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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Intelligent data monitoring anomaly detection system based on statistical and machine learning approaches⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Yurii Klots</string-name>
          <email>klots@khmnu.edu.ua</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Vira Titova</string-name>
          <email>titovav@khmnu.edu.ua</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nataliia Petliak</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Dmytro Tymoshchuk</string-name>
          <email>dmytro.tymoshchuk@gmail.com</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nataliya Zagorodna</string-name>
          <email>Zagorodna.n@gmail.com</email>
        </contrib>
      </contrib-group>
      <fpage>80</fpage>
      <lpage>89</lpage>
      <abstract>
        <p>One of the significant outcomes of society's digitalization is the rapid expansion of network services. This trend has heightened the demand for reliable and secure information systems administration. Ensuring system reliability and security requires regular equipment status checks, optimal software performance, and robust data protection measures-tasks typically managed through system administration and cybersecurity practices. Data analysis methods are crucial, as they process service statistics from monitoring systems to identify abnormal metric values. Anomaly detection plays a key role by pinpointing patterns or data points that deviate from normal behaviour, allowing for the early detection of issues such as fraud, security breaches, or equipment failures. This paper explores the primary performance indicators for servers, compares various computing system monitoring solutions, and configures the Zabbix monitoring system. Additionally, it considers the main types of anomalies and the methods used to detect them. An anomaly detection system was developed using an autoregressive integrated moving average (ARIMA) model, complemented by a neural network utilizing long short-term memory (LSTM) techniques.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Anomalies</kwd>
        <kwd>monitoring systems</kwd>
        <kwd>time series analysis</kwd>
        <kwd>forecasting</kwd>
        <kwd>ARIMA model</kwd>
        <kwd>LSTM</kwd>
        <kwd>machine learning</kwd>
        <kwd>cybersecurity</kwd>
        <kwd>information security</kwd>
        <kwd>abnormalities</kwd>
        <kwd>abnormality detection</kwd>
        <kwd>cyberattacks</kwd>
        <kwd>intrusion detection</kwd>
        <kwd>network</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>One of the key manifestations of the digitalization of society is the extensive development of
network
services. Consequently, there is an increasing
need for information
systems
administration tasks to ensure system reliability and security. This involves promptly checking
equipment status, maintaining optimal software performance, and ensuring data security. These
challenges are addressed within the domains of computer security and system administration. Data
analysis methods play a crucial role in tackling these issues. By processing service data from
statistics provided by monitoring systems, these tools can verify various metrics of the information
system to detect anomalous values.</p>
      <p>Anomaly detection identifies unusual patterns or data emissions that deviate from expected
behaviour, facilitating the early identification of fraud, security threats, or equipment failures.</p>
      <p>This work aims to develop a system for detecting anomalies in server performance indicators.
To accomplish this, it is essential to examine the main types of potential anomalies, explore
established methods for their detection, configure virtual server monitoring, build time series
forecasting models, and create an anomaly detection program utilizing the implemented models.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Analysis of existing network resource monitoring systems</title>
      <p>The primary method for automating the management of such data involves monitoring systems
like Zabbix, Nagios, and others. A comprehensive definition of monitoring encompasses the
oversight of computer networks. This entails ongoing surveillance within the network, including
traffic analysis and diagnostics, and assessing the load on network devices and connections. The
goal is to identify slow or malfunctioning systems and inform network administrators of any
failures or issues using various notification tools.</p>
      <p>Timely detection of these failures facilitates a thorough evaluation of the system’s performance
by analyzing its components’ and monitored entities’ functioning and efficiency. A monitoring
object refers to any device or service that is consistently overseen to assess its condition, analyze
its processes, and identify and anticipate abnormal situations.</p>
      <p>Server monitoring involves the collection and analysis of data regarding the current
performance of computer systems. When evaluating and analyzing server performance, adopting a
systems approach that considers the interdependencies of hardware components is crucial. Server
load analysis entails gathering and processing statistics related to key components, including the
processor, memory, disk, and network interface.</p>
      <p>The timely detection and resolution of malfunctions are essential for the efficient operation of
any computer network. Identifying failures is a complex challenge that necessitates a thorough
analysis of the interaction between software and hardware components within the system, which is
addressed through monitoring systems.</p>
      <p>
        A monitoring system encompasses a set of technical tools designed to oversee and collect
information continuously within a local computer network. This is achieved through statistical
data analysis to identify faulty or improperly functioning nodes and to alert responsible personnel.
