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<front>
<journal-meta>
<journal-id journal-id-type="pmc">CSSE</journal-id>
<journal-id journal-id-type="nlm-ta">CSSE</journal-id>
<journal-id journal-id-type="publisher-id">CSSE</journal-id>
<journal-title-group>
<journal-title>Computer Systems Science &#x0026; Engineering</journal-title>
</journal-title-group>
<issn pub-type="ppub">0267-6192</issn>
<publisher>
<publisher-name>Tech Science Press</publisher-name>
<publisher-loc>USA</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">37545</article-id>
<article-id pub-id-type="doi">10.32604/csse.2023.037545</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Article</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Blockchain Assisted Optimal Machine Learning Based Cyberattack Detection and Classification Scheme</article-title>
<alt-title alt-title-type="left-running-head">Blockchain Assisted Optimal Machine Learning Based Cyberattack Detection and Classification Scheme</alt-title>
<alt-title alt-title-type="right-running-head">Blockchain Assisted Optimal Machine Learning Based Cyberattack Detection and Classification Scheme</alt-title>
</title-group>
<contrib-group>
<contrib id="author-1" contrib-type="author">
<name name-style="western"><surname>Alohali</surname><given-names>Manal Abdullah</given-names></name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-2" contrib-type="author">
<name name-style="western"><surname>Elsadig</surname><given-names>Muna</given-names></name><xref ref-type="aff" rid="aff-1">1</xref></contrib>
<contrib id="author-3" contrib-type="author" corresp="yes">
<name name-style="western"><surname>Al-Wesabi</surname><given-names>Fahd N.</given-names></name><xref ref-type="aff" rid="aff-2">2</xref><email>falwesabi@kku.edu.sa</email></contrib>
<contrib id="author-4" contrib-type="author">
<name name-style="western"><surname>Duhayyim</surname><given-names>Mesfer Al</given-names></name><xref ref-type="aff" rid="aff-3">3</xref></contrib>
<contrib id="author-5" contrib-type="author">
<name name-style="western"><surname>Hilal</surname><given-names>Anwer Mustafa</given-names></name><xref ref-type="aff" rid="aff-4">4</xref></contrib>
<contrib id="author-6" contrib-type="author">
<name name-style="western"><surname>Motwakel</surname><given-names>Abdelwahed</given-names></name><xref ref-type="aff" rid="aff-4">4</xref></contrib>
<aff id="aff-1"><label>1</label><institution>Department of Information Systems, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428</institution>, <addr-line>Riyadh, 11671</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-2"><label>2</label><institution>Department of Computer Science, College of Science &#x0026; Art at Mahayil, King Khalid University</institution>, <addr-line>Abha, 62529</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-3"><label>3</label><institution>Department of Computer Science, College of Sciences and Humanities-Aflaj, Prince Sattam bin Abdulaziz University</institution>, <addr-line>Al-Kharj 16278</addr-line>, <country>Saudi Arabia</country></aff>
<aff id="aff-4"><label>4</label><institution>Department of Computer and Self Development, Preparatory Year Deanship, Prince Sattam bin Abdulaziz University Al-Kharj</institution>, <addr-line>16278</addr-line>, <country>Saudi Arabia</country></aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>&#x002A;</label>Corresponding Author: Fahd N. Al-Wesabi. Email: <email>falwesabi@kku.edu.sa</email></corresp>
</author-notes>
<pub-date date-type="collection" publication-format="electronic">
<year>2023</year></pub-date>
<pub-date date-type="pub" publication-format="electronic">
<day>31</day>
<month>3</month>
<year>2023</year>
</pub-date>
<volume>46</volume>
<issue>3</issue>
<fpage>3583</fpage>
<lpage>3598</lpage>
<history>
<date date-type="received">
<day>08</day>
<month>11</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>02</day>
<month>2</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2023 Alohali et al.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Alohali et al.</copyright-holder>
<license xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>This work is licensed under a <ext-link ext-link-type="uri" xlink:type="simple" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</ext-link>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
</license>
</permissions>
<self-uri content-type="pdf" xlink:href="TSP_CSSE_37545.pdf"></self-uri>
<abstract>
<p>With recent advancements in information and communication technology, a huge volume of corporate and sensitive user data was shared consistently across the network, making it vulnerable to an attack that may be brought some factors under risk: data availability, confidentiality, and integrity. Intrusion Detection Systems (IDS) were mostly exploited in various networks to help promptly recognize intrusions. Nowadays, blockchain (BC) technology has received much more interest as a means to share data without needing a trusted third person. Therefore, this study designs a new Blockchain Assisted Optimal Machine Learning based Cyberattack Detection and Classification (BAOML-CADC) technique. In the BAOML-CADC technique, the major focus lies in identifying cyberattacks. To do so, the presented BAOML-CADC technique applies a thermal equilibrium algorithm-based feature selection (TEA-FS) method for the optimal choice of features. The BAOML-CADC technique uses an extreme learning machine (ELM) model for cyberattack recognition. In addition, a BC-based integrity verification technique is developed to defend against the misrouting attack, showing the innovation of the work. The experimental validation of BAOML-CADC algorithm is tested on a benchmark cyberattack dataset. The obtained values implied the improved performance of the BAOML-CADC algorithm over other techniques.</p>
</abstract>
<kwd-group kwd-group-type="author">
<kwd>Cyberattack</kwd>
<kwd>machine learning</kwd>
<kwd>blockchain</kwd>
<kwd>thermal equilibrium algorithm</kwd>
<kwd>feature selection</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<label>1</label>
<title>Introduction</title>
<p>Data analysis methods were used extensively in the cyber security field, and the current diffusion of advanced machine learning (ML) methods has permitted to precisely detect cyber-attacks and identify threats [<xref ref-type="bibr" rid="ref-1">1</xref>], both in post-incident analysis and real-time. Both unsupervised and supervised ML techniques were successfully used for supporting prevention systems and intrusion detection (ID), along with identifying security breaches and system misuses [<xref ref-type="bibr" rid="ref-2">2</xref>,<xref ref-type="bibr" rid="ref-3">3</xref>]. The scenarios of interest were generally characterized by a continuous data stream (like application-level or packet-level) that summarizes the conduct of the underlying system or network [<xref ref-type="bibr" rid="ref-4">4</xref>]. The ML methods&#x2019; role is either in detecting familiar attacks, anomalous behaviour (unsupervised method) (supervised method), or Anomaly-related approaches that fit normal system functioning status, identifying and isolating anomalies as unexpected behavioural deviations. Therefore, anomaly detection methods are attractive for their capability to identify zero-day attacks, which are attacks using unknown vulnerabilities [<xref ref-type="bibr" rid="ref-5">5</xref>,<xref ref-type="bibr" rid="ref-6">6</xref>]. <xref ref-type="fig" rid="fig-1">Fig. 1</xref> represents the overview of the blockchain (BC)-assisted cyberattack detection.</p>
<fig id="fig-1">
<label>Figure 1</label>
<caption>
<title>Blockchain-assisted cyberattack detection</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-1.tif"/>
</fig>
<p>In recent times, deep learning (DL) is becoming a hopeful analytic pattern because of its excellent function in examining huge volumes of data [<xref ref-type="bibr" rid="ref-7">7</xref>]. Dissimilar to the conventional ML method, DL supported effective feature engineering by handling automatic and reliable feature representation and extraction [<xref ref-type="bibr" rid="ref-8">8</xref>,<xref ref-type="bibr" rid="ref-9">9</xref>]. Since a strong analytic device, DL delivered existing latency and accuracy than the conventional ML method, and it is positioned for examining huge amounts of data in the 5G-based Internet of Things (IoT) [<xref ref-type="bibr" rid="ref-10">10</xref>]. This DL disposition supported forecasting future events, recognising assaults, and offering important data for placement and content caching in dynamic cases of 5G-assisted IoT [<xref ref-type="bibr" rid="ref-11">11</xref>].</p>
<p>Since an evolving technology, BC has become a hopeful choice for managing privacy and security in next-generation transmission structures [<xref ref-type="bibr" rid="ref-12">12</xref>,<xref ref-type="bibr" rid="ref-13">13</xref>]. It constitutes a peer-to-peer (P2P) transactions platform where the data is exchanged, recorded, and authenticated in a decentralized way for delivering verification data and security independent from centralized authorities [<xref ref-type="bibr" rid="ref-14">14</xref>]. The significant features of BC involving anonymity, decentralization, and security can apply secure data transactions and overcome centralized server dependence to support security in 5G-based IoT. Additionally, the inimitable property of dispersed data storage, smart contracts, and asset tracking make BC technology required for 5G-based IoT [<xref ref-type="bibr" rid="ref-15">15</xref>].</p>
<p>This study designs a new Blockchain Assisted Optimal Machine Learning based Cyberattack Detection and Classification (BAOML-CADC) technique. In the BAOML-CADC technique, the major focus lies in identifying cyberattacks. To do so, the presented BAOML-CADC technique applies a thermal equilibrium algorithm-based feature selection (TEA-FS) method for the optimal choice of features. The BAOML-CADC technique uses the extreme learning machine (ELM) model for cyberattack recognition. In addition, a BC-based integrity verification technique is developed to protect against the misrouting attack. The experimental validation of BAOML-CADC algorithm is tested on a benchmark cyberattack dataset.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Related Works</title>
