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A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump
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} div.type-section h2 { font-size: 20px; line-height: 26px; font-weight: 300; } div.type-section h3 { margin-left: 15px; margin-bottom: 0px; font-weight: 300; } .journal-tabs .tab-title.active a { } </style> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/slick.css?f38b2db10e01b157?1732615622"> <meta name="title" content="A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump"> <meta name="description" content="Screw pumps’ faulty working conditions affect the stability of oil production. At project sites, different sensors are used simultaneously to collect multi-dimensional signals; the data fault labels and location are not clear, and how to comprehensively use multi-source information in effective fault feature extraction has become an urgent issue. Existing diagnostic methods use a single signal or part of a signal and do not fully utilize the acquired signal, which makes it difficult to achieve the required accuracy of diagnostic results. This paper focuses on the model-driven approach to extract multi-source fault features of screw pumps. Firstly, it constructs a fault data model (FDM) by analyzing the fault mechanism of the screw pump. Secondly, it uses the FDM to select an effective data set. Thirdly, it constructs a multi-dimensional fault feature extraction model (MDFEM) to extract featured signal features and data features, for which we also comprehensively used multi-source signals in effective fault feature extraction, while other traditional methods only use one or two signals. Finally, after feature selection, unsupervised fault diagnosis was achieved by using the k-means method. After experimental verification, the method can comprehensively use multi-source information to construct an effective data set and extract multi-dimensional, effective fault features for screw pump fault diagnosis." > <link rel="image_src" href="https://pub.mdpi-res.com/img/journals/processes-logo.png?8600e93ff98dbf14" > <meta name="dc.title" content="A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump"> <meta name="dc.creator" content="Weigang Wen"> <meta name="dc.creator" content="Jingqi Qin"> <meta name="dc.creator" content="Xiangru Xu"> <meta name="dc.creator" content="Kaifu Mi"> <meta name="dc.creator" content="Meng Zhou"> <meta name="dc.type" content="Article"> <meta name="dc.source" content="Processes 2024, Vol. 12, Page 2571"> <meta name="dc.date" content="2024-11-17"> <meta name ="dc.identifier" content="10.3390/pr12112571"> <meta name="dc.publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="dc.rights" content="http://creativecommons.org/licenses/by/3.0/"> <meta name="dc.format" content="application/pdf" > <meta name="dc.language" content="en" > <meta name="dc.description" content="Screw pumps’ faulty working conditions affect the stability of oil production. At project sites, different sensors are used simultaneously to collect multi-dimensional signals; the data fault labels and location are not clear, and how to comprehensively use multi-source information in effective fault feature extraction has become an urgent issue. Existing diagnostic methods use a single signal or part of a signal and do not fully utilize the acquired signal, which makes it difficult to achieve the required accuracy of diagnostic results. This paper focuses on the model-driven approach to extract multi-source fault features of screw pumps. Firstly, it constructs a fault data model (FDM) by analyzing the fault mechanism of the screw pump. Secondly, it uses the FDM to select an effective data set. Thirdly, it constructs a multi-dimensional fault feature extraction model (MDFEM) to extract featured signal features and data features, for which we also comprehensively used multi-source signals in effective fault feature extraction, while other traditional methods only use one or two signals. Finally, after feature selection, unsupervised fault diagnosis was achieved by using the k-means method. After experimental verification, the method can comprehensively use multi-source information to construct an effective data set and extract multi-dimensional, effective fault features for screw pump fault diagnosis." > <meta name="dc.subject" content="feature extraction" > <meta name="dc.subject" content="model-driven" > <meta name="dc.subject" content="multi-source information" > <meta name="dc.subject" content="screw pump" > <meta name="dc.subject" content="fault diagnosis" > <meta name ="prism.issn" content="2227-9717"> <meta name ="prism.publicationName" content="Processes"> <meta name ="prism.publicationDate" content="2024-11-17"> <meta name ="prism.volume" content="12"> <meta name ="prism.number" content="11"> <meta name ="prism.section" content="Article" > <meta name ="prism.startingPage" content="2571" > <meta name="citation_issn" content="2227-9717"> <meta name="citation_journal_title" content="Processes"> <meta name="citation_publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="citation_title" content="A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump"> <meta name="citation_publication_date" content="2024/11"> <meta name="citation_online_date" content="2024/11/17"> <meta name="citation_volume" content="12"> <meta name="citation_issue" content="11"> <meta name="citation_firstpage" content="2571"> <meta name="citation_author" content="Wen, Weigang"> <meta name="citation_author" content="Qin, Jingqi"> <meta name="citation_author" content="Xu, Xiangru"> <meta name="citation_author" content="Mi, Kaifu"> <meta name="citation_author" content="Zhou, Meng"> <meta name="citation_doi" content="10.3390/pr12112571"> <meta name="citation_id" content="mdpi-pr12112571"> <meta name="citation_abstract_html_url" content="https://www.mdpi.com/2227-9717/12/11/2571"> <meta name="citation_pdf_url" content="https://www.mdpi.com/2227-9717/12/11/2571/pdf?version=1731913633"> <link rel="alternate" type="application/pdf" title="PDF Full-Text" href="https://www.mdpi.com/2227-9717/12/11/2571/pdf?version=1731913633"> <meta name="fulltext_pdf" content="https://www.mdpi.com/2227-9717/12/11/2571/pdf?version=1731913633"> <meta name="citation_fulltext_html_url" content="https://www.mdpi.com/2227-9717/12/11/2571/htm"> <link rel="alternate" type="text/html" title="HTML Full-Text" href="https://www.mdpi.com/2227-9717/12/11/2571/htm"> <meta name="fulltext_html" content="https://www.mdpi.com/2227-9717/12/11/2571/htm"> <link rel="alternate" type="text/xml" title="XML Full-Text" href="https://www.mdpi.com/2227-9717/12/11/2571/xml"> <meta name="fulltext_xml" content="https://www.mdpi.com/2227-9717/12/11/2571/xml"> <meta name="citation_xml_url" content="https://www.mdpi.com/2227-9717/12/11/2571/xml"> <meta name="twitter:card" content="summary" /> <meta name="twitter:site" content="@MDPIOpenAccess" /> <meta name="twitter:image" content="https://pub.mdpi-res.com/img/journals/processes-logo-social.png?8600e93ff98dbf14" /> <meta