Modern platforms that facilitate the stable and real-time detection of anomalies within extensive
systems can be categorized based on the characteristics illustrated in Figure 1 [
        <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
        ].
      </p>
      <p>In comparing contemporary network monitoring systems according to the outlined
classification, parameters such as the method of data collection and the application areas will be
considered. All systems, characterized by the nature of the data analyzed, primarily employ highly
accurate statistical methods for monitoring data analysis. The paper demonstrates the
characteristics of network monitoring systems and their comparative analysis.</p>
      <p>Evaluation
characteristic</p>
      <sec id="sec-2-1">
        <title>Trend forecasting</title>
      </sec>
      <sec id="sec-2-2">
        <title>Plugins</title>
      </sec>
      <sec id="sec-2-3">
        <title>Notification</title>
      </sec>
      <sec id="sec-2-4">
        <title>Complete control</title>
      </sec>
      <sec id="sec-2-5">
        <title>Distributed monitoring Final assessment 1</title>
        <p>1
1
1
1
5
Let’s emphasize the key parameters necessary for a point assessment of the described systems,
where the presence of a function is awarded 1 point and its absence receives 0 points:




</p>
        <p>Trend forecasting—the existence of algorithms designed to predict network statistics.
Plugins—the availability of plugins that enhance functionality.</p>
        <p>Notification—the capability to detect and alert on anomalies.</p>
        <p>Complete control—the presence of a web interface that facilitates access to all system
services.</p>
        <p>Distributed monitoring—the ability to utilize multiple servers.</p>
        <p>By synthesizing the above information about the analyzed network monitoring systems, we can
comprehensively assess their parameters in Table 1.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Overview of Anomaly Detection Methods</title>
      <p>
        An anomaly generally refers to a deviation from expected behaviour. In the context of system and
network monitoring data, anomalies are viewed as changes in the behaviour of the system and its
indicators over time. Anomalies can be classified in various ways, with one standard classification
identifying three types: point, contextual, and collective [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ].
      </p>
      <p>A point anomaly refers to a singular measurement that stands out as an outlier, differing
significantly from the other measurements. These anomalies can be identified by evaluating the
mathematical expectation and standard deviation. Any values that exceed a specified threshold
based on the standard deviation are deemed abnormal.</p>
      <p>On the other hand, a contextual anomaly occurs when a measurement is considered abnormal
only within a specific context. For instance, if a server is conducting a scheduled backup at night,
an increase in processor utilization during that timeframe may be regarded as usual. In contrast,
the same increase during the daytime would be perceived as abnormal. In this scenario, it is
essential to assess not only the behaviour of the measurement itself but also the context,
particularly the range of values that defines when a measurement is considered abnormal.
0
1
1
1
1
4
0
1
1
0
1
3
1
1
1
0
1
4
1
1
1
1
1
5
In the context of collective anomalies, a sequence of related data instances (such as a time series
segment) is deemed anomalous when considering the entire dataset. Within collective anomalies,
we can identify two types: shift anomalies, which alter the mathematical expectation in a time
series, and distribution change anomalies, which are characterized by changes in standard
deviation.</p>
      <p>
        As highlighted in [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], anomaly detection encompasses a range of methods and systems aimed at
identifying unusual behaviour and states within systems and their observable indicators. The
techniques for detecting anomalies can be broadly classified into statistical methods and machine
learning approaches.
      </p>
      <p>
        Machine learning methods are categorized into supervised (such as Decision Trees, SVM, and
LSTM) and unsupervised (including K-means, hierarchical clustering, and DBSCAN). Supervised
methods require a training dataset to build a model that distinguishes normal behaviour from
anomalies. Machine learning methods allow for the detection of more complex, hidden, and
nonobvious anomalies [
        <xref ref-type="bibr" rid="ref5 ref6 ref7">5–7</xref>
        ], which often go unnoticed when using traditional statistical approaches.
Due to the ability to build flexible models that are trained on real data [
        <xref ref-type="bibr" rid="ref8 ref9">8, 9</xref>
        ], these methods can
detect complex dependencies, relationships between parameters, and non-standard behavioral
patterns. This makes them useful for solving a wide range of tasks, from detecting cyber threats
and fraudulent activities to diagnosing technical malfunctions in complex information systems.
Machine learning offers a number of methods for detecting anomalies, such as: LSTM, SVM, and
Kmeans.