<p>In [<xref ref-type="bibr" rid="ref-16">16</xref>], the authors identify false data injection attack (FDIA) in the microgrid mechanism, Hilbert-Huang transforms technique, along with BC-related ledger technology, was employed to scale up the security in smart direct current (DC)-microgrids by evaluating the voltage and current signals in controller and smart sensor nodes by deriving signal information. Ajayi et al. [<xref ref-type="bibr" rid="ref-17">17</xref>] devised a BC-related solution that guarantees the consistency and integrity of attack features shared in a cooperative ID mechanism. The modelled structure attains by preventing and identifying compromised intrusion detection system (IDS) nodes and fake feature injection. It even enables scalable attack features to exchange amongst IDS nodes, assures heterogeneous IDS node contribution, and is powerful to public IDS node leaving and joining the networks.</p>
<p>Kumar et al. [<xref ref-type="bibr" rid="ref-18">18</xref>] presented a new BC system for secured clinical data management that minimizes the computational and communicational overhead cost than the lightweight BC architecture and the prevailing bitcoin network. Kumar et al. [<xref ref-type="bibr" rid="ref-19">19</xref>] present a Privacy-Preserving and Secure Framework (PPSF) for IoT-driven smart city. This devised method is dependent upon 2 main systems: an ID system and a two-level privacy system. Firstly, in a 2-level privacy method, a BC was devised to transfer information of IoT securely, and the PCA method can be adapted to convert raw IoT data into a new structure. A Gradient Boosting Anomaly Detector (GBAD) was implemented in the ID method to evaluate and train the devised two-level privacy method related to IoT network datasets, such as BoT-IoT and ToN-IoT.</p>
<p>In [<xref ref-type="bibr" rid="ref-20">20</xref>], modelled a new process based on DL and Hilbert-Huang Transform for cyberattack recognition in DC-MGs along with identifying the assaults in distributed generation (DG) sensors and units. Then, an innovative elective group DL approach and Krill Herd Optimization (KHO) was devised. Then, Hilbert-Huang Transform was employed to extract the signals feature. Then such attributes were implemented as multiple deep input basis methods were constituted for capturing sentient traits automatically from raw fluctuation signals. Liang et al. [<xref ref-type="bibr" rid="ref-21">21</xref>] modelled a novel, distributed BC-related security system to improve modern power systems&#x0027; self-defensive ability against cyberattacks. The authors discussed how BC technology improves the power grid&#x0027;s security and robustness by leveraging meters as nodes in dispersed networks and encapsulating meter measurements as blocks.</p>
</sec>
<sec id="s3">
<label>3</label>
<title>The Proposed Model</title>
<p>In this study, we have developed a new BAOML-CADC technique for Cyberattack Detection and Classification process. In the BAOML-CADC technique, the major focus lies in identifying cyberattacks. Initially, the presented BAOML-CADC technique applied the TEA-FS approach for the optimal choice of features. For cyberattack recognition, the BAOML-CADC technique used the ELM model. In addition, a BC-based integrity verification technique is developed to defend against the misrouting attack.</p>
<sec id="s3_1">
<label>3.1</label>
<title>Algorithmic Steps of TEA-FS Technique</title>
<p>Primarily, the presented BAOML-CADC technique applied the TEA-FS approach for the optimal choice of features. TEA was simulated by thermodynamic phenomena and is classified as an evolutionary technique [<xref ref-type="bibr" rid="ref-22">22</xref>]. During this approach, the coordinates of all the systems can be transformed into volume or temperature, which are thermodynamic parameters. The study aims to search for an optimum solution based on the problem variable. In genetic algorithm (GA), the group of variables should be enhanced, often known as the chromosome. However, the term can be replaced by the thermodynamic system. In the <inline-formula id="ieqn-1"><mml:math id="mml-ieqn-1"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>-dimension problems, every system is a dimensional array determined using the following expression:</p>
<p><disp-formula id="eqn-1">
<label>(1)</label>
<mml:math id="mml-eqn-1" display="block"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-1">Eq. (1)</xref>, <inline-formula id="ieqn-2"><mml:math id="mml-ieqn-2"><mml:mi>T</mml:mi></mml:math></inline-formula> denotes the temperature, and <inline-formula id="ieqn-3"><mml:math id="mml-ieqn-3"><mml:mi>V</mml:mi></mml:math></inline-formula> indicates the volume that might have multiple parameters. Thus, for ease of use, the problem became 2D problems by describing a new parameter <inline-formula id="ieqn-4"><mml:math id="mml-ieqn-4"><mml:mi mathvariant="normal">&#x2200;</mml:mi></mml:math></inline-formula> termed &#x201C;overall volume&#x201D;:</p>
<p><disp-formula id="eqn-2">
<label>(2)</label>
<mml:math id="mml-eqn-2" display="block"><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi mathvariant="normal">&#x03A3;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>Here, the thermodynamic state of all the systems is determined by the following expression:</p>
<p><disp-formula id="eqn-3">
<label>(3)</label>
<mml:math id="mml-eqn-3" display="block"><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The cost of every system can be defined using <inline-formula id="ieqn-5"><mml:math id="mml-ieqn-5"><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mi>f</mml:mi></mml:math></inline-formula> cost function.</p>
<p><disp-formula id="eqn-4">
<label>(4)</label>
<mml:math id="mml-eqn-4" display="block"><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>At first, the initial population can be generated by the number of <inline-formula id="ieqn-6"><mml:math id="mml-ieqn-6"><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>s</mml:mi><mml:mi>y</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>. Based on upper and lower boundaries, the system is arbitrarily scattered in the function domain.</p>
<p>In coupling the Thermodynamic System, firstly, every system is combined to the closest system in the function domain. Next, the combined system exchanges heat or implements work together to reach equilibrium progressively. Eventually, the temperature gradient is reduced, the scope of the optimization technique is well analyzed, as well as the optimum value is found. Afterwards, the system is coupled, and heat exchange and work are executed, leading to changes in the volume and temperature of the system. The volume and temperature are distinct. However, the pressure can be similar. Moreover, the piston in the two systems moves freely. Hence every system implements either negative or positive work. In every thermodynamic procedure, the pressure in two systems is equivalent:</p>
<p><disp-formula id="eqn-5">
<label>(5)</label>
<mml:math id="mml-eqn-5" display="block"><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mi>Q</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>W</mml:mi></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-5">Eq. (5)</xref>, <inline-formula id="ieqn-7"><mml:math id="mml-ieqn-7"><mml:mi>Q</mml:mi></mml:math></inline-formula> represents the amount of heat transferred, and <inline-formula id="ieqn-8"><mml:math id="mml-ieqn-8"><mml:mi>W</mml:mi></mml:math></inline-formula> denotes the work done by every system. Because of the conservation law of energy, the heat absorbed from the system is equivalent to the heat lost by the others <inline-formula id="ieqn-9"><mml:math id="mml-ieqn-9"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>Q</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>:</p>
<p><disp-formula id="eqn-6">
<label>(6)</label>
<mml:math id="mml-eqn-6" display="block"><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>W</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The energy change for an ideal gas is evaluated as <inline-formula id="ieqn-10"><mml:math id="mml-ieqn-10"><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mi>m</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi>T</mml:mi></mml:math></inline-formula>, and the thermodynamic work by <inline-formula id="ieqn-11"><mml:math id="mml-ieqn-11"><mml:mi>W</mml:mi><mml:mo>=</mml:mo><mml:mi>P</mml:mi><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:mi mathvariant="normal">&#x2200;</mml:mi></mml:math></inline-formula>. By replacing the term into <xref ref-type="disp-formula" rid="eqn-6">Eq. (6)</xref> and divide with <inline-formula id="ieqn-12"><mml:math id="mml-ieqn-12"><mml:mi>P</mml:mi></mml:math></inline-formula>, <xref ref-type="disp-formula" rid="eqn-7">Eq. (7)</xref> can be attained:</p>
<p><disp-formula id="eqn-7">
<label>(7)</label>
<mml:math id="mml-eqn-7" display="block"><mml:mfrac><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mrow><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mi>P</mml:mi></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi>P</mml:mi></mml:mfrac><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-7">Eq. (7)</xref>, the subscript <inline-formula id="ieqn-13"><mml:math id="mml-ieqn-13"><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:math></inline-formula> denotes the thermodynamic state at equilibrium. Consider that <inline-formula id="ieqn-14"><mml:math id="mml-ieqn-14"><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> and for easiness <inline-formula id="ieqn-15"><mml:math id="mml-ieqn-15"><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>v</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>, <xref ref-type="disp-formula" rid="eqn-7">Eq. (7)</xref> is formulated by:</p>
<p><disp-formula id="eqn-8">
<label>(8)</label>
<mml:math id="mml-eqn-8" display="block"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>Alternatively, the ideal gas law is represented as:</p>