property="fb:app_id" content="131189377574"/> <meta property="og:site_name" content="MDPI"/> <meta property="og:type" content="article"/> <meta property="og:url" content="https://www.mdpi.com/2227-9717/12/11/2571" /> <meta property="og:title" content="A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump" /> <meta property="og:description" content="Screw pumps’ faulty working conditions affect the stability of oil production. At project sites, different sensors are used simultaneously to collect multi-dimensional signals; the data fault labels and location are not clear, and how to comprehensively use multi-source information in effective fault feature extraction has become an urgent issue. Existing diagnostic methods use a single signal or part of a signal and do not fully utilize the acquired signal, which makes it difficult to achieve the required accuracy of diagnostic results. This paper focuses on the model-driven approach to extract multi-source fault features of screw pumps. Firstly, it constructs a fault data model (FDM) by analyzing the fault mechanism of the screw pump. Secondly, it uses the FDM to select an effective data set. Thirdly, it constructs a multi-dimensional fault feature extraction model (MDFEM) to extract featured signal features and data features, for which we also comprehensively used multi-source signals in effective fault feature extraction, while other traditional methods only use one or two signals. Finally, after feature selection, unsupervised fault diagnosis was achieved by using the k-means method. After experimental verification, the method can comprehensively use multi-source information to construct an effective data set and extract multi-dimensional, effective fault features for screw pump fault diagnosis." /> <meta property="og:image" content="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g001-550.jpg?1731913718" /> <link rel="alternate" type="application/rss+xml" title="MDPI Publishing - Latest articles" href="https://www.mdpi.com/rss"> <meta name="google-site-verification" content="PxTlsg7z2S00aHroktQd57fxygEjMiNHydKn3txhvwY"> <meta name="facebook-domain-verification" content="mcoq8dtq6sb2hf7z29j8w515jjoof7" /> <script id="Cookiebot" data-cfasync="false" src="https://consent.cookiebot.com/uc.js" data-cbid="51491ddd-fe7a-4425-ab39-69c78c55829f" type="text/javascript" async></script> <!--[if lt IE 9]> <script>var browserIe8 = true;</script> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/ie8foundationfix.css?50273beac949cbf0?1732615622"> <script src="//html5shiv.googlecode.com/svn/trunk/html5.js"></script> <script src="//cdnjs.cloudflare.com/ajax/libs/html5shiv/3.6.2/html5shiv.js"></script> <script src="//s3.amazonaws.com/nwapi/nwmatcher/nwmatcher-1.2.5-min.js"></script> <script src="//html5base.googlecode.com/svn-history/r38/trunk/js/selectivizr-1.0.3b.js"></script> <script src="//cdnjs.cloudflare.com/ajax/libs/respond.js/1.1.0/respond.min.js"></script> <script src="https://pub.mdpi-res.com/assets/js/ie8/ie8patch.js?9e1d3c689a0471df?1732615622"></script> <script src="https://pub.mdpi-res.com/assets/js/ie8/rem.min.js?94b62787dcd6d2f2?1732615622"></script> <![endif]--> <script type="text/plain" data-cookieconsent="statistics"> (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); 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href="/cdn-cgi/l/email-protection#91bef2fff5bcf2f6f8befdbef4fcf0f8fdbce1e3fee5f4f2e5f8feffb2a1a1a1f5a6a9a1a1a1f0a0f2a1f0a2a9a0f3a0a7a1a9a0f3a4a7a0f3a0a6a0a4a4a7a0f3a0a7"><sup><i class="fa fa-envelope-o"></i></sup></a>, </span><span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop13408092' data-options='is_hover:true, hover_timeout:5000'> Kaifu Mi</div><div id="profile-card-drop13408092" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Kaifu Mi</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a 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href="/cdn-cgi/l/email-protection#331c505d571e50545a1c5f1c565e525a5f1e43415c475650475a5c5d1003030307055703050351030a0255015703560300025703560700035603010303070003560300"><sup><i class="fa fa-envelope-o"></i></sup></a> and </span><span class="inlineblock "><div class='profile-card-drop' data-dropdown='profile-card-drop13408093' data-options='is_hover:true, hover_timeout:5000'> Meng Zhou</div><div id="profile-card-drop13408093" data-dropdown-content class="f-dropdown content profile-card-content" aria-hidden="true" tabindex="-1"><div class="profile-card__title"><div class="sciprofiles-link" style="display: inline-block"><div class="sciprofiles-link__link"><img class="sciprofiles-link__image" src="/bundles/mdpisciprofileslink/img/unknown-user.png" style="width: auto; height: 16px; border-radius: 50%;"><span class="sciprofiles-link__name">Meng Zhou</span></div></div></div><div class="profile-card__buttons" style="margin-bottom: 10px;"><a 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fa-envelope-o"></i></sup></a></span> </div> <div class="nrm"></div> <span style="display:block; height:6px;"></span> <div></div> <div style="margin: 5px 0 15px 0;" class="hypothesis_container"> <div class="art-affiliations"> <div class="affiliation "> <div class="affiliation-item"><sup>1</sup></div> <div class="affiliation-name ">School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China</div> </div> <div class="affiliation "> <div class="affiliation-item"><sup>2</sup></div> <div class="affiliation-name ">Branch of Industry, Beijing Petroleum Machinery Co., Ltd., Beijing 102206, China</div> </div> <div class="affiliation"> <div class="affiliation-item"><sup>*</sup></div> <div class="affiliation-name ">Author to whom correspondence should be addressed. </div> </div> </div> </div> <div class="bib-identity" style="margin-bottom: 10px;"> <em>Processes</em> <b>2024</b>, <em>12</em>(11), 2571; <a href="https://doi.org/10.3390/pr12112571">https://doi.org/10.3390/pr12112571</a> </div> <div class="pubhistory" style="font-weight: bold; padding-bottom: 10px;"> <span style="display: inline-block">Submission received: 24 September 2024</span> / <span style="display: inline-block">Revised: 5 November 2024</span> / <span style="display: inline-block">Accepted: 15 November 2024</span> / <span style="display: inline-block">Published: 17 November 2024</span> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/processes/sections/process_control_monitoring">Process Control and Monitoring</a>)<br/> </div> <div class="highlight-box1"> <div class="download"> <a class="button button--color-inversed button--drop-down" data-dropdown="drop-download-1522713" aria-controls="drop-supplementary-1522713" aria-expanded="false"> Download <i class="material-icons">keyboard_arrow_down</i> </a> <div id="drop-download-1522713" class="f-dropdown 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id="article-popup" class="popupgallery" style="display: inline; line-height: 200%"> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g001.png?1731913717" title=" <strong>Figure 1</strong><br/> <p>Screw pump fault diagnosis framework.