      </p>
      <p>
        LSTM (long short-term memory) is a specific architecture of recurrent neural networks [
        <xref ref-type="bibr" rid="ref10 ref11 ref12">10–12</xref>
        ].
It predicts the value of the next time interval based on an input time series by maintaining a state.
The model is trained on normal time series data, which allows it to identify anomalies. LSTM
networks feature specialized compartments equipped with three gates: an input gate, a forget gate,
and an output gate. These gates facilitate information flow control within the network, enabling
the LSTM to determine which information to retain, discard, or transmit to the next step. The
advantages of using LSTM networks for anomaly detection are twofold [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. First, the training data
does not require labeling, eliminating the need to provide the model with specific examples of
anomalies. Second, the trained model can detect previously unseen anomalies. However, LSTMs
also have several drawbacks. Their complex architecture, which includes multiple gates and
memory cells, makes them computationally intensive, leading to increased training times and
higher memory consumption.
      </p>
      <p>Support Vector Machine (SVM) is a classification technique that transforms original vectors
representing values into a higher-dimensional space. In this space, it identifies a separating
hyperplane that maximizes the margin between normal and abnormal values [14, 15]. The
advantages of SVM include the ability to derive a classification function with minimal error, the
capability of applying a linear classifier to nonlinear data, and the effectiveness in handling
heterogeneous datasets. However, SVM also has its drawbacks: the decision function relies heavily
on pre-set parameters and is sensitive to noise present in the training set. To address these
limitations, the integration of fuzzy set theory has been proposed as one potential solution, though
this approach increases the algorithm’s computational complexity.</p>
      <p>
        The K-means method is a clustering algorithm associated with unsupervised machine learning
techniques [
        <xref ref-type="bibr" rid="ref16 ref17 ref18">16–18</xref>
        ]. Its primary objective is to group data into clusters centered around predefined
key points, the number of which must be specified beforehand. Elements that do not belong to any
cluster are regarded as anomalous. When applied to anomaly detection, K-means presents several
advantages, such as its simplicity, efficiency, and scalability, making it particularly suitable for
large datasets. Additionally, since it operates unsupervised, it does not require pre-labeled data and
allows for customization regarding the number of clusters. K-means can effectively identify
deviations from the norm by pinpointing data points significantly distant from established cluster
centroids. However, there are drawbacks: the algorithm necessitates prior knowledge to determine
the number of cluster centers (the value of K), struggles with outliers and noisy data due to
potential skewing of centroids, and may be inefficient with large datasets as it requires
considerable computational time.
      </p>
      <p>
        Statistical anomaly detection methods include the Holt-Winters model and the autoregressive
integrated moving average (ARIMA). These statistical methods rely on the premise that typical
time series data are generated by a specific statistical process, with values that deviate from this
process being classified as anomalies [
        <xref ref-type="bibr" rid="ref19 ref20 ref21">19–21</xref>
        ]. A crucial aspect of these methods involves analyzing
the parameters of the statistical process based on a training time series and evaluating how well a
test time series aligns with the derived parameters.
      </p>
      <p>When employing statistical analysis methods, it is important to recognize that time series can be
decomposed into three components: the trend, which indicates the overall direction of the series in
terms of increasing or decreasing values; seasonality, which represents periodic fluctuations linked
to factors such as the day of the week or month; and the random component, which consists of the
residuals remaining after the trend and seasonality have been accounted for, and is typically where
anomalies are sought. The primary function of the ARIMA and Holt-Winters models is to forecast
future values in a time series.</p>
      <p>
        ARIMA models effectively analyze time series data with a pronounced trend [
        <xref ref-type="bibr" rid="ref22 ref23 ref24">22–24</xref>
        ]. ARIMA
and neural networks, such as LSTM, have emerged as prominent techniques for detecting
anomalies within time series data. ARIMA’s key strengths lie in its interpretability and accuracy
when applied to stationary datasets. In contrast, neural networks excel at modeling complex
nonlinear patterns. However, a downside of ARIMA is that over-differencing can strip away
meaningful patterns from the data, resulting in poor forecasting outcomes. This dependence on
manual preprocessing renders ARIMA less flexible for datasets exhibiting complex non-stationary
behaviour. Furthermore, ARIMA typically assumes linear relationships between past and future
values.