<p><disp-formula id="eqn-9">
<label>(9)</label>
<mml:math id="mml-eqn-9" display="block"><mml:mi>P</mml:mi><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mo>=</mml:mo><mml:mi>n</mml:mi><mml:mi>R</mml:mi><mml:mi>T</mml:mi></mml:math></disp-formula></p>
<p>The overall molar mass at the equilibrium state is equivalent to the sum of molar mass according to the conservation law of mass:</p>
<p><disp-formula id="eqn-10">
<label>(10)</label>
<mml:math id="mml-eqn-10" display="block"><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>By substituting <xref ref-type="disp-formula" rid="eqn-9">Eqs. (9)</xref> with <xref ref-type="disp-formula" rid="eqn-10">(10)</xref>,</p>
<p><disp-formula id="eqn-11">
<label>(11)</label>
<mml:math id="mml-eqn-11" display="block"><mml:mfrac><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mfrac><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mfrac><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mfrac></mml:math></disp-formula></p>
<p>By integrating <xref ref-type="disp-formula" rid="eqn-8">Eqs. (8)</xref> and <xref ref-type="disp-formula" rid="eqn-11">(11)</xref>, the following expression can attain <inline-formula id="ieqn-16"><mml:math id="mml-ieqn-16"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula>:</p>
<p><disp-formula id="eqn-12">
<label>(12)</label>
<mml:math id="mml-eqn-12" display="block"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>In addition, <inline-formula id="ieqn-17"><mml:math id="mml-ieqn-17"><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is derived by:</p>
<p><disp-formula id="eqn-13">
<label>(13)</label>
<mml:math id="mml-eqn-13" display="block"><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>By using the ideal gas law and the first law of thermodynamics the equilibrium state of hypothetical system is evaluated. If every system attains equilibrium instantly, the state of two systems would be equivalent, and they won&#x0027;t exchange energy. In such cases, the function&#x0027;s domain won&#x0027;t be explored further, and the optimum solution cannot be attained. To avoid that, the subsequent relationship is suggested for overall volume and new temperature:</p>
<p><disp-formula id="eqn-14">
<label>(14)</label>
<mml:math id="mml-eqn-14" display="block"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:math></disp-formula></p>
<p><disp-formula id="eqn-15">
<label>(15)</label>
<mml:math id="mml-eqn-15" display="block"><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:mfrac></mml:math></disp-formula></p>
<p>Now the term <inline-formula id="ieqn-18"><mml:math id="mml-ieqn-18"><mml:mi>i</mml:mi></mml:math></inline-formula> signifies the system number. When the <inline-formula id="ieqn-19"><mml:math id="mml-ieqn-19"><mml:mi mathvariant="normal">&#x2200;</mml:mi></mml:math></inline-formula> values are encompassed of multiple parameters like the case in a three or higher-dimension problem, <inline-formula id="ieqn-20"><mml:math id="mml-ieqn-20"><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> is attained by:</p>
<p><disp-formula id="eqn-16">
<label>(16)</label>
<mml:math id="mml-eqn-16" display="block"><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:math></disp-formula></p>
<p>The two systems grow nearer to equilibrium at every phase, which causes the whole domain to be examined progressively and the optimum point to be found. The relationships between entropy and cost function are determined by:</p>
<p><disp-formula id="eqn-17">
<label>(17)</label>
<mml:math id="mml-eqn-17" display="block"><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">p</mml:mi><mml:mi mathvariant="italic">y</mml:mi></mml:mrow></mml:mfrac><mml:mo>&#x2261;</mml:mo><mml:mfrac><mml:mrow><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">m</mml:mi><mml:mi mathvariant="italic">p</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">a</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">u</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow><mml:mrow><mml:mi>h</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>Thus, the study aims to diminish the cost function leads to maximizing the entropy of the system (<italic>S</italic>):</p>
<p><disp-formula id="eqn-18">
<label>(18)</label>
<mml:math id="mml-eqn-18" display="block"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2264;</mml:mo><mml:mn>0</mml:mn></mml:math></disp-formula></p>
<p>By transforming entropy into a cost function, the condition is transformed to:</p>
<p><disp-formula id="eqn-19">
<label>(19)</label>
<mml:math id="mml-eqn-19" display="block"><mml:mrow><mml:mi>f</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mo stretchy='false'>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:msup><mml:mi>w</mml:mi><mml:mo>&#x0027;</mml:mo></mml:msup></mml:mrow></mml:msub><mml:msub><mml:mo>&#x2200;</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo stretchy='false'>)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>f</mml:mi><mml:mtext>&#x00A0;</mml:mtext><mml:mo stretchy='false'>(</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:msup><mml:mi>q</mml:mi><mml:mo>&#x0027;</mml:mo></mml:msup></mml:mrow></mml:msub><mml:msub><mml:mo>&#x2200;</mml:mo><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo stretchy='false'>)</mml:mo><mml:mo>&#x2265;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></disp-formula></p>
<p>The abovementioned conditions cause the algorithm to move towards the optimization function. When the criterion isn&#x2019;t satisfied, a counter is determined for counting the number of failed attempts, then the thermodynamic condition is upgraded:</p>
<p><disp-formula id="eqn-20">
<label>(20)</label>
<mml:math id="mml-eqn-20" display="block"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>j</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p><disp-formula id="eqn-21">
<label>(21)</label>
<mml:math id="mml-eqn-21" display="block"><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x2200;</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>j</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:math></disp-formula></p><p>Whereas <inline-formula id="ieqn-21"><mml:math id="mml-ieqn-21"><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>w</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>j</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>. Because of the abovementioned relationship, in these cases, the system move towards the balance state at the lower speed than <xref ref-type="disp-formula" rid="eqn-14">Eqs. (14)</xref> and <xref ref-type="disp-formula" rid="eqn-15">(15)</xref> for satisfying the abovementioned conditions (<xref ref-type="disp-formula" rid="eqn-19">Eq. (19)</xref>). This process is same as inspecting the second law of thermodynamics and preventing blind search of the function domain.</p>
<p>Lastly, many coupled systems reached equilibrium and accumulated at any point, excluding a few that might be trapped. This technique has the benefit that only some systems have an equivalent state. Hence the cost of every system differs from the thermodynamic equilibrium method.</p>
<p>The fitness function (FF) employed in the TEA-FS approach was modelled to maintain a balance amongst the classification accuracy (maximum), and the number of selected features in each solution (minimum) acquired through the selected attributes, <xref ref-type="disp-formula" rid="eqn-22">Eq. (22)</xref> signifies the FF for evaluating solutions.</p>
<p><disp-formula id="eqn-22">
<label>(22)</label>
<mml:math id="mml-eqn-22" display="block"><mml:mrow><mml:mi mathvariant="italic">F</mml:mi><mml:mi mathvariant="italic">i</mml:mi><mml:mi mathvariant="italic">t</mml:mi><mml:mi mathvariant="italic">n</mml:mi><mml:mi mathvariant="italic">e</mml:mi><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">s</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:msub><mml:mi>&#x03B3;</mml:mi><mml:mrow><mml:mi>R</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x03B2;</mml:mi><mml:mfrac><mml:mrow><mml:mo>|</mml:mo><mml:mi>R</mml:mi><mml:mo>|</mml:mo></mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>C</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mfrac></mml:math></disp-formula></p>
<p>Here <inline-formula id="ieqn-22"><mml:math id="mml-ieqn-22"><mml:mrow><mml:mo>|</mml:mo><mml:mi>R</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> signifies the cardinality of the selected subset, and <inline-formula id="ieqn-23"><mml:math id="mml-ieqn-23"><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow><mml:mi>C</mml:mi><mml:mrow><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math></inline-formula> is the total features in the database; <inline-formula id="ieqn-24"><mml:math id="mml-ieqn-24"><mml:mi>&#x03B3;</mml:mi><mml:mi>r</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>D</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> designates the classification error rate of a given classifier. <inline-formula id="ieqn-25"><mml:math id="mml-ieqn-25"><mml:mi>&#x03B2;</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-26"><mml:math id="mml-ieqn-26"><mml:mi>&#x03B1;</mml:mi></mml:math></inline-formula> were 2 parameters concerning the significance of subset length and classification quality. <inline-formula id="ieqn-27"><mml:math id="mml-ieqn-27"><mml:mo>&#x2208;</mml:mo></mml:math></inline-formula> [1,0] and <inline-formula id="ieqn-28"><mml:math id="mml-ieqn-28"><mml:mi>&#x03B2;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mi>&#x03B1;</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula></p>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Cyberattack Detection Using ELM Model</title>
