experiment with multiple methods and compare

their performance to choose the best one for sensor

data forecast.

3.1 Model Configurations

Hyperparameters for the developed models are

chosen based on hyperparameter optimization

techniques, including random search, [19], [20], and

grid search, [21], [22], to identify the optimal

parameter set which gives the highest accuracy. The

parameters and their boundaries are described as

follows.

3.1.1 LSTM Model

In the given example, LSTM hyperparameter

optimization was performed using a random search

approach with the Keras Tuner. The objective was

to minimize the loss while searching for the best

combination of hyperparameters.

The hyperparameters that were optimized, and

their respective search ranges include:

 units_1: The number of units in the first

LSTM layer. It was tested with values

ranging from 30 to 100 with a step of 10.

 units_2: The number of units in the second

LSTM layer. It was tested with values

ranging from 30 to 100 with a step of 10.

 max_trials: The maximum number of

hyperparameter combinations to try. It was

set to 5.

 executions_per_trial: The number of times to

execute each trial with the same

hyperparameters. It was set to 2.

The LSTM model was built with two LSTM

layers followed by a dense output layer. The model

was compiled using the Adam optimizer and the

mean squared error (MSE) loss function. The

random search explored various combinations of

hyperparameters within the specified ranges,

evaluating the performance of each combination

using a 20% validation split on the training data.

3.1.2 VAR Model

For VAR model implementation, the primary

hyperparameter to optimize is the number of lags (p)

included in the model. The selection of the optimal

lag order can significantly impact the model's

forecasting performance. Selecting the optimal lag

order based on an information criterion like AIC

(Akaike's Information Criterion), [23]. For the given

dataset, the AIC value was identified as 15.

3.1.3 CNN Model

The CNN hyperparameter optimization was carried

out using a grid search approach. The "Keras

Regressor" was utilized to create a compatible

model for a grid search. The model's parameters are

explored within a specified range, and the optimal

combination of these parameters is determined to

provide the best performance, [24].

Here are the hyperparameters being optimized

and their respective search ranges:

 filters: The number of filters in the

convolutional layer. It was tested with 16,

32, and 64 filters.

 kernel_size: The size of the convolutional

kernel (window). It was tested with kernel

sizes of 2, 3, and 4.

 pool_size: The size of the pooling window in

the max-pooling layer. It was tested with

pool sizes of 1, 2, and 3.

 dense_units: The number of units in the

dense (fully connected) layer. It was tested

with 30, 50, and 100 units.

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The grid search method performed a search over

the specified parameter ranges, evaluating the

performance of each combination.

3.1.4 ANN Model

Artificial Neural Network (ANN) hyperparameter

optimization was performed using a random search

approach with the "Keras Tuner". The objective was

to minimize the validation loss while searching for

the best combination of hyperparameters:

 units_input: The number of units in the input

layer. It was tested with values ranging from

32 to 512 with a step of 32.

 units_hidden: The number of units in the

hidden layer. It was tested with values

ranging from 32 to 512 with a step of 32.

 learning_rate: The learning rate for the

Adam optimizer. It was tested with values of

0.01, 0.001, and 0.0001.

The random search was configured with the

following settings:

 max_trials: The maximum number of

hyperparameter combinations to try. It was

set to 5.

 executions_per_trial: The number of times to

execute each trial with the same

hyperparameters. It was set to 3.

The random search explored various

combinations of hyperparameters within the

specified ranges, evaluating the performance of each

combination. The best combination of

hyperparameters was selected based on the lowest

validation loss.

3.1.5 Random Forest Model

Random forest model hyperparameter optimization

was carried out by using a grid search approach by

experimenting with different numbers of decision

trees. The hyperparameters that were optimized, and

their respective search ranges include:

 n_estimators: The number of decision trees

in the forest. It was tested on 10, 50, 100,

and 200 trees. It was observed that there was

no significant decrease in the prediction error

with more decision trees beyond the tested

values, which informed the decision to limit

the number of decision trees in the Random

Forest model to these ranges.

 max_depth: The maximum depth of each

decision tree. It was tested with no limit

(None), 10, 20, and 30 levels.

 min_samples_split: The minimum number of

samples required to split an internal node. It

was tested with values of 2, 5, and 10.

 min_samples_leaf: The minimum number of

samples required to be at a leaf node. It was

tested with values of 1, 2, and 4.

 max_features: The number of features to

consider when looking for the best split. It

was tested with 'auto' (equivalent to 'sqrt')

and 'sqrt' options.

The models were trained and evaluated with each

of these configurations to determine the optimal

values of parameters that would yield the best

performance in terms of error reduction, [22].

For predicting environmental sensor data,

selecting the optimal number of layers in a neural

network and the number of trees in a random forest

model is dependent on different variables, like the

size of the dataset, the available computation

resources, the complexity of the problem, and the

quality of the data. The below points are some

general rules to keep in mind.