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g002.png?1731913718" title=" <strong>Figure 2</strong><br/> <p>Screw pump fault data model.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g003.png?1731913719" title=" <strong>Figure 3</strong><br/> <p>Slide sampling method.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g004.png?1731913720" title=" <strong>Figure 4</strong><br/> <p>Heat map of signal correlation coefficients.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g005.png?1731913721" title=" <strong>Figure 5</strong><br/> <p>Results of comparison of Experiment I. (<b>a</b>) Clustering results of Feature Set-1; (<b>b</b>) clustering results of Feature Set-2.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g006.png?1731913721" title=" <strong>Figure 6</strong><br/> <p>CHI of different feature sets with the number of clusters.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g007.png?1731913722" title=" <strong>Figure 7</strong><br/> <p>Diagnosis results for different datasets after clustering: (<b>a</b>) average of accuracy; (<b>b</b>) RMSE.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g008.png?1731913723" title=" <strong>Figure 8</strong><br/> <p>Results of comparison of Experiment II. (<b>a</b>) Clustering results of Feature Set-3; (<b>b</b>) clustering results of Feature Set-4; (<b>c</b>) clustering results of Feature Set-5; (<b>d</b>) clustering results of Feature Set-6.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g009.png?1731913724" title=" <strong>Figure 9</strong><br/> <p>CHI of different feature sets with the number of clusters.</p> "> </a> <a href="https://pub.mdpi-res.com/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g010.png?1731913725" title=" <strong>Figure 10</strong><br/> <p>Diagnosis results for different datasets after clustering: (<b>a</b>) average of accuracy; (<b>b</b>) RMSE.</p> "> </a> </div> <a class="button button--color-inversed" href="/2227-9717/12/11/2571/notes">Versions Notes</a> </div> </div> <div class="responsive-moving-container small hidden" data-id="article-counters" style="margin-top: 15px;"></div> <div class="html-dynamic"> <section> <div class="art-abstract art-abstract-new in-tab hypothesis_container"> <p> <div><section class="html-abstract" id="html-abstract"> <h2 id="html-abstract-title">Abstract</h2><b>:</b> <div class="html-p">Screw pumps’ faulty working conditions affect the stability of oil production. At project sites, different sensors are used simultaneously to collect multi-dimensional signals; the data fault labels and location are not clear, and how to comprehensively use multi-source information in effective fault feature extraction has become an urgent issue. Existing diagnostic methods use a single signal or part of a signal and do not fully utilize the acquired signal, which makes it difficult to achieve the required accuracy of diagnostic results. This paper focuses on the model-driven approach to extract multi-source fault features of screw pumps. Firstly, it constructs a fault data model (FDM) by analyzing the fault mechanism of the screw pump. Secondly, it uses the FDM to select an effective data set. Thirdly, it constructs a multi-dimensional fault feature extraction model (MDFEM) to extract featured signal features and data features, for which we also comprehensively used multi-source signals in effective fault feature extraction, while other traditional methods only use one or two signals. Finally, after feature selection, unsupervised fault diagnosis was achieved by using the k-means method. After experimental verification, the method can comprehensively use multi-source information to construct an effective data set and extract multi-dimensional, effective fault features for screw pump fault diagnosis.</div> </section> <div id="html-keywords"> <div class="html-gwd-group"><div id="html-keywords-title">Keywords: </div><a href="/search?q=feature+extraction">feature extraction</a>; <a href="/search?q=model-driven">model-driven</a>; <a href="/search?q=multi-source+information">multi-source information</a>; <a href="/search?q=screw+pump">screw pump</a>; <a href="/search?q=fault+diagnosis">fault diagnosis</a></div> <div> </div> </div> </div> </p> </div> </section> </div> <div class="hypothesis_container"> <ul class="menu html-nav" data-prev-node="#html-quick-links-title"> </ul> <div class="html-body"> <section id='sec1-processes-12-02571' type='intro'><h2 data-nested='1'> 1. Introduction</h2><div class='html-p'>The screw pump has become one of the widely used oil lifting methods due to the advantages of small size of system equipment, easy maintenance and management, smooth liquid flow, and high pumping efficiency. With the development of oilfield exploration, the lifting height is increasing. The working conditions of the screw pump are affected by various factors when it works in a complex environment, and the faults, such as rod and pipe breakage, pump leakage, sand jamming, and waxing of tubing, occur from time to time [<a href="#B1-processes-12-02571" class="html-bibr">1</a>,<a href="#B2-processes-12-02571" class="html-bibr">2</a>], which seriously restricts the production efficiency of the oil wells. Therefore, screw pump fault diagnosis is of great significance. The traditional screw pump fault diagnosis methods require a lot of expert experience, and using single current or torque and other signals for diagnosis is ineffective.</div><div class='html-p'>In recent years, scholars from various countries have conducted extensive research on the fault diagnosis of screw pumps. Aiming at the screw pump fault diagnosis problems of inefficiency and lack of precision, one proposal to improve the wavelet packet transform is by introducing the idea of power spectrum refinement combined with cuckoo search (CS) to optimize the diagnosis method of the back propagation (BP) neural network [<a href="#B3-processes-12-02571" class="html-bibr">3</a>]. Based on the statistical process control, extended discriminant criterion, and the multi-parameter rule, the field fault diagnosis model of electric submersible screw pump unit is constructed, and a multi-parameter process control fault diagnosis method is proposed [<a href="#B4-processes-12-02571" class="html-bibr">4</a>]. A supervised neural network was established using Bayes classification decision theory to build a PNN model for fault classification of a certain type of screw pump [<a href="#B5-processes-12-02571" class="html-bibr">5</a>]. Scholars proposed that the current method and holding pressure method can be used to comprehensively diagnose the pumping condition of screw pump wells, combined with production, liquid level, and other parameters to synthesize the research and judgment, in order to accurately determine the specific operation of downhole pumps [<a href="#B6-processes-12-02571" class="html-bibr">6</a>]. One study selected rod torque and axial force as parameters for comparing working condition