<p>To detect cyberattacks, the BAOML-CADC technique used the ELM model. Huang et al. developed an ELM to increase overall performance and prevent time-consuming backward iterative training [<xref ref-type="bibr" rid="ref-23">23</xref>]. ELM is a Single hidden Layer Feedforward Network (SLFN) with random weight and biases amongst the hidden and input layers. ELM is commonly applied in different areas because of its quick training speed and easier realization. <xref ref-type="fig" rid="fig-2">Fig. 2</xref> depicts the framework of ELM. Data of <inline-formula id="ieqn-29"><mml:math id="mml-ieqn-29"><mml:mi>N</mml:mi></mml:math></inline-formula> instances are provided <inline-formula id="ieqn-30"><mml:math id="mml-ieqn-30"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, where input matrix I <inline-formula id="ieqn-31"><mml:math id="mml-ieqn-31"><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and output matrices <inline-formula id="ieqn-32"><mml:math id="mml-ieqn-32"><mml:mn>0</mml:mn><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">]</mml:mo></mml:math></inline-formula>, whereas <inline-formula id="ieqn-33"><mml:math id="mml-ieqn-33"><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>i</mml:mi><mml:mrow><mml:mi>p</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-34"><mml:math id="mml-ieqn-34"><mml:msub><mml:mi>o</mml:mi><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> <inline-formula id="ieqn-35"><mml:math id="mml-ieqn-35"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula id="ieqn-36"><mml:math id="mml-ieqn-36"><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>p</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>p</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mn>0</mml:mn><mml:mrow><mml:mi>p</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and <inline-formula id="ieqn-37"><mml:math id="mml-ieqn-37"><mml:mi>n</mml:mi></mml:math></inline-formula> and <inline-formula id="ieqn-38"><mml:math id="mml-ieqn-38"><mml:mi>m</mml:mi></mml:math></inline-formula> characterize the input and output dimensions, correspondingly. Initially, the ELM arbitrarily allows the bias <inline-formula id="ieqn-39"><mml:math id="mml-ieqn-39"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">]</mml:mo><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>N</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> and the weight <inline-formula id="ieqn-40"><mml:math id="mml-ieqn-40"><mml:mi>E</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">]</mml:mo><mml:mo>&#x2208;</mml:mo><mml:msup><mml:mi>R</mml:mi><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x00D7;</mml:mo><mml:mi>L</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> that links the hidden and input layers. In contrast, <inline-formula id="ieqn-41"><mml:math id="mml-ieqn-41"><mml:mi>L</mml:mi></mml:math></inline-formula> signifies the hidden node count with activation function <inline-formula id="ieqn-42"><mml:math id="mml-ieqn-42"><mml:mi>h</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, <inline-formula id="ieqn-43"><mml:math id="mml-ieqn-43"><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>q</mml:mi><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>q</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mrow><mml:mi>q</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> represents the weight connecting vector which connects <inline-formula id="ieqn-44"><mml:math id="mml-ieqn-44"><mml:mi>n</mml:mi></mml:math></inline-formula> input node with <inline-formula id="ieqn-45"><mml:math id="mml-ieqn-45"><mml:mi>q</mml:mi></mml:math></inline-formula>-<inline-formula id="ieqn-46"><mml:math id="mml-ieqn-46"><mml:mi>t</mml:mi><mml:mi>h</mml:mi></mml:math></inline-formula> hidden nodes.</p>
<fig id="fig-2">
<label>Figure 2</label>
<caption>
<title>ELM structure</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-2.tif"/>
</fig>
<p><disp-formula id="eqn-23">
<label>(23)</label>
<mml:math id="mml-eqn-23" display="block"><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mi>E</mml:mi><mml:mo>+</mml:mo><mml:mi>D</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></disp-formula></p>
<p>The following formula can be expressed as output matrix O.</p>
<p><disp-formula id="eqn-24">
<label>(24)</label>
<mml:math id="mml-eqn-24" display="block"><mml:mi>M</mml:mi><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mi>O</mml:mi></mml:math></disp-formula></p><p>Whereas <inline-formula id="ieqn-47"><mml:math id="mml-ieqn-47"><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mo stretchy="false">]</mml:mo><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> signifies an output weight matrix that connects output to the hidden layers. The output weight matrices <inline-formula id="ieqn-48"><mml:math id="mml-ieqn-48"><mml:mi>F</mml:mi></mml:math></inline-formula> are calculated using the least-square method.</p>
<p><disp-formula id="eqn-25">
<label>(25)</label>
<mml:math id="mml-eqn-25" display="block"><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mi>O</mml:mi></mml:math></disp-formula></p>
<p>In <xref ref-type="disp-formula" rid="eqn-25">Eq. (25)</xref>, <inline-formula id="ieqn-49"><mml:math id="mml-ieqn-49"><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math></inline-formula> signifies the Moore-Penrose (MP) generalized inverse of M matrix. When <inline-formula id="ieqn-50"><mml:math id="mml-ieqn-50"><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mi>M</mml:mi></mml:math></inline-formula> is non-singular, then <inline-formula id="ieqn-51"><mml:math id="mml-ieqn-51"><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mi>M</mml:mi><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>. In such cases, <inline-formula id="ieqn-52"><mml:math id="mml-ieqn-52"><mml:mi>L</mml:mi></mml:math></inline-formula> is lesser than <inline-formula id="ieqn-53"><mml:math id="mml-ieqn-53"><mml:mi>N</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula> If <inline-formula id="ieqn-54"><mml:math id="mml-ieqn-54"><mml:mi>M</mml:mi><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula> is non-singular, then <inline-formula id="ieqn-55"><mml:math id="mml-ieqn-55"><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>M</mml:mi><mml:msup><mml:mi>M</mml:mi><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. In such cases, <inline-formula id="ieqn-56"><mml:math id="mml-ieqn-56"><mml:mi>L</mml:mi></mml:math></inline-formula> is higher than <inline-formula id="ieqn-57"><mml:math id="mml-ieqn-57"><mml:mi>N</mml:mi><mml:mo>.</mml:mo></mml:math></inline-formula></p>
<fig id="fig-11">
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-11.tif"/>
</fig>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>BC-Based Integrity Verification</title>
<p>Finally, a BC-based integrity verification technique is developed to defend against the misrouting attack. Over the last few decades, BC technology has provided privacy and security in different networks [<xref ref-type="bibr" rid="ref-24">24</xref>]. Despite the remarkable features of BC, it is still susceptible to fraudulent activity. The malicious entity might carry out fraudulent and invalid transactions using different technologies, namely double-spending attacks. BC can be fused with ML algorithms to resolve these problems in this work. The dataset of bitcoin transactions has been utilized in the fundamental process, and the presented ML approach has been trained on the database. The pattern of transactions saved in the dataset can be analyzed for added applications. Simultaneously, the transaction can be done on the Ethereum network. The pattern of this transaction is the same as that of bitcoin transactions saved in the bitcoin transaction data. The transaction pattern is analysed and compared to the bitcoin transaction patterns. Once the pattern matches these transactions, the new transaction is categorized as malicious or legitimate. A double-spending attack has been performed in the fundamental process for additional testing of the robustness of the model.</p>
<p>The BC is a building block of the reliable authentication system. The major objective is to provide a solution where each flow made from the controller is stored in an immutable and verifiable dataset. The BC involves a sequence of blocks connected through hash value. In the BC system, the user contains a pair of keys, such as a public key represents the irreplaceable address and a private key to sign the BC transaction. The client sign a transaction using the private key and transfers it to another one in the network for authentication. If the transmission block gets confirmed, then it is added to BC. Once stored, the data in the presented block can&#x0027;t be modified without changing each subsequent block. Also, the data is presented in the host simultaneously. Thus, the modification is rejected by the peer host. Now, a private BC is presented in contradiction to public BC. The private BC determines who should participate in the network and represented action in addition to permission allocated to the identifiable applicant. Hence, the requirement has been limited for a consensus mechanism, including Proof of Work.</p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Results and Discussion</title>
<p>In this section, the performance validation of the BAOML-CADC method can be performed through a benchmark dataset [<xref ref-type="bibr" rid="ref-25">25</xref>], which has 1000 distinct classes of events. The dataset comprises multiclass (Attack, No event, and Natural) and binary (Attack and Natural) labels.</p>
<p><xref ref-type="table" rid="table-1">Table 1</xref> demonstrates the experimental results offered by the BAOML-CADC method on the binary class dataset. In <xref ref-type="fig" rid="fig-3">Fig. 3</xref>, a detailed <inline-formula id="ieqn-67"><mml:math id="mml-ieqn-67"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-68"><mml:math id="mml-ieqn-68"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> outcomes of the BAOML-CADC model on the binary dataset are provided. The outcomes implied the improved values of <inline-formula id="ieqn-69"><mml:math id="mml-ieqn-69"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-70"><mml:math id="mml-ieqn-70"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> under all classes. For instance, with SD-1 class, the BAOML-CADC model has provided <inline-formula id="ieqn-71"><mml:math id="mml-ieqn-71"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-72"><mml:math id="mml-ieqn-72"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.44% and 99.99%, respectively. On the other hand, with SD-2 class, the BAOML-CADC approach has offered <inline-formula id="ieqn-73"><mml:math id="mml-ieqn-73"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-74"><mml:math id="mml-ieqn-74"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.89% and 99.97% singly. Meanwhile, with the SD-10 class, the BAOML-CADC method has correspondingly rendered <inline-formula id="ieqn-75"><mml:math id="mml-ieqn-75"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-76"><mml:math id="mml-ieqn-76"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 97.56% and 99.50%. Moreover, with the SD-15 class, the BAOML-CADC approach has presented <inline-formula id="ieqn-77"><mml:math id="mml-ieqn-77"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-78"><mml:math id="mml-ieqn-78"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 96.83% and 99.87%, correspondingly.</p>