Models employing the random forest approach

have the following characteristics:

For determining how many trees are optimal for

a given problem and dataset, cross-validation

techniques like k-fold cross-validation come in

handy, [25]. Based on the amount of data available

and the complexity of the problem, it is possible to

determine the number of layers to use.

While a small dataset with rudimentary designs

may only require one or two hidden layers, a more

extensive dataset with complicated patterns might

demand more hidden layers. If one were to make the

model more intricate, it might increase one's

capacity to grasp ambiguous patterns. Still, if the

model becomes overly complicated, it could also

heighten the chance of overfitting.

A given problem and the dataset's ideal layers

can be found using early stopping and cross-

validation techniques, [25].

For optimal performance, it's crucial to properly

tune the hyperparameters of the models, like

learning rate, regularization, and activation

functions, among other things.

4 Data Processing and

Experimentation

The accuracy of the sensor forecasting data was

evaluated by comparing the error between actual

sensor readings and forecasted sensor values. The

experiment included comparing forecast accuracy

with models such as Random Forest, Convolutional

Neural Networks (CNNs), Artificial Neural

Networks (ANN), Vector Autoregressive (VAR)

model forecast, and Long Short-Term Memory

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(LSTM) networks. Several models were developed

to compare the forecast accuracy and performance

(Fig. 1).

Fig. 1: The implemented sensor data forecasting

models

Each model has 2 inputs or sensor parameters,

such as Humidity and CO2, and the output of the

models is a forecast, for example, temperature.

4.1 Experiment Preparation

Handling missing values and normalizing the

temperature, humidity, and CO2 readings were

initial preprocessing steps for raw sensor data.

Additionally, the time-series data was transformed

into a proper format for model input. As a result,

sensor measurements are converted into individual

variables in a multivariate time-series organization.

A basic model was developed using CNN,

consisting of a single convolutional layer followed

by several pooling layers, and then completed with

fully connected layers. The convolutional layers are

designed to identify local patterns within the input

data, while the pooling layers serve to decrease

spatial dimensions and reduce computational

complexity. The highly established layers remap the

extracted distinctive attributes to dictate the

conclusive prediction. Concerning the time-series

information, the model applies 1D convolutions

instead of the standard 2D convolutions in image

processing. Sensor measurements are subjected to

local pattern recognition by sliding convolutions

over input data. Filters are utilized to capture

multiple patterns, followed by merging resultant

outputs to form feature maps. ReLU (Rectified

Linear Unit) activation is applied to post-

convolutional and fully connected layers to

introduce nonlinearity, which enables the model to

learn intricate relationships and patterns, [26], [27],

[28].

The CNN and LSTM models were rigorously

evaluated, with the forecast and actual sensor

readings being compared using the Mean Squared

Error (MSE) as the loss metric. To adjust the

network's weights during training, "Adam," an

optimization algorithm, was called to minimize the

loss function. The final predictions are mapped via

the fully connected layer following two LSTM

layers in the LSTM network model. Temporal

dependencies are captured by the LSTM layers

while extracting features.

Recognition of local patterns in the time-series

data was possible using 1D convolutions. At the

same time, introducing the ReLU activation

function was integral in enabling the learning of

complex patterns with nonlinearity. The LSTM

model utilized the dense layer to generate final

predictions from the data with captured temporal

dependencies. For the VAR model, coefficients

were estimated to forecast upcoming sensor

measurements after data preprocessing and

determining the lag order using AIC. Measuring the

distinction between forecasted and actual

measurements was done with the loss function mean

squared error. The "Adam" optimization algorithm

was implemented to minimize the loss function.

To use the VAR model, missing values must be

taken care of, followed by a check for stationarity.

In the event of non-stationarity, different

transformations or differencing must be applied.

The process of selecting the ideal lag order for

the VAR model, which determines how many prior

time steps should be considered when forecasting

future values, is known as model selection. The

Akaike Information Criterion (AIC) is utilized for

this purpose. After confirming that the residuals are

acceptable, the VAR model can be utilized to

anticipate future sensor readings. The forecasts are

generated using the past temperature, humidity, and

CO2 data values in conjunction with the estimated

coefficients, [29].

4.2 Running Experiments

Having conducted several trials on each model, 15

sensor forecast models were compared based on

their ability to forecast the latest 100 entries in the

dataset. The most accurate results for LSTM and

CNN were obtained after 10 epochs. To ensure the

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credibility of the results, each model underwent

training at least 30 times, and the outcome was

determined by calculating the average error value.

The processing time of each model was also

recorded using the same methodology. The models

were trained using a hardware configuration of

20GB RAM and a 1.60GHz Intel Core i5-8250U

CPU.

4 Results

To evaluate the performance of developed forecast

models, Mean Squared Error (MSE) and Mean

Absolute Error (MAE) were used (Table 1.). Also,

the training time was noted when training different

models.