status, stating that using a diagnosis model to calculate the reasonable area of two parameters and comparing them with the actual test data can diagnose the various situations, determine whether there is a fault and analyzing failure [<a href="#B7-processes-12-02571" class="html-bibr">7</a>]. Another paper proposed an unsupervised fault diagnosis methodology to leverage readily available dynamometer cards (DCs) to diagnose collected unlabeled MPCs, and a mathematical model of the SRPS was presented to convert actual DCs to MPCs [<a href="#B8-processes-12-02571" class="html-bibr">8</a>]. Ren Weijian proposed using a wavelet packet to filter and eliminate noise from an active power signal and decomposed fault signal, then they used an Elman neural network to identify the decomposed fault feature [<a href="#B9-processes-12-02571" class="html-bibr">9</a>]. Wavelet packet theory was used to decompose and reconstruct the active power signal of a submersible screw pump, extracted the main fault information contained in the power signal, and constructed the fault feature vector of a submersible screw pump combined with parameters such as output, oil pressure, casing pressure, and dynamic liquid level [<a href="#B10-processes-12-02571" class="html-bibr">10</a>]. A thesis aimed to accurately and efficiently identify the fault forms of a submersible screw pump, and proposed a fault diagnosis method of the submersible screw pump based on random forest. An HDFS storage system and MapReduce processing system were established based on the Hadoop big data processing platform [<a href="#B11-processes-12-02571" class="html-bibr">11</a>]. Xu Jun developed a screw pump condition-monitoring system based on dual micro-controllers, which uses real-time drive electrical parameters to calculate the rod torque and speed and to make a comparative analysis, and achieved the fault diagnosis of the screw pump [<a href="#B12-processes-12-02571" class="html-bibr">12</a>]. Min Li established a screw pump fault diagnosis expert system based on fuzzy neural network. The test results showed that the diagnosis of this fault diagnosis expert system is operable, and the fuzzy neural network is reliable, which enriched the diagnosis method of the screw pump well [<a href="#B13-processes-12-02571" class="html-bibr">13</a>]. Xue Jianquan proposed a screw pump diagnosis method based on the BP neural network and expert system, and developed the fault diagnosis software with Basic and Matlab nnet toolbox, and the test results of the well plant data proved the feasibility of the diagnosis method [<a href="#B14-processes-12-02571" class="html-bibr">14</a>]. Qu Wentao used the node system method to establish a relationship model between active power and pump energy consumption and analyzed the influence of different faults on the screw operating performance [<a href="#B15-processes-12-02571" class="html-bibr">15</a>]. Chen Shiwen calculated and analyzed the force of the screw pump and rod and proposed the method of dividing the fault feature into different thresholds and diagnosing screw pump working conditions by means of the support vector machine algorithm [<a href="#B16-processes-12-02571" class="html-bibr">16</a>]. Zheng Chunfeng studied the system and operation performance of an electric submersible screw pump, analyzed the correspondence between operation parameters and fault types, and used a BP neural network to diagnose faults of electric submersible screw pump [<a href="#B17-processes-12-02571" class="html-bibr">17</a>].</div><div class='html-p'>However, the project site data are multi-dimensional signals collected simultaneously by multiple sensors, including current, voltage, power, torque, rotation speed, load, oil pressure, and casing pressure, and the data type is complex, and the collection period is long. Additionally, the fault label of the data is not clear, and the position of the fault information in the whole signal data is not clear as well, which will lead to a low diagnostic accuracy if using this kind of signal data to carry out the fault diagnosis. Traditional screw pump fault diagnosis methods rely on a large number of expert experiences, and diagnosis accuracy using a single signal is low [<a href="#B18-processes-12-02571" class="html-bibr">18</a>,<a href="#B19-processes-12-02571" class="html-bibr">19</a>]. The current method is affected by the combination of all parts of the system [<a href="#B20-processes-12-02571" class="html-bibr">20</a>]; the torque method has an error between the calculated result and the actual torque; the fluid production method does not directly reflect the type of fault; the pressure method involves holding the wellhead to a higher pressure, which must be used on specific conditions. In the field of fault diagnosis, multi-source information technology comprehensively collects equipment fault state information by using multiple sensors, taps the coupled complementary information between multi-source sensor data, takes multi-dimensional feature fusion analysis as a way to greatly improve the reliability and accuracy of fault diagnosis, and overcomes the shortcomings such as limited fault information contained in a single segmentation and large uncertainty [<a href="#B21-processes-12-02571" class="html-bibr">21</a>,<a href="#B22-processes-12-02571" class="html-bibr">22</a>,<a href="#B23-processes-12-02571" class="html-bibr">23</a>,<a href="#B24-processes-12-02571" class="html-bibr">24</a>,<a href="#B25-processes-12-02571" class="html-bibr">25</a>,<a href="#B26-processes-12-02571" class="html-bibr">26</a>].</div><div class='html-p'>The main contributions of the paper are described as follows:</div><div class='html-p'><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>The fault data model (FDM) is proposed and applied to select an effective data set from the original data with no fault labels and unclear fault locations.</div></dd><dt id=''>(2)</dt><dd><div class='html-p'>A multi-dimensional fault feature extraction model (MDFEM) is proposed and applied to extract featured signal feature and data feature from multi-source information.</div></dd></dl></div><div class='html-p'>Therefore, this paper proposes a multi-source fault feature extraction method for a screw pump based on model-driven data. The chapters of the paper are as follows: <a href="#sec2-processes-12-02571" class="html-sec">Section 2</a> analyzes the screw pump fault mechanism and constructs the FDM; <a href="#sec3-processes-12-02571" class="html-sec">Section 3</a> uses the FDM to select the fault data and construct an effective data set, then constructs a MDFEM, and extracts multi-dimensional fault features; <a href="#sec4-processes-12-02571" class="html-sec">Section 4</a> verifies the validity and accuracy of the proposed method; and <a href="#sec5-processes-12-02571" class="html-sec">Section 5</a> is the conclusion.