<table-wrap id="table-1">
<label>Table 1</label>
<caption>
<title>Results analysis of BAOML-CADC approach under binary class database</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Binary dataset</th>
<th><inline-formula id="ieqn-79"><mml:math id="mml-ieqn-79"><mml:msub><mml:mrow><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-80"><mml:math id="mml-ieqn-80"><mml:msub><mml:mrow><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-81"><mml:math id="mml-ieqn-81"><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-82"><mml:math id="mml-ieqn-82"><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-83"><mml:math id="mml-ieqn-83"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>SD-1</td>
<td>99.79</td>
<td>96.46</td>
<td>98.44</td>
<td>99.99</td>
<td>97.39</td>
</tr>
<tr>
<td>SD-2</td>
<td>98.22</td>
<td>96.76</td>
<td>98.89</td>
<td>99.97</td>
<td>96.81</td>
</tr>
<tr>
<td>SD-3</td>
<td>99.36</td>
<td>99.32</td>
<td>97.88</td>
<td>98.57</td>
<td>98.69</td>
</tr>
<tr>
<td>SD-4</td>
<td>99.43</td>
<td>97.02</td>
<td>98.20</td>
<td>99.53</td>
<td>98.81</td>
</tr>
<tr>
<td>SD-5</td>
<td>98.73</td>
<td>97.53</td>
<td>97.62</td>
<td>98.69</td>
<td>96.96</td>
</tr>
<tr>
<td>SD-6</td>
<td>98.83</td>
<td>97.19</td>
<td>97.79</td>
<td>99.12</td>
<td>98.22</td>
</tr>
<tr>
<td>SD-7</td>
<td>99.49</td>
<td>97.79</td>
<td>96.75</td>
<td>99.87</td>
<td>97.03</td>
</tr>
<tr>
<td>SD-8</td>
<td>97.92</td>
<td>97.61</td>
<td>97.84</td>
<td>98.86</td>
<td>97.11</td>
</tr>
<tr>
<td>SD-9</td>
<td>99.77</td>
<td>96.84</td>
<td>96.98</td>
<td>99.52</td>
<td>99.02</td>
</tr>
<tr>
<td>SD-10</td>
<td>99.22</td>
<td>97.36</td>
<td>97.56</td>
<td>99.50</td>
<td>98.18</td>
</tr>
<tr>
<td>SD-11</td>
<td>99.07</td>
<td>98.50</td>
<td>97.50</td>
<td>99.11</td>
<td>98.51</td>
</tr>
<tr>
<td>SD-12</td>
<td>99.48</td>
<td>99.39</td>
<td>97.77</td>
<td>98.73</td>
<td>98.25</td>
</tr>
<tr>
<td>SD-13</td>
<td>99.21</td>
<td>97.70</td>
<td>97.42</td>
<td>99.18</td>
<td>98.31</td>
</tr>
<tr>
<td>SD-14</td>
<td>99.25</td>
<td>97.97</td>
<td>97.11</td>
<td>98.89</td>
<td>98.69</td>
</tr>
<tr>
<td>SD-15</td>
<td>99.29</td>
<td>98.85</td>
<td>96.83</td>
<td>99.87</td>
<td>97.56</td>
</tr>
<tr>
<td><bold>Average values</bold></td>
<td><bold>99.14</bold></td>
<td><bold>97.75</bold></td>
<td><bold>97.64</bold></td>
<td><bold>99.29</bold></td>
<td><bold>97.97</bold></td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-3">
<label>Figure 3</label>
<caption>
<title><inline-formula id="ieqn-84"><mml:math id="mml-ieqn-84"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-85"><mml:math id="mml-ieqn-85"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of BAOML-CADC system under binary class database</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-3.tif"/>
</fig>
<p><xref ref-type="fig" rid="fig-4">Fig. 4</xref> presents a comprehensive <inline-formula id="ieqn-86"><mml:math id="mml-ieqn-86"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-87"><mml:math id="mml-ieqn-87"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> outcomes of the BAOML-CADC method on the binary dataset. The outcomes exhibited improved values of <inline-formula id="ieqn-88"><mml:math id="mml-ieqn-88"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-89"><mml:math id="mml-ieqn-89"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> under all classes. For example, with SD-1 class, the BAOML-CADC algorithm has provided <inline-formula id="ieqn-90"><mml:math id="mml-ieqn-90"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-91"><mml:math id="mml-ieqn-91"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 96.46% and 97.39%, correspondingly. In contrast, with SD-2 class, the BAOML-CADC technique has offered <inline-formula id="ieqn-92"><mml:math id="mml-ieqn-92"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-93"><mml:math id="mml-ieqn-93"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 96.76% and 96.81%, correspondingly. In the meantime, with the SD-10 class, the BAOML-CADC model has provided <inline-formula id="ieqn-94"><mml:math id="mml-ieqn-94"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-95"><mml:math id="mml-ieqn-95"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 97.36% and 98.18% correspondingly. Likewise, with the SD-15 class, the BAOML-CADC methodology has correspondingly provided <inline-formula id="ieqn-96"><mml:math id="mml-ieqn-96"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-97"><mml:math id="mml-ieqn-97"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 98.85% and 97.56%.</p>
<fig id="fig-4">
<label>Figure 4</label>
<caption>
<title><inline-formula id="ieqn-98"><mml:math id="mml-ieqn-98"><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-99"><mml:math id="mml-ieqn-99"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> analysis of BAOML-CADC system under binary class database</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-4.tif"/>
</fig>
<p>In <xref ref-type="fig" rid="fig-5">Fig. 5</xref>, detailed <inline-formula id="ieqn-100"><mml:math id="mml-ieqn-100"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> outcomes of the BAOML-CADC approach on the binary dataset are provided. The outcomes displayed the improved value of <inline-formula id="ieqn-101"><mml:math id="mml-ieqn-101"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> under all classes. For example, with SD-1 class, the BAOML-CADC method has rendered <inline-formula id="ieqn-102"><mml:math id="mml-ieqn-102"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.79%. On the other hand, with SD-2 class, the BAOML-CADC approach has provided <inline-formula id="ieqn-103"><mml:math id="mml-ieqn-103"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.22%. In the meantime, with the SD-10 class, the BAOML-CADC technique has provided an <inline-formula id="ieqn-104"><mml:math id="mml-ieqn-104"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.22%. Additionally, with the SD-15 class, the BAOML-CADC methodology has provided an <inline-formula id="ieqn-105"><mml:math id="mml-ieqn-105"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.29%.</p>
<fig id="fig-5">
<label>Figure 5</label>
<caption>
<title><inline-formula id="ieqn-106"><mml:math id="mml-ieqn-106"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of BAOML-CADC system under binary class database</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-5.tif"/>
</fig>
<p>In <xref ref-type="table" rid="table-2">Table 2</xref>, the experimental results offered by the BAOML-CADC model on the Multiclass class dataset are represented. In <xref ref-type="fig" rid="fig-6">Fig. 6</xref>, a brief <inline-formula id="ieqn-107"><mml:math id="mml-ieqn-107"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-108"><mml:math id="mml-ieqn-108"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> outcomes of the BAOML-CADC methodology on the Multiclass dataset are offered. The figure exhibited the improved values of <inline-formula id="ieqn-109"><mml:math id="mml-ieqn-109"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-110"><mml:math id="mml-ieqn-110"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> under all classes. For example, with SD-1 class, the BAOML-CADC algorithm has provided <inline-formula id="ieqn-111"><mml:math id="mml-ieqn-111"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-112"><mml:math id="mml-ieqn-112"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 93.30% and 95.07%, correspondingly. Instead, with SD-2 class, the BAOML-CADC model has presented <inline-formula id="ieqn-113"><mml:math id="mml-ieqn-113"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-114"><mml:math id="mml-ieqn-114"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 91.04% and 94.03%, correspondingly. Meanwhile, with the SD-10 class, the BAOML-CADC method has provided <inline-formula id="ieqn-115"><mml:math id="mml-ieqn-115"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-116"><mml:math id="mml-ieqn-116"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 93.05% and 95.57%, correspondingly. Also, with the SD-15 class, the BAOML-CADC model has provided <inline-formula id="ieqn-117"><mml:math id="mml-ieqn-117"><mml:mi>s</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-118"><mml:math id="mml-ieqn-118"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 90.99% and 95.36%, correspondingly.</p>
<table-wrap id="table-2">
<label>Table 2</label>
<caption>
<title>Results analysis of proposed BAOML-CADC method on multiclass dataset</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Multiclass dataset</th>
<th><inline-formula id="ieqn-119"><mml:math id="mml-ieqn-119"><mml:msub><mml:mrow><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-120"><mml:math id="mml-ieqn-120"><mml:msub><mml:mrow><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-121"><mml:math id="mml-ieqn-121"><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-122"><mml:math id="mml-ieqn-122"><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
<th><inline-formula id="ieqn-123"><mml:math id="mml-ieqn-123"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula></th>
</tr>
</thead>
<tbody>
<tr>
<td>SD-1</td>
<td>93.64</td>
<td>79.32</td>
<td>93.30</td>
<td>95.07</td>
<td>82.16</td>
</tr>
<tr>