      </p>
      <p>
        On the other hand, the Holt-Winters model is adept at handling trends and seasonality in time
series data [
        <xref ref-type="bibr" rid="ref25">25</xref>
        ]. Particularly when integrated with Brutlag’s algorithm, the Holt-Winters model
provides several advantages for anomaly detection, especially in seasonal contexts. It effectively
captures trends and seasonal patterns, aiding in identifying deviations from expected behaviour. Its
adaptability, ease of implementation, capacity to manage changing trends, and low computational
complexity make it a compelling choice for various anomaly detection scenarios. Nevertheless, the
Holt-Winters model does have some notable limitations. It requires initial values for level, trend,
and seasonal components, which can be challenging to determine accurately. Moreover, its
performance may suffer if the data exhibits non-stationary behaviour or inconsistent seasonality.
Additionally, the model’s reliance on smoothing constants (alpha, beta, and gamma) can complicate
the selection of optimal values, and it may be sensitive to outliers or extreme values present in the
data.
      </p>
      <p>
        Recent studies demonstrate the effectiveness of combining natural language processing and
machine learning techniques for real-time ransomware detection using eBPF technology, which
enhances anomaly detection in cybersecurity contexts [
        <xref ref-type="bibr" rid="ref26">26</xref>
        ]. Furthermore, advances in neural
network architectures have proven successful in identifying deepfake modifications in biometric
images, underlining the growing importance of sophisticated machine learning models for anomaly
and fraud detection [
        <xref ref-type="bibr" rid="ref27 ref28 ref29 ref30">27–30</xref>
        ]. Comparative analyses of deep learning models for speaker verification
also highlight the potential for high-accuracy anomaly detection in audio data streams, expanding
the applicability of AI-based monitoring systems across diverse data types [
        <xref ref-type="bibr" rid="ref31">31</xref>
        ].
      </p>
      <p>Considering the advantages and disadvantages, forecasting algorithms based on ARIMA and
LSTM neural network models were implemented for anomaly detection. This involved calculating
sequence elements across subsequent time intervals based on the training sequence. An outlier
anomaly was recorded if the predicted values diverged from the input values by a specified
threshold.</p>
      <p>To prepare the input data, we set up a virtual server using the Zabbix monitoring system, which
collects data on the server’s performance, including processor load, RAM capacity, network
interface speed, hard drive usage, and more.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Data monitoring anomalies detection systems</title>
      <p>The API offered by the Zabbix system enables users to send requests to configure the server-side
aspects of the system and retrieve Zabbix configuration data. Additionally, the API allows access to
historical data for specific performance indicators. Requests are made through procedures defined
in the JSON-RPC protocol, with communication between clients and the API using the JSON
format. To interact with this API in Python, one can utilize the pyzabbix library.</p>
      <p>Using the Zabbix monitoring system API, the program collects system indicators for a given
data element key at specified intervals and saves the obtained values in a CSV file. Let us look at
the server load indicator as a percentage (Figure 2) as an example.</p>
      <p>After that, a Pandas.Dataframe table is created from the csv-file, in which the series are divided
into two time periods: the training and forecast parts. In the training part, the coefficients for
ARIMA are selected, which will be used for forecasting.</p>
      <p>The auto_arima function selects the parameters p, d, and q. With its help, the parameters that
will give the lowest value of the Akaike information criterion are searched for by the enumeration
method.</p>
      <p>After training the model, forecasting is performed in batches of 10 values specified in the
forecast_length variable. Then the predicted values are added to the model so that the following
predictions are calculated based on them: the model is updated.</p>
      <p>For example, the prediction for the ARIMA(4, 1, 4) model is shown in Figure 3. In this graph, the
mean square error was 3.294.