</div></section><section id='sec2-processes-12-02571' type=''><h2 data-nested='1'> 2. Fault Model Construction</h2><section id='sec2dot1-processes-12-02571' type=''><h4 class='html-italic' data-nested='2'> 2.1. Methodological Framework</h4><div class='html-p'>The flow of the multi-source fault feature extraction method for a screw pump based on model-driven data is shown in <a href="#processes-12-02571-f001" class="html-fig">Figure 1</a>. The process is described as follows: (1) analyzing the fault mechanism and establishing the current, load, rotational speed, and oil pressure fault mechanism; (2) revealing the mechanism characterization and establishing the FDM; (3) analyzing the original data and carrying out data pre-processing, including data cleaning, normalization, and slice enhancement; (4) using the FDM to select fault data and constructing an effective data set; (5) studying the multi-dimensional feature extraction method, extracting signal and data features, and obtaining effective multi-dimensional features; (6) using the k-means unsupervised clustering method to carry out experimental validation to realize the diagnosis of screw pump faults.</div></section><section id='sec2dot2-processes-12-02571' type=''><h4 class='html-italic' data-nested='2'> 2.2. Fault Mechanism Model</h4><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>Current Fault Model</div></dd></dl><div class='html-p'>The current method is the quantitative long-time measurement of parameters such as operating current, voltage, and power of the drive motor using specialized instruments. The motor input current is deduced based on the motor output power:<div class='html-disp-formula-info' id='FD1-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>=</mo> <msqrt> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msubsup> <mi>N</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> <mrow> <msubsup> <mi>N</mi> <mi>e</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> </mstyle> <mo>×</mo> <mfenced> <mrow> <msubsup> <mi>I</mi> <mi>N</mi> <mn>2</mn> </msubsup> <mo>−</mo> <msubsup> <mi>I</mi> <mn>0</mn> <mn>2</mn> </msubsup> </mrow> </mfenced> <mo>+</mo> <msubsup> <mi>I</mi> <mn>0</mn> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>=</mo> <msqrt> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msubsup> <mi>M</mi> <mi>g</mi> <mn>2</mn> </msubsup> <msubsup> <mi>n</mi> <mi>g</mi> <mn>2</mn> </msubsup> </mrow> <mrow> <msup> <mrow> <mn>9549</mn> </mrow> <mn>2</mn> </msup> <mo>×</mo> <msubsup> <mi>η</mi> <mi>t</mi> <mn>2</mn> </msubsup> <msubsup> <mi>N</mi> <mi>e</mi> <mn>2</mn> </msubsup> </mrow> </mfrac> </mstyle> <mo>×</mo> <mfenced> <mrow> <msubsup> <mi>I</mi> <mi>N</mi> <mn>2</mn> </msubsup> <mo>−</mo> <msubsup> <mi>I</mi> <mn>0</mn> <mn>2</mn> </msubsup> </mrow> </mfenced> <mo>+</mo> <msubsup> <mi>I</mi> <mn>0</mn> <mn>2</mn> </msubsup> </mrow> </msqrt> </mrow> </semantics></math> </div> <div class='l'> <label >(1)</label> </div> </div> where <span class='html-italic'>I</span><sub>1</sub> is the motor input current, A; <span class='html-italic'>N<sub>e</sub></span> is the power under a rated load, kW; <span class='html-italic'>I<sub>N</sub></span> is the stator current of the motor under a rated load, A; <span class='html-italic'>I</span><sub>0</sub> is the no-load current of the motor, A. <span class='html-italic'>N</span><sub>1</sub> is the output shaft power of the motor, kW; <span class='html-italic'>M<sub>g</sub></span> is the driving torque of the rod, N⋅m; <span class='html-italic'>n<sub>g</sub></span> is the rotational speed of the rod, r/min; and <span class='html-italic'>η<sub>t</sub></span> is the total transmission efficiency of the motor, %.</div><div class='html-p'>After analysis, the relationship between electrical parameters and torque can be obtained as shown below:<div class='html-disp-formula-info' id='FD2-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msubsup> <mi>I</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>∝</mo> <msubsup> <mi>M</mi> <mi>g</mi> <mn>2</mn> </msubsup> </mrow> </semantics></math> </div> <div class='l'> <label >(2)</label> </div> </div></div><div class='html-p'>The analysis shows that the square of the motor input current is proportional to the square of the rod torque.</div><div class='html-p'>According to Equation (2), it can be deduced that when the current drops to the no-load current, which means the rod torque drops to the no-load torque, the oil rod or oil pipe may break off; when the current is smaller than the lower limit of the reasonable range and higher than the lower limit of the limit range, the pump may leak or the oil pipe may leak; when the current fluctuates in the upper limit of the limit range, the oil pipe may be waxed; when the current increases to the outside of the limit range, the stator may be dissolved or the parameters may be high; when the current is smaller than the lower limit of the reasonable range and fluctuates, the stator may be waxed. When the current fluctuates, the stator may be degumming.</div><dl class='html-order'><dt id=''>(2)</dt><dd><div class='html-p'>Load Fault Model</div></dd></dl><div class='html-p'>The axial load F on the screw pump rod can be expressed by the following formula:<div class='html-disp-formula-info' id='FD3-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <mi>F</mi> <mo>=</mo> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>F</mi> <mn>3</mn> </msub> <mo>−</mo> <msub> <mi>F</mi> <mn>4</mn> </msub> </mrow> </semantics></math> </div> <div class='l'> <label >(3)</label> </div> </div> where <span class='html-italic'>F</span><sub>1</sub> is the rod’s own gravity, N; <span class='html-italic'>F</span><sub>2</sub> is the axial load generated by the pressure difference between the inlet and outlet of the pump, N; <span class='html-italic'>F</span><sub>3</sub> is the friction force between the well fluid and the rod when it flows upward in the pipe, N; and <span class='html-italic'>F</span><sub>4</sub> is the upward buoyancy force that the rod receives in the well fluid, N.</div><div class='html-p'>The gravity of the pumping rod can be expressed by the following equation:<div class='html-disp-formula-info' id='FD4-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>G</mi> <mi>L</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(4)</label> </div> </div> where <span class='html-italic'>G</span> is the linear density of the rod, N/m; <span class='html-italic'>L</span> is the total length of the pumping rod, m.</div><div class='html-p'>The axial load generated by the pressure difference between the inlet and outlet of the pump can be expressed by the following equation:<div class='html-disp-formula-info' id='FD5-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced> <mrow> <mi>π</mi> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>16</mn> <mi>e</mi> <mi>R</mi> </mrow> </mfenced> <mi mathvariant="sans-serif">Δ</mi> <mi>p</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(5)</label> </div> </div> where <math display='inline'><semantics> <mi>e</mi> </semantics></math> is the eccentric moment of the screw pump, m; <span class='html-italic'>R</span> is the rotor radius of the screw pump, m; <math display='inline'><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <mi>p</mi> </mrow> </semantics></math> is the differential pressure between the inlet and outlet of the pump, MPa.