<td>SD-2</td>
<td>94.67</td>
<td>82.35</td>
<td>91.04</td>
<td>94.03</td>
<td>80.83</td>
</tr>
<tr>
<td>SD-3</td>
<td>94.32</td>
<td>83.45</td>
<td>89.06</td>
<td>92.88</td>
<td>83.90</td>
</tr>
<tr>
<td>SD-4</td>
<td>94.05</td>
<td>81.66</td>
<td>91.05</td>
<td>94.19</td>
<td>82.43</td>
</tr>
<tr>
<td>SD-5</td>
<td>92.91</td>
<td>80.70</td>
<td>90.64</td>
<td>92.62</td>
<td>82.21</td>
</tr>
<tr>
<td>SD-6</td>
<td>92.81</td>
<td>84.05</td>
<td>93.57</td>
<td>94.73</td>
<td>80.81</td>
</tr>
<tr>
<td>SD-7</td>
<td>92.45</td>
<td>80.33</td>
<td>92.76</td>
<td>94.00</td>
<td>85.14</td>
</tr>
<tr>
<td>SD-8</td>
<td>93.70</td>
<td>83.28</td>
<td>90.66</td>
<td>95.24</td>
<td>81.29</td>
</tr>
<tr>
<td>SD-9</td>
<td>92.47</td>
<td>81.09</td>
<td>92.09</td>
<td>95.31</td>
<td>80.59</td>
</tr>
<tr>
<td>SD-10</td>
<td>94.05</td>
<td>83.39</td>
<td>93.05</td>
<td>95.57</td>
<td>80.16</td>
</tr>
<tr>
<td>SD-11</td>
<td>93.39</td>
<td>80.37</td>
<td>91.91</td>
<td>93.97</td>
<td>82.96</td>
</tr>
<tr>
<td>SD-12</td>
<td>93.09</td>
<td>82.16</td>
<td>89.71</td>
<td>92.60</td>
<td>82.06</td>
</tr>
<tr>
<td>SD-13</td>
<td>93.11</td>
<td>83.51</td>
<td>90.53</td>
<td>94.27</td>
<td>80.25</td>
</tr>
<tr>
<td>SD-14</td>
<td>91.16</td>
<td>85.02</td>
<td>89.86</td>
<td>94.89</td>
<td>80.68</td>
</tr>
<tr>
<td>SD-15</td>
<td>91.77</td>
<td>79.36</td>
<td>90.99</td>
<td>95.36</td>
<td>83.77</td>
</tr>
<tr>
<td><bold>Average values</bold></td>
<td><bold>93.17</bold></td>
<td><bold>82.00</bold></td>
<td><bold>91.35</bold></td>
<td><bold>94.32</bold></td>
<td><bold>81.95</bold></td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-6">
<label>Figure 6</label>
<caption>
<title><inline-formula id="ieqn-124"><mml:math id="mml-ieqn-124"><mml:mi>S</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-125"><mml:math id="mml-ieqn-125"><mml:mi>s</mml:mi><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of BAOML-CADC system under multiclass database</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-6.tif"/>
</fig>
<p>In <xref ref-type="fig" rid="fig-7">Fig. 7</xref>, detailed <inline-formula id="ieqn-126"><mml:math id="mml-ieqn-126"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-127"><mml:math id="mml-ieqn-127"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> outcomes of the BAOML-CADC method on the Multiclass dataset are provided. The figure exhibited the improved values of <inline-formula id="ieqn-128"><mml:math id="mml-ieqn-128"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-129"><mml:math id="mml-ieqn-129"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> under all classes. For instance, with SD-1 class, the BAOML-CADC model has provided <inline-formula id="ieqn-130"><mml:math id="mml-ieqn-130"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-131"><mml:math id="mml-ieqn-131"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 79.32% and 82.16%, correspondingly. Otherwise, with SD-2 class, the BAOML-CADC technique has presented <inline-formula id="ieqn-132"><mml:math id="mml-ieqn-132"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-133"><mml:math id="mml-ieqn-133"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 82.35% and 80.83%, correspondingly. In the meantime, with the SD-10 class, the BAOML-CADC model has provided <inline-formula id="ieqn-134"><mml:math id="mml-ieqn-134"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-135"><mml:math id="mml-ieqn-135"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 83.39% and 80.16% correspondingly. Besides, with the SD-15 class, the BAOML-CADC method has presented <inline-formula id="ieqn-136"><mml:math id="mml-ieqn-136"><mml:mi>p</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-137"><mml:math id="mml-ieqn-137"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> of 79.36% and 83.77%, correspondingly.</p>
<fig id="fig-7">
<label>Figure 7</label>
<caption>
<title><inline-formula id="ieqn-138"><mml:math id="mml-ieqn-138"><mml:mi>P</mml:mi><mml:mi>r</mml:mi><mml:mi>e</mml:mi><mml:msub><mml:mi>c</mml:mi><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> and <inline-formula id="ieqn-139"><mml:math id="mml-ieqn-139"><mml:msub><mml:mi>F</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="italic">s</mml:mi><mml:mi mathvariant="italic">c</mml:mi><mml:mi mathvariant="italic">o</mml:mi><mml:mi mathvariant="italic">r</mml:mi><mml:mi mathvariant="italic">e</mml:mi></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula> analysis of BAOML-CADC system under multiclass database</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-7.tif"/>
</fig>
<p>In <xref ref-type="fig" rid="fig-8">Fig. 8</xref>, a complete <inline-formula id="ieqn-140"><mml:math id="mml-ieqn-140"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> outcomes of the BAOML-CADC method on the Multiclass dataset are provided. The results show the improved value of <inline-formula id="ieqn-141"><mml:math id="mml-ieqn-141"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> under all classes. For example, with SD-1 class, the BAOML-CADC method has provided an <inline-formula id="ieqn-142"><mml:math id="mml-ieqn-142"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 93.64%. On the other hand, with SD-2 class, the BAOML-CADC approach has shown <inline-formula id="ieqn-143"><mml:math id="mml-ieqn-143"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 94.67%. In the meantime, with the SD-10 class, the BAOML-CADC algorithm has rendered <inline-formula id="ieqn-144"><mml:math id="mml-ieqn-144"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 94.05%. Furthermore, with the SD-15 class, the BAOML-CADC technique has an <inline-formula id="ieqn-145"><mml:math id="mml-ieqn-145"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 91.77%.</p>
<fig id="fig-8">
<label>Figure 8</label>
<caption>
<title><inline-formula id="ieqn-154"><mml:math id="mml-ieqn-154"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of BAOML-CADC system under multiclass database</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-8.tif"/>
</fig>
<p><xref ref-type="table" rid="table-3">Table 3</xref> presents a comparative analysis of the BAOML-CADC with existing approaches [<xref ref-type="bibr" rid="ref-26">26</xref>]. The comprehensive comparative examination of the BAOML-CADC method with existing models on binary class is described in <xref ref-type="fig" rid="fig-9">Fig. 9</xref>. The outcomes exhibited that the RF technique has reached poor performance with <inline-formula id="ieqn-146"><mml:math id="mml-ieqn-146"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 80.61% while the JRip model has managed to obtain slightly improved outcomes. Additionally, the Adaboost&#x002B;JRip and k-nearest neighbour (KNN) methods have accomplished closer performance with <inline-formula id="ieqn-147"><mml:math id="mml-ieqn-147"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 95.56% and 95.49%, respectively. Although the BDLE-CAD technique has resulted in reasonable outcomes with <inline-formula id="ieqn-148"><mml:math id="mml-ieqn-148"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 98.63%, the BAOML-CADC technique surpassed the other ones with <inline-formula id="ieqn-149"><mml:math id="mml-ieqn-149"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 99.14%.</p>
<table-wrap id="table-3">
<label>Table 3</label>
<caption>
<title>Comparative analysis of BAOML-CADC approach under binary and multiclass datasets</title>
</caption>
<table frame="hsides">
<colgroup>
<col align="left"/>
<col align="left"/>
<col align="left"/>
</colgroup>
<thead>
<tr>
<th>Methods</th>
<th>Binary class</th>
<th>Multi-class</th>
</tr>
</thead>
<tbody>
<tr>
<td>BAOML-CADC</td>
<td>99.14</td>
<td>93.17</td>
</tr>
<tr>
<td>BDLE-CAD</td>
<td>98.63</td>
<td>92.63</td>
</tr>
<tr>
<td>KNN</td>
<td>95.49</td>
<td>87.66</td>
</tr>
<tr>
<td>Random forest</td>
<td>80.61</td>
<td>80.51</td>
</tr>
<tr>
<td>JRip</td>
<td>90.10</td>
<td>90.09</td>
</tr>
<tr>
<td>Adaboost&#x002B;JRip</td>
<td>95.56</td>
<td>91.44</td>
</tr>
</tbody>
</table>
</table-wrap><fig id="fig-9">
<label>Figure 9</label>
<caption>
<title><inline-formula id="ieqn-155"><mml:math id="mml-ieqn-155"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of BAOML-CADC approach under binary class dataset</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-9.tif"/>
</fig>
<p>The comprehensive comparative examination of the BAOML-CADC model with existing methods on multiclass is given in <xref ref-type="fig" rid="fig-10">Fig. 10</xref>. The outcomes show that the RF method has reached poor performance with <inline-formula id="ieqn-150"><mml:math id="mml-ieqn-150"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 80.51% while the JRip algorithm has managed to gain slightly improved outcomes. Also, the Adaboost&#x002B;JRip and KNN methodologies have accomplished closer performance with <inline-formula id="ieqn-151"><mml:math id="mml-ieqn-151"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 91.44% and 87.66%, correspondingly. Although the BDLE-CAD method has resulted in reasonable outcomes with <inline-formula id="ieqn-152"><mml:math id="mml-ieqn-152"><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mspace width="thinmathspace" /><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 92.63%, the BAOML-CADC approach surpassed the other ones with an <inline-formula id="ieqn-153"><mml:math id="mml-ieqn-153"><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> of 93.17%.</p>
<fig id="fig-10">
<label>Figure 10</label>
<caption>
<title><inline-formula id="ieqn-156"><mml:math id="mml-ieqn-156"><mml:mi>A</mml:mi><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:math></inline-formula> analysis of BAOML-CADC approach under multiclass dataset</title>
</caption>
<graphic mimetype="image" mime-subtype="tif" xlink:href="CSSE_37545-fig-10.tif"/>
</fig>
<p>These results demonstrated the supremacy of the BAOML-CADC model on cyberattack classification.</p>
</sec>
<sec id="s5">
<label>5</label>
<title>Conclusion</title>