To determine the time points with anomalies, the forecast error is calculated for each value:
test_df['error'] = test_df['value'] - test_df['predicted']</p>
      <p>For the error, the moving average and the moving standard deviation are calculated on a given
number of previous values, for example, 12:
df['err_meanval'] = df['error'].rolling(window=12).mean()
df['err_deviation'] = df['error'].rolling(window=12).std()</p>
      <p>Based on the moving average and the standard deviation, a confidence interval of two standard
deviations is constructed:
df['-lim'] = df['err_meanval'] - (2 * df['err_deviation'])
df['+lim'] = df['err_meanval'] + (2 * df['err_deviation'])</p>
      <p>If the error value goes beyond the confidence interval, then at the point in time at which this
occurred, an anomaly is noted:</p>
      <p>df['anomaly_points'] = np.where(((df['error'] &gt; df['+lim']) | (df['error'] &lt; df['-lim'])), df['value'],
np.nan)</p>
      <p>Similar to the ARIMA model, the software implementation of the LSTM network works with
data from a CSV file, which contains data collected from the Zabbix system.</p>
      <p>Before starting the neural network training, the time series is processed. At the initial stage, a
Pandas.Series array is created from the values. Then, the resulting series is differentiated, which in
most cases allows achieving stationarity (Figure 4).</p>
      <p>To make the data suitable for training, a matrix is created based on the array, where each row
contains a fragment of the time series with a length determined by the variable time_steps. Each
subsequent row in this matrix contains a shift of 1 value relative to the previous one.</p>
      <p>
        Next, the values are normalized using the MinMaxScaler function of the scikit-learn package to
be in the range [
        <xref ref-type="bibr" rid="ref1">–1, 1</xref>
        ]. Given a data set in the form of a shift matrix, the neural network is trained
to predict the last column of the matrix based on the previous columns. Then the data is divided
into training and test samples, where the test sample consists of values whose number is specified
in the forecast_length variable, for example, 50. These are the last rows of the matrix in which the
last column must be predicted. The Keras library was used to implement the LSTM neural network
model.
      </p>
      <p>The parameters were time_steps = 40, batch_size = 10, epochs = 50, neurons = 20. The
parameters mean the following:


time_steps is the length of the time interval by which the next value is predicted.
batch_size is the size of the input sequence packet after which the weights are updated.
epochs is the number of epochs of the neural network.
neurons is the number of elements in the state vector, meaning the number of neurons in
the expanded form of LSTM.</p>
      <p>The network consists of an LSTM layer that saves the state for each subsequent row from the
matrix. The next Dense layer is a neuron that combines 20 values (the output of the LSTM layer)
into one, which is considered a forecast.</p>
      <p>The mean square error is the loss function, and the Adam optimizer is selected to minimize it.
Since the model saves the state from each row, the state must be explicitly reset after each pass
through the entire matrix (the end of the epoch). Therefore, the model is trained in a cycle for one
epoch. Since the input data form a sequence, we prohibit shuffling samples—matrix rows, by setting
the shuffle=False parameter during training.</p>
      <p>After training the model, it is used to obtain the last columns of the matrix on the test sample.
The prediction is performed in parts with several rows equal to batch_size; then the network is
trained with new values. After receiving all the values from the test sample, the inverse
transformation is performed from normalized values to the 20th form, and from differentiated to
differentiated-undifferentiated. Then the search for anomalies begins—those values that deviate
most from the predicted ones. They are determined similarly to the ARIMA model using the
moving average of the forecast error. The result of the model is shown in Figure 5. The
root-meansquare error on the forecast interval is 4.810.</p>
      <p>The LSTM model may demonstrate increasing deviation in forecasts when processing large
input data. However, when using a smaller dataset (90 minutes of history for 20 forecasts), both
models accurately capture abnormal values in the same areas. Given this observation, the ARIMA
model is favoured for its stability and speed, requiring only 10 seconds of training compared to
over 60 seconds for the LSTM.</p>
    </sec>
    <sec id="sec-5">
      <title>Conclusions</title>
      <p>The objective of developing an anomaly detection system is to manage and uphold the reliability
and security of computing systems and networks. Primarily, identifying anomalous behaviour
streamlines the analysis of server load, shortens the time required for server performance audits
and incident investigations, and accelerates decision-making regarding the optimization of
configurations.</p>
      <p>The study accomplished several key tasks:




</p>
      <p>Reviewed the key performance indicators for servers.</p>
      <p>Conducted an analysis of server monitoring systems.</p>
      <p>Examined the primary types of anomalies and methods for their detection.</p>
      <p>Configured server monitoring using the Zabbix system to gather initial data.</p>
      <p>Developed autoregressive integrated moving average (ARIMA) time series forecasting
models and a long short-term memory (LSTM) neural network for anomaly detection.</p>
      <p>Created a program to identify anomalies within the data collected by the configured
monitoring system.</p>
      <p>Consequently, the following objectives were achieved: a system for detecting anomalies in
monitoring data was established by applying machine learning and forecasting techniques.</p>
    </sec>
    <sec id="sec-6">
      <title>Declaration on Generative AI</title>
      <p>While preparing this work, the authors used the AI programs Grammarly Pro to correct text
grammar and Strike Plagiarism to search for possible plagiarism. After using this tool, the authors
reviewed and edited the content as needed and took full responsibility for the publication’s content.</p>
    </sec>
  </body>
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