</div><div class='html-p'>The friction force between the well fluid and the rod can be expressed by the following equation:<div class='html-disp-formula-info' id='FD6-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>F</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>2</mn> <mi>π</mi> <msub> <mi>μ</mi> <mi>l</mi> </msub> <msub> <mi>e</mi> <mi>l</mi> </msub> <mi>ν</mi> <mi mathvariant="sans-serif">Δ</mi> <mi>L</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(6)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>e</mi> <mi>l</mi> </msub> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msup> <mi>m</mi> <mn>2</mn> </msup> <mo>−</mo> <mn>1</mn> </mrow> <mrow> <mfenced> <mrow> <msup> <mi>m</mi> <mn>2</mn> </msup> <mo>+</mo> <mn>1</mn> </mrow> </mfenced> <mi>ln</mi> <mi>m</mi> <mo>−</mo> <mfenced> <mrow> <msup> <mi>m</mi> <mn>2</mn> </msup> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> </mrow> </mfrac> </mstyle> <mo>,</mo> <mo> </mo> <mi>m</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msub> <mi>d</mi> <mi>t</mi> </msub> </mrow> <mrow> <msub> <mi>d</mi> <mi>r</mi> </msub> </mrow> </mfrac> </mstyle> </mrow> </semantics></math>, <math display='inline'><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <mi>L</mi> </mrow> </semantics></math> is the length of the section, m; <math display='inline'><semantics> <mrow> <msub> <mi>μ</mi> <mi>l</mi> </msub> </mrow> </semantics></math> is the average viscosity of the well fluid, mPa⋅s; <math display='inline'><semantics> <mi>ν</mi> </semantics></math> is the average flow speed of the well fluid in the section, m/s.</div><div class='html-p'>The buoyancy of the rod generated by well fluid can be expressed by the following equation:<div class='html-disp-formula-info' id='FD7-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>F</mi> <mn>4</mn> </msub> <mo>=</mo> <msub> <mi>ρ</mi> <mi>l</mi> </msub> <mi>g</mi> <mi>π</mi> <msup> <mrow> <mfenced> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> </mfenced> </mrow> <mn>2</mn> </msup> <mi>L</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(7)</label> </div> </div> where <math display='inline'><semantics> <mi>g</mi> </semantics></math> is the acceleration of gravity, N/kg; <math display='inline'><semantics> <mrow> <msub> <mi>ρ</mi> <mi>l</mi> </msub> </mrow> </semantics></math> is the density of the fluid in the wellbore, kg/m<sup>3</sup>.</div><div class='html-p'>After analyzing, it can be obtained that when <math display='inline'><semantics> <mrow> <msub> <mi>F</mi> <mn>2</mn> </msub> </mrow> </semantics></math> decreases, it means the liquid in the screw pump decreases; when <math display='inline'><semantics> <mrow> <msub> <mi>F</mi> <mn>3</mn> </msub> </mrow> </semantics></math> increases, it means the oil velocity increases, i.e., the oil production increases. According to Equations (3)–(7), we can conclude that when <span class='html-italic'>F</span> is zero, there may be a rod break; when <span class='html-italic'>F</span> is reduced, there may be an oil pipe leakage, a broken oil pipe, or pump leakage, etc.; when <span class='html-italic'>F</span> is increased, there may be waxing of the oil pipe or high parameters.</div><dl class='html-order'><dt id=''>(3)</dt><dd><div class='html-p'>Rotation Speed Fault Model</div></dd></dl><div class='html-p'>The rotate speed of a screw pump is closely related to the oil production, as shown in the following equation:<div class='html-disp-formula-info' id='FD8-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <mi>Q</mi> <mo>=</mo> <mn>1440</mn> <mo>×</mo> <mn>4</mn> <mi>n</mi> <mi>E</mi> <mi>D</mi> <mi>T</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(8)</label> </div> </div> where <span class='html-italic'>Q</span> is the theoretical oil production, m<sup>3</sup>/d; <span class='html-italic'>n</span> is the rotor speed, r/min; <span class='html-italic'>E</span> is the eccentricity of the rotor, m; <span class='html-italic'>D</span> is the truncated circle diameter of the rotor, m; <span class='html-italic'>T</span> is the stator lead, m.</div><div class='html-p'>The actual oil production of a screw pump can be expressed by the following equation:<div class='html-disp-formula-info' id='FD9-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msup> <mi>Q</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>Q</mi> <msub> <mi>η</mi> <mi>v</mi> </msub> <mo>=</mo> <msub> <mi>η</mi> <mi>v</mi> </msub> <mn>1440</mn> <mo>×</mo> <mn>4</mn> <mi>E</mi> <mi>D</mi> <mi>T</mi> <mi>n</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(9)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>η</mi> <mi>v</mi> </msub> </mrow> </semantics></math> is the volumetric efficiency of the screw pump; <math display='inline'><semantics> <msup> <mi>Q</mi> <mo>′</mo> </msup> </semantics></math> is the actual oil production, m<sup>3</sup>/d.</div><div class='html-p'>It can be seen that after the structural parameters <span class='html-italic'>E</span>, <span class='html-italic'>D</span>, and <span class='html-italic'>T</span> of the screw pump are determined, the oil production is only related to the rotational speed n and the volumetric efficiency <math display='inline'><semantics> <mrow> <msub> <mi>η</mi> <mi>v</mi> </msub> </mrow> </semantics></math>, and the rotational speed needs to be increased in order to achieve higher oil production.</div><div class='html-p'>Increasing the rotational speed of the screw pump can improve oil production, but extremely high rotational speed will lead to an increase in the centrifugal force of the rod, which will cause vibration and decrease the oil lifting height. At the same time, high speed rotation will also accelerate the wear of stator rubber.</div><div class='html-p'>After analyzing, it can be concluded from Equation (9) that when <span class='html-italic'>n</span> is zero, the pump may be jammed; when <span class='html-italic'>n</span> is reduced, the rod and pipe may show biased wear, or the oil pipe may be waxed, etc.; when <span class='html-italic'>n</span> increases, there may be an oil rod break, oil pipe breakage, oil pipe leakage, or pump leakage, and so on.