<p>In this study, we have developed a new BAOML-CADC technique for Cyberattack Detection and Classification process. In the BAOML-CADC technique, the major focus lies in identifying cyberattacks. Initially, the presented BAOML-CADC technique applied the TEA-FS approach for the optimal choice of features. For cyberattack recognition, the BAOML-CADC technique used the ELM model. In addition, a BC-based integrity verification technique is developed to protect against the misrouting attack. The experimental validation of BAOML-CADC technique is tested on a benchmark cyberattack dataset. The obtained values implied the improved performance of the BAOML-CADC algorithm over other models with maximum accuracy of 93.17%. In the future, the performance of BOAML-CADC technique can be improved using a hyperparameter tuning process.</p>
</sec>
</body>
<back>
<sec><title>Funding Statement</title>
<p>This work was funded by the <funding-source> of Scientific Research at Princess Nourah bint Abdulrahman University</funding-source>, through the Research Groups Program Grant No. (<award-id>RGP-1443-0051</award-id>).</p>
</sec>
<sec sec-type="COI-statement"><title>Conflicts of Interest</title>
<p>The authors declare that they have no conflicts of interest to report regarding the present study.</p>
</sec>
<ref-list content-type="authoryear">
<title>References</title>
<ref id="ref-1"><label>[1]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D. G.</given-names> <surname>Roy</surname></string-name> and <string-name><given-names>S. N.</given-names> <surname>Srirama</surname></string-name></person-group>, &#x201C;<article-title>A blockchain-based cyber attack detection scheme for decentralized internet of things using the software-defined network</article-title>,&#x201D; <source>Software: Practice and Experience</source>, vol. <volume>51</volume>, no. <issue>7</issue>, pp. <fpage>1540</fpage>&#x2013;<lpage>1556</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-2"><label>[2]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Abdel-Basset</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Moustafa</surname></string-name> and <string-name><given-names>H.</given-names> <surname>Hawash</surname></string-name></person-group>, &#x201C;<article-title>Privacy-preserved cyberattack detection in industrial edge of things (IeoT): A blockchain-orchestrated federated learning approach</article-title>,&#x201D; <source>IEEE Transactions on Industrial Informatics</source>, vol. <volume>18</volume>, no. <issue>11</issue>, pp. <fpage>7920</fpage>&#x2013;<lpage>7934</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-3"><label>[3]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>J.</given-names> <surname>Zhang</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Pan</surname></string-name>, <string-name><given-names>Q. L.</given-names> <surname>Han</surname></string-name>, <string-name><given-names>C.</given-names> <surname>Chen</surname></string-name>, <string-name><given-names>S.</given-names> <surname>Wen</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Deep learning based attack detection for cyber-physical system cybersecurity: A survey</article-title>,&#x201D; <source>IEEE/CAA Journal of Automatica Sinica</source>, vol. <volume>9</volume>, no. <issue>3</issue>, pp. <fpage>377</fpage>&#x2013;<lpage>391</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-4"><label>[4]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>O.</given-names> <surname>Ajayi</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Cherian</surname></string-name> and <string-name><given-names>T.</given-names> <surname>Saadawi</surname></string-name></person-group>, &#x201C;<article-title>Secured cyber-attack signatures distribution using blockchain technology</article-title>,&#x201D; in <conf-name>IEEE Int. Conf. on Computational Science and Engineering (CSE) and IEEE Int. Conf. on Embedded and Ubiquitous Computing (EUC)</conf-name>, <publisher-loc>New York, NY, USA</publisher-loc>, pp. <fpage>482</fpage>&#x2013;<lpage>488</lpage>, <year>2019</year>. </mixed-citation></ref>
<ref id="ref-5"><label>[5]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>V.</given-names> <surname>Kelli</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Sarigiannidis</surname></string-name>, <string-name><given-names>V.</given-names> <surname>Argyriou</surname></string-name>, <string-name><given-names>T.</given-names> <surname>Lagkas</surname></string-name> and <string-name><given-names>V.</given-names> <surname>Vitsas</surname></string-name></person-group>, &#x201C;<article-title>A cyber resilience framework for NG-IoT healthcare using machine learning and blockchain</article-title>,&#x201D; in <conf-name>CC-IEEE Int. Conf. on Communications</conf-name>, <publisher-loc>Montreal, QC, Canada</publisher-loc>, pp. <fpage>1</fpage>&#x2013;<lpage>6</lpage>, <year>2021</year>. </mixed-citation></ref>
<ref id="ref-6"><label>[6]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>T. V.</given-names> <surname>Khoa</surname></string-name>, <string-name><given-names>Y. M.</given-names> <surname>Saputra</surname></string-name>, <string-name><given-names>D. T.</given-names> <surname>Hoang</surname></string-name>, <string-name><given-names>N. L.</given-names> <surname>Trung</surname></string-name>, <string-name><given-names>D.</given-names> <surname>Nguyen</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Collaborative learning model for cyberattack detection systems in IoT industry 4.0</article-title>,&#x201D; in <conf-name>IEEE Wireless Communications and Networking Conf. (WCNC)</conf-name>, <publisher-loc>Seoul, Korea (South)</publisher-loc>, pp. <fpage>1</fpage>&#x2013;<lpage>6</lpage>, <year>2020</year>. </mixed-citation></ref>
<ref id="ref-7"><label>[7]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Dehghani</surname></string-name>, <string-name><given-names>T.</given-names> <surname>Niknam</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Ghiasi</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Bayati</surname></string-name> and <string-name><given-names>M.</given-names> <surname>Savaghebi</surname></string-name></person-group>, &#x201C;<article-title>Cyber-attack detection in dc microgrids based on deep machine learning and wavelet singular values approach</article-title>,&#x201D; <source>Electronics</source>, vol. <volume>10</volume>, no. <issue>16</issue>, pp. <fpage>1914</fpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-8"><label>[8]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Waheed</surname></string-name>, <string-name><given-names>X.</given-names> <surname>He</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Ikram</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Usman</surname></string-name>, <string-name><given-names>S. S.</given-names> <surname>Hashmi</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Security and privacy in IoT using machine learning and blockchain: Threats and countermeasures</article-title>,&#x201D; <source>ACM Computing Surveys (CSUR)</source>, vol. <volume>53</volume>, no. <issue>6</issue>, pp. <fpage>1</fpage>&#x2013;<lpage>37</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-9"><label>[9]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Javadpour</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Pinto</surname></string-name>, <string-name><given-names>F.</given-names> <surname>Ja&#x2019;fari</surname></string-name> and <string-name><given-names>W.</given-names> <surname>Zhang</surname></string-name></person-group>, &#x201C;<article-title>DMAIDPS: A distributed multi-agent intrusion detection and prevention system for cloud IoT environments</article-title>,&#x201D; <source>Cluster Computing</source>, vol. <volume>7</volume>, no. <issue>3</issue>, pp. <fpage>150.936</fpage>, <year>2022</year>. <pub-id pub-id-type="doi">10.1007/s10586-022-03621-3</pub-id></mixed-citation></ref>
<ref id="ref-10"><label>[10]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Hajizadeh</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Afraz</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Ruffini</surname></string-name> and <string-name><given-names>T.</given-names> <surname>Bauschert</surname></string-name></person-group>, &#x201C;<article-title>Collaborative cyber attack defense in SDN networks using blockchain technology</article-title>,&#x201D; in <conf-name>6th IEEE Conf. on Network Softwarization (NetSoft)</conf-name>, <publisher-loc>Ghent, Belgium</publisher-loc>, pp. <fpage>487</fpage>&#x2013;<lpage>492</lpage>, <year>2020</year>. </mixed-citation></ref>
<ref id="ref-11"><label>[11]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>N.</given-names> <surname>Mhaisen</surname></string-name>, <string-name><given-names>N.</given-names> <surname>Fetais</surname></string-name> and <string-name><given-names>A.</given-names> <surname>Massoud</surname></string-name></person-group>, &#x201C;<article-title>Secure smart contract-enabled control of battery energy storage systems against cyber-attacks</article-title>,&#x201D; <source>Alexandria Engineering Journal</source>, vol. <volume>58</volume>, no. <issue>4</issue>, pp. <fpage>1291</fpage>&#x2013;<lpage>1300</lpage>, <year>2019</year>.</mixed-citation></ref>
<ref id="ref-12"><label>[12]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Komar</surname></string-name>, <string-name><given-names>V.</given-names> <surname>Dorosh</surname></string-name>, <string-name><given-names>G.</given-names> <surname>Hladiy</surname></string-name> and <string-name><given-names>A.</given-names> <surname>Sachenko</surname></string-name></person-group>, &#x201C;<article-title>Deep neural network for detection of cyber attacks</article-title>,&#x201D; in <conf-name>IEEE First Int. Conf. on System Analysis &#x0026; Intelligent Computing (SAIC)</conf-name>, <publisher-loc>Kyiv, Ukraine</publisher-loc>, pp. <fpage>1</fpage>&#x2013;<lpage>4</lpage>, <year>2018</year>. </mixed-citation></ref>