Table 1. Comparison Of Forecast Errors

Forecasted sensor

Temper

ature

(humidi

ty and

CO2 as

inputs)

Humidity

(temperatu

re and

CO2 as

inputs)

CO2

(humidity

and

temperatu

re as

inputs)

Model

LSTM

MAE:

0.0696,

MSE:

0.00712,

Time:

134.88 s

MAE:

1.019,

MSE:

1.516,

Time:

108.65 s

MAE:

95.952,

MSE:

15529.301,

Time:

109.17 s

VAR

MAE:

0.0696,

MSE:

0.00675,

Time:0.6

MAE:

27.074,

MSE:

733.033,

Time:0.70 s

MAE:

1424.80,

MSE:

2030813.5,

Time:

0.70s

CNN

MAE:

0.147,

MSE:

0.0289,

Time:

11.256 s

MAE:

0.533,

MSE:

0.4006,

Time:

11.377 s

MAE:

264.951,

MSE:

86007.97,

Time:

11.301 s

ANN

MAE:

0.378,

MSE:

0.293,

Time:

25.869 s

MAE: 3.30,

MSE:

17.87,

Time:

25.494 s

MAE:

184.35,

MSE:

61684.87,

Time:

26.01s

Random

Forest

MAE:

0.1607,

MSE:

0.132,

Time:

3.989 s

MAE:

1.178,

MSE:

5.4687,

Time:

3.841 s

MAE:

32.582,

MSE:

6651.02,

Time:

2.803 s

The Mean Absolute Error result for all models is

provided in "Fig. 2".

Fig. 2: MAE indicators

The Mean Squared Error results for all models

are provided in "Fig. 3".

Fig. 3: MSE indicators

Model performance result for all models is

provided in "Fig. 4".

200

400

600

800

1000

1200

1400

1600

LSTM VAR CNN ANN Random

Forest

Temperature Humidity CO2

500000

1000000

1500000

2000000

2500000

LSTM VAR CNN ANN Random

Forest

Temperature Humidity CO2

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Fig. 4: Time indicators

Based on the results in the chart provided, we

can gain a few insights about the ability of various

machine learning models to predict environmental

factors such as CO2 levels, humidity, and

temperature. In terms of Mean Absolute Error

(MAE) and Mean Squared Error (MSE), it is

generally observed that LSTM and VAR models are

superior to the other models across all three

categories. CO2 levels were found to have the lowest

value on the VAR model. In contrast, the LSTM

model recorded the lowest MAE and MSE values

for humidity and temperature. ANN and CNN

models poorly forecast CO2 levels, while

temperature and humidity perform moderately.

Mostly, the Random Forest model forecasts the

temperature and humidity with high accuracy,

although not when it comes to CO2 forecasts. Other

models have performed better in this regard.

5 Conclusion

Multiple techniques for predicting time series exist

depending on the data and problem. Some popular

options include Artificial Neural Networks (ANNs),

Convolutional Neural Networks (CNNs), Long

Short-Term Memory (LSTM) networks, Vector

Autoregressive (VAR) models, and Random

Forests. Particularly useful with large datasets, the

CNN method excels at recognizing localized

patterns and acquiring knowledge of hierarchical

feature representations, thus being highly efficient

in computation. Despite these benefits, it may not be

well-suited to handling distant dependencies in time

series data, and one must be cautious of overfitting

if proper regularization is not implemented.

Training the LSTM model could be

computationally expensive, requiring additional

time and resources, particularly for extensive input

sequences or large datasets. Nonetheless, the LSTM

is crucially outfitted to manage time series data with

long-range dependencies and can memorize and

learn patterns over extended durations, providing

the most precise outcomes. When forecasting

temperature from humidity and CO2 data, LSTM

can be used to achieve the highest accuracy if the

training time is not a constraint.

Though the VAR model can efficiently

implement and catch linear relationships among

numerous time series, its dependency on stationarity

and assumption of linearity may need to be revised

for complex or nonlinear situations. While it

functions optimally during constant correlation over

time, problems surface when handling vast

quantities of data or high-dimensional inputs.

The results reveal that the environmental sensor

data can be forecasted using VAR or LSTM models.

Across all three temperature, humidity, and CO2

levels categories, these models outperformed the

others in both mean absolute and squared errors. For

temperature and humidity predictions, the LSTM

model proves most effective. The least error was

achieved when forecasting temperature from CO2

and humidity inputs, thereby potentially serving as

substitutes for physical temperature sensor devices.

When it comes to CO2, however, the forecast

accuracy was low in comparison to other

parameters.

Among the models tested, CNN and ANN show

acceptable results regarding temperature and

humidity, but they fared poorly regarding CO2

levels. Although Random Forest performed well for

temperature and humidity, its CO2 forecast accuracy

was less accurate than the other models. Regarding

computation time, VAR and Random Forest stood

out as the quickest, while LSTM and ANN proved

to be the slowest.

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed to the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

The research has been supported by the RTU

internal project competition for strengthening the

capacity of scientific staff.

Conflict of Interest

The authors have no conflicts of interest to declare

that are relevant to the content of this article.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

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