</div><dl class='html-order'><dt id=''>(4)</dt><dd><div class='html-p'>Oil Pressure Fault Model</div></dd></dl><div class='html-p'>Letting the oil pressure be <span class='html-italic'>P</span> at the moment of starting pumping <span class='html-italic'>t</span>, the relationship between pressure and volume is:<div class='html-disp-formula-info' id='FD10-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>β</mi> <mi>m</mi> </msub> <msub> <mi>V</mi> <mi>t</mi> </msub> <mi mathvariant="sans-serif">Δ</mi> <mi>P</mi> <mo>=</mo> <msub> <mi>V</mi> <mi>p</mi> </msub> <mi mathvariant="sans-serif">Δ</mi> <mi>t</mi> </mrow> </semantics></math> </div> <div class='l'> <label >(10)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>β</mi> <mi>m</mi> </msub> </mrow> </semantics></math> is the compression coefficient of the gas–liquid mixture in the oil pipe; <math display='inline'><semantics> <mrow> <mo>Δ</mo> <mi>t</mi> </mrow> </semantics></math> is the amount of time change, s; <math display='inline'><semantics> <mrow> <mo>Δ</mo> <mi>P</mi> </mrow> </semantics></math> is the amount of pressure change, MPa; and <math display='inline'><semantics> <mrow> <msub> <mi>V</mi> <mi>t</mi> </msub> </mrow> </semantics></math> is the pumping volume flow rate m<sup>3</sup>/s.</div><div class='html-p'>When pipe leakage occurs, the relationship between the leakage flow rate and the pressure difference between the inside and outside of the oil pipe at the leaking place is:<div class='html-disp-formula-info' id='FD11-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>V</mi> <mrow> <mi>l</mi> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mi>ε</mi> <mi>φ</mi> <mi>A</mi> <msqrt> <mrow> <mn>2</mn> <mi>g</mi> <mi>h</mi> </mrow> </msqrt> </mrow> </semantics></math> </div> <div class='l'> <label >(11)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>V</mi> <mrow> <mi>l</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math> is the leakage flow rate, m<sup>3</sup>/s; <span class='html-italic'>ε</span> is the shrinkage coefficient of the leakage section due to the inertia of the liquid; <math display='inline'><semantics> <mi>φ</mi> </semantics></math> is the flow coefficient associated with the liquid; <span class='html-italic'>A</span> is the size of the cross-sectional area at the orifice of the liquid leakage, m<sup>2</sup>; <span class='html-italic'>g</span> is the acceleration of gravity, m/s<sup>2</sup>; <span class='html-italic'>h</span> is the difference in liquid pressure between the inside of the tubing at the location of the leakage and the outside of the tubing, m.</div><div class='html-p'>Since the leakage flow rate <math display='inline'><semantics> <mrow> <msub> <mi>V</mi> <mrow> <mi>l</mi> <mi>e</mi> </mrow> </msub> </mrow> </semantics></math> is a function of pressure <span class='html-italic'>P</span>, and increases nonlinearly with <span class='html-italic'>P</span>, the relationship between pressure and time is broken when leakage occurs, resulting in a slower rate of pressure increase.</div></section><section id='sec2dot3-processes-12-02571' type=''><h4 class='html-italic' data-nested='2'> 2.3. Fault Data Model</h4><div class='html-p'>After the mechanism analysis, a FDM can be established to reveal the mechanism characterization from various aspects, as shown in <a href="#processes-12-02571-f002" class="html-fig">Figure 2</a>.</div><div class='html-p'>The screw pump FDM uses the mechanism analysis of the screw pump and historical data to hierarchically reveal the mechanistic characterization of the faults, such as pump jamming, stator swelling, and pipe waxing, to classify faults and obtain the corresponding fault labels.</div></section></section><section id='sec3-processes-12-02571' type=''><h2 data-nested='1'> 3. Effective Data and Feature</h2><section id='sec3dot1-processes-12-02571' type=''><h4 class='html-italic' data-nested='2'> 3.1. Data Preprocessing</h4><div class='html-p'>By analyzing the actual working data for pump wells of an oil field in Xinjiang province, China, it can be concluded that the actual signals are collected by a variety of sensors simultaneously, the data types are complex, and the collection cycle is long, with a collection length of about 1150 sampling points. The signals start from about the 100th sampling point, showing a gradual upward trend, and continue to about the 300th sampling point, and fault data are concentrated in the area between about the 100th and 500th sampling points; the abnormal data of the oil pressure signals are also found in the area between about the 100th and 400th sampling points. From the above analysis, it can be seen that most of the signal fault data are concentrated in a small range, and do not cover the entire signal collection length. If the original data are used for fault diagnosis, the diagnostic accuracy will be adversely affected.</div><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>Data cleaning</div></dd></dl><div class='html-p'>Voltage and current signals contain noise because of the non-stationarity of the system; and pressure and load signals contain random fluctuation caused by the oil pump and environment. This may lead to inaccurate features because some features are sensitive to small fluctuations, while others are the opposite.</div><div class='html-p'>The actual data collected from the sensors contain abnormal values. The 3<math display='inline'><semantics> <mi>σ</mi> </semantics></math> method is considered according to the data characteristics.</div><div class='html-p'>The 3<math display='inline'><semantics> <mi>σ</mi> </semantics></math> method default is that data obey normal distribution, the probability of data distributed within the interval <math display='inline'><semantics> <mrow> <mrow> <mo>(</mo> <mi mathvariant="sans-serif">μ</mi> <mo>-</mo> <mn>3</mn> <mi mathvariant="sans-serif">σ</mi> <mo>,</mo> <mtext> </mtext> <mi mathvariant="sans-serif">μ</mi> <mo>+</mo> <mn>3</mn> <mi mathvariant="sans-serif">σ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> is 99.73%, and data distributed outside the interval is considered outlier data. In this section, the sliding window method is used for outlier determination. The standard deviation of the data within the sliding window is calculated as follows:<div class='html-disp-formula-info' id='FD12-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <mi>a</mi> <mi>ν</mi> <mi>g</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>+</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>x</mi> <mi>l</mi> </msub> </mrow> <mi>l</mi> </mfrac> </mstyle> </mrow> </semantics></math> </div> <div class='l'> <label >(12)</label> </div> </div><div class='html-disp-formula-info' id='FD13-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <msqrt> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <mstyle displaystyle="true"> <munderover> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> </mstyle> <msup> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>−</mo> <mrow> <mi>a</mi> <mi>ν</mi> <mi>g</mi> </mrow> </mrow> <mn>2</mn> </msup> </msqrt> </mrow> </semantics></math> </div> <div class='l'> <label >(13)</label> </div> </div> where <math display='inline'><semantics> <mrow> <mi>a</mi> <mi>ν</mi> <mi>g</mi> </mrow> </semantics></math> is the mean value of each parameter within the sliding window; <math display='inline'><semantics> <mi>σ</mi> </semantics></math> is the standard deviation of the group of data.