<ref id="ref-13"><label>[13]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>R. M. A.</given-names> <surname>Ujjan</surname></string-name>, <string-name><given-names>Z.</given-names> <surname>Pervez</surname></string-name> and <string-name><given-names>K.</given-names> <surname>Dahal</surname></string-name></person-group>, &#x201C;<article-title>Snort based collaborative intrusion detection system using blockchain in SDN</article-title>,&#x201D; in <conf-name>13th Int. Conf. on Software, Knowledge, Information Management and Applications (SKIMA)</conf-name>, <publisher-loc>Island of Ulkulhas, Maldives</publisher-loc>, pp. <fpage>1</fpage>&#x2013;<lpage>8</lpage>, <year>2019</year>. </mixed-citation></ref>
<ref id="ref-14"><label>[14]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>O. O.</given-names> <surname>Malomo</surname></string-name>, <string-name><given-names>D. B.</given-names> <surname>Rawat</surname></string-name> and <string-name><given-names>M.</given-names> <surname>Garuba</surname></string-name></person-group>, &#x201C;<article-title>Next-generation cybersecurity through a blockchain-enabled federated cloud framework</article-title>,&#x201D; <source>The Journal of Supercomputing</source>, vol. <volume>74</volume>, no. <issue>10</issue>, pp. <fpage>5099</fpage>&#x2013;<lpage>5126</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-15"><label>[15]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>D.</given-names> <surname>Said</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Elloumi</surname></string-name> and <string-name><given-names>L.</given-names> <surname>Khoukhi</surname></string-name></person-group>, &#x201C;<article-title>Cyber-attack on P2P energy transaction between connected electric vehicles: A false data injection detection based machine learning model</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>10</volume>, pp. <fpage>63640</fpage>&#x2013;<lpage>63647</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-16"><label>[16]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Ghiasi</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Dehghani</surname></string-name>, <string-name><given-names>T.</given-names> <surname>Niknam</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Kavousi-Fard</surname></string-name>, <string-name><given-names>P.</given-names> <surname>Siano</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Cyber-attack detection and cyber-security enhancement in smart DC-microgrid based on blockchain technology and Hilbert Huang transform</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>9</volume>, pp. <fpage>29429</fpage>&#x2013;<lpage>29440</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-17"><label>[17]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>O.</given-names> <surname>Ajayi</surname></string-name> and <string-name><given-names>T.</given-names> <surname>Saadawi</surname></string-name></person-group>, &#x201C;<article-title>Blockchain-based architecture for secured cyber-attack features exchange</article-title>,&#x201D; in <conf-name>7th IEEE Int. Conf. on Cyber Security and Cloud Computing (CSCloud)/2020 6th IEEE Int. Conf. on Edge Computing and Scalable Cloud (EdgeCom)</conf-name>, <publisher-loc>New York, NY, USA</publisher-loc>, pp. <fpage>100</fpage>&#x2013;<lpage>107</lpage>, <year>2020</year>. </mixed-citation></ref>
<ref id="ref-18"><label>[18]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Kumar</surname></string-name>, <string-name><given-names>A. K.</given-names> <surname>Singh</surname></string-name>, <string-name><given-names>I.</given-names> <surname>Ahmad</surname></string-name>, <string-name><given-names>P. K.</given-names> <surname>Singh</surname></string-name>, <string-name><given-names>P. K.</given-names> <surname>Verma</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>A novel decentralized blockchain architecture for the preservation of privacy and data security against cyberattacks in healthcare</article-title>,&#x201D; <source>Sensors</source>, vol. <volume>22</volume>, no. <issue>15</issue>, pp. <fpage>5921</fpage>, <year>2022</year>; <pub-id pub-id-type="pmid">35957478</pub-id></mixed-citation></ref>
<ref id="ref-19"><label>[19]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>P.</given-names> <surname>Kumar</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Kumar</surname></string-name>, <string-name><given-names>G.</given-names> <surname>Srivastava</surname></string-name>, <string-name><given-names>G. P.</given-names> <surname>Gupta</surname></string-name>, <string-name><given-names>R.</given-names> <surname>Tripathi</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>PPSF: A privacy-preserving and secure framework using blockchain-based machine-learning for IoT-driven smart cities</article-title>,&#x201D; <source>IEEE Transactions on Network Science and Engineering</source>, vol. <volume>8</volume>, no. <issue>3</issue>, pp. <fpage>2326</fpage>&#x2013;<lpage>2341</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-20"><label>[20]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>H.</given-names> <surname>Cui</surname></string-name>, <string-name><given-names>X.</given-names> <surname>Dong</surname></string-name>, <string-name><given-names>H.</given-names> <surname>Deng</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Dehghani</surname></string-name>, <string-name><given-names>K.</given-names> <surname>Alsubhi</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Cyber attack detection process in sensor of DC micro-grids under electric vehicle based on Hilbert-Huang transform and deep learning</article-title>,&#x201D; <source>IEEE Sensors Journal</source>, vol. <volume>21</volume>, no. <issue>14</issue>, pp. <fpage>15885</fpage>&#x2013;<lpage>15894</lpage>, <year>2020</year>.</mixed-citation></ref>
<ref id="ref-21"><label>[21]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>G.</given-names> <surname>Liang</surname></string-name>, <string-name><given-names>S. R.</given-names> <surname>Weller</surname></string-name>, <string-name><given-names>F.</given-names> <surname>Luo</surname></string-name>, <string-name><given-names>J.</given-names> <surname>Zhao</surname></string-name> and <string-name><given-names>Z. Y.</given-names> <surname>Dong</surname></string-name></person-group>, &#x201C;<article-title>Distributed blockchain-based data protection framework for modern power systems against cyber-attacks</article-title>,&#x201D; <source>IEEE Transactions on Smart Grid</source>, vol. <volume>10</volume>, no. <issue>3</issue>, pp. <fpage>3162</fpage>&#x2013;<lpage>3173</lpage>, <year>2018</year>.</mixed-citation></ref>
<ref id="ref-22"><label>[22]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>W.</given-names> <surname>Pakdee</surname></string-name> and <string-name><given-names>T.</given-names> <surname>Sakkarangkoon</surname></string-name></person-group>, &#x201C;<article-title>Numerical study of an unsteady non-premixed flame in a porous medium based on the thermal equilibrium model</article-title>,&#x201D; <source>Journal of Theoretical and Applied Mechanics</source>, vol. <volume>59</volume>, no. <issue>3</issue>, pp. <fpage>401</fpage>&#x2013;<lpage>412</lpage>, <year>2021</year>.</mixed-citation></ref>
<ref id="ref-23"><label>[23]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>L.</given-names> <surname>Li</surname></string-name>, <string-name><given-names>Z.</given-names> <surname>Liu</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Lu</surname></string-name>, <string-name><given-names>F.</given-names> <surname>Wang</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Jeon</surname></string-name></person-group>, &#x201C;<article-title>Hard-rock tunnel thrust prediction with TBM construction big data using an improved two-hidden-layer extreme learning machine</article-title>,&#x201D; <source>IEEE Access</source>, vol. <volume>10</volume>, pp. <fpage>112695</fpage>&#x2013;<lpage>112712</lpage>, <year>2022</year>.</mixed-citation></ref>
<ref id="ref-24"><label>[24]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>A.</given-names> <surname>Derhab</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Guerroumi</surname></string-name>, <string-name><given-names>A.</given-names> <surname>Gumaei</surname></string-name>, <string-name><given-names>L.</given-names> <surname>Maglaras</surname></string-name>, <string-name><given-names>M. A.</given-names> <surname>Ferrag</surname></string-name> <etal>et al.</etal></person-group><italic>,</italic> &#x201C;<article-title>Blockchain and random subspace learning-based IDS for SDN-enabled industrial IoT security</article-title>,&#x201D; <source>Sensors</source>, vol. <volume>19</volume>, no. <issue>14</issue>, pp. <fpage>3119</fpage>, <year>2019</year>; <pub-id pub-id-type="pmid">31311136</pub-id></mixed-citation></ref>
<ref id="ref-25"><label>[25]</label><mixed-citation publication-type="conf-proc"><person-group person-group-type="author"><string-name><given-names>S.</given-names> <surname>Abe</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Uchida</surname></string-name>, <string-name><given-names>M.</given-names> <surname>Hori</surname></string-name>, <string-name><given-names>Y.</given-names> <surname>Hiraoka</surname></string-name> and <string-name><given-names>S.</given-names> <surname>Horata</surname></string-name></person-group>, &#x201C;<article-title>Cyber threat information sharing system for industrial control system (ICS)</article-title>,&#x201D; in <conf-name>2018 57th Annual Conf. of the Society of Instrument and Control Engineers of Japan (SICE)</conf-name>, <publisher-loc>Nara, Japan</publisher-loc>, pp. <fpage>374</fpage>&#x2013;<lpage>379</lpage>, <year>2018</year>. </mixed-citation></ref>
<ref id="ref-26"><label>[26]</label><mixed-citation publication-type="journal"><person-group person-group-type="author"><string-name><given-names>M.</given-names> <surname>Ragab</surname></string-name> and <string-name><given-names>A.</given-names> <surname>Altalbe</surname></string-name></person-group>, &#x201C;<article-title>A blockchain-based architecture for enabling cybersecurity in the internet-of-critical infrastructures</article-title>,&#x201D; <source>Computers, Materials &#x0026; Continua</source>, vol. <volume>72</volume>, no. <issue>1</issue>, pp. <fpage>1579</fpage>&#x2013;<lpage>1592</lpage>, <year>2022</year>.</mixed-citation></ref>
</ref-list>
</back>
</article>