</div><div class='html-p'>According to Equations (12) and (13), if the distance between a data value and the <math display='inline'><semantics> <mrow> <mi>a</mi> <mi>ν</mi> <mi>g</mi> </mrow> </semantics></math> is greater than 3<math display='inline'><semantics> <mi>σ</mi> </semantics></math>, the data will be rounded off, and the rounded data will be filled in using the mean of the neighbouring numbers.</div><dl class='html-order'><dt id=''>(2)</dt><dd><div class='html-p'>Data normalization</div></dd></dl><div class='html-p'>There are different unit dimension features that cannot provide an evaluation in such a multidimensional system. The purpose of normalization is to make data be limited to a certain range (e.g., [0, 1] or [−1, 1]), thus eliminating the adverse effects caused by singular sample data. As the sample data does not involve distance measures or covariance calculation, and the data does not meet the normal distribution, the maximum–minimum normalization (min-max normalization) can be used, and the linear function will convert the original data to the range of [0 1]. The equation is as follows:<div class='html-disp-formula-info' id='FD133-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>x</mi> <mo>−</mo> <mi>min</mi> <mfenced> <mi>x</mi> </mfenced> </mrow> <mrow> <mi>max</mi> <mfenced> <mi>x</mi> </mfenced> <mo>−</mo> <mi>min</mi> <mfenced> <mi>x</mi> </mfenced> </mrow> </mfrac> </mstyle> </mrow> </semantics></math> </div> <div class='l'> <label >(14)</label> </div> </div> where <math display='inline'><semantics> <msup> <mi>x</mi> <mo>′</mo> </msup> </semantics></math> is the data after normalization; <math display='inline'><semantics> <mi>x</mi> </semantics></math> is the data before normalization.</div><dl class='html-order'><dt id=''>(3)</dt><dd><div class='html-p'>Data slicing enhancements</div></dd></dl><div class='html-p'>Using the proposed FDM, the collected signals with unequal lengths are cut into signal segments with a length of 500 sampling points. Data slicing can reduce the data volume of a piece of input signal and improve the model computation efficiency; and the data segments containing fault information can be intercepted, so that the fault information features are more obvious, which is conducive to improving the accuracy of the results.</div><div class='html-p'>Due to the limited number of actual fault data samples at the site, the data set needs to be enhanced in order to increase the generalization ability of the model. Since the collected samples involving fault data are generally longer than the required input signal, the data enhancement method proposed in this paper is the sliding window sampling (SWS) method. Sliding window sampling takes a time window of the same size as the standard sample, with a step size smaller than the standard sample. The sampling method is shown in <a href="#processes-12-02571-f003" class="html-fig">Figure 3</a>. The blue irregular curve represents the timing signal. The green rectangular box represents the time window with a width of “sample length”. After the first window captures the signal fragment, it moves a distance of “sliding step” to the right and become the second window. And so on, after moving to the right for n − 1 “sliding steps”, the nth time window is obtained. In this way, a total of n signal segments are obtained. The data set after data enhancement contains a total of 13,000 samples.</div></section><section id='sec3dot2-processes-12-02571' type=''><h4 class='html-italic' data-nested='2'> 3.2. Effective Data Set</h4><div class='html-p'>After data pre-processing, the effective data set can be constructed by using FDM to select data containing fault information from original signals.</div><div class='html-p'>The FDM provides rules and principles for selecting effective data from a long-period signal. FDM describes the change modality of current, load, rotate speed, oil pressure, etc. on the fault working conditions, including average value, fluctuation, increase or decrease, and so on. Taking oil pipe waxing as an example, when it happens, the current exceeds the maximum limit and wildly fluctuates; the load increases from a low limit to a nearly maximum limit, and wildly fluctuates; the rotate speed steadily stays below the normal range and larger than the minimum limit; the oil pressure increases stably, with small fluctuations.</div><div class='html-p'>It is important for the improvement of the accuracy and efficiency of the screw pump fault diagnosis. <a href="#processes-12-02571-t001" class="html-table">Table 1</a> shows some fault data.</div></section><section id='sec3dot3-processes-12-02571' type=''><h4 class='html-italic' data-nested='2'> 3.3. Multidimensional Fault Feature Extraction</h4><div class='html-p'>According to the fluctuation of the featured signal we can extract data features that reflect the changes in the featured signal, that is, reflecting the changes in the production data, and then we can judge the fault types.</div><section id='sec3dot3dot1-processes-12-02571' type=''><h4 class='' data-nested='3'> 3.3.1. Extraction of Signal Feature</h4><div class='html-p'>Since the collected original signals contain 17-dimensional signals such as voltage, current, power, load, torque, and oil pressure, which are a large amount of data and have considerable redundancy, the 17-dimensional data will be analyzed by correlation.</div><div class='html-p'>The Pearson correlation coefficient method is defined as the covariance product of two continuously distributed parameters x and y divided by their standard deviation, as in the following equation:<div class='html-disp-formula-info' id='FD14-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>ρ</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mrow> <mi>cov</mi> <mfenced> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> </mfenced> </mrow> <mrow> <msub> <mi>σ</mi> <mi>x</mi> </msub> <msub> <mi>σ</mi> <mi>y</mi> </msub> </mrow> </mfrac> </mstyle> </mrow> </semantics></math> </div> <div class='l'> <label >(15)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>σ</mi> <mi>x</mi> </msub> <mo> </mo> <msub> <mi>σ</mi> <mi>y</mi> </msub> </mrow> </semantics></math> is the standard deviation of variables x and y, respectively, and <math display='inline'><semantics> <mrow> <mi>cov</mi> <mfenced> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> </mfenced> </mrow> </semantics></math> denotes the covariance of the two variables. The covariance formula is provided in the following equation: <div class='html-disp-formula-info' id='FD16-processes-12-02571'> <div class='f'> <math display='block'><semantics> <mrow> <mi>cov</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mstyle displaystyle="true"> <msubsup> <mo>∑</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </msubsup> </mstyle> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>−</mo> <mover> <mi>x</mi> <mo>−</mo> </mover> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>−</mo> <mover> <mi>y</mi> <mo>−</mo> </mover> <mo>)</mo> </mrow> </mrow> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </semantics></math> </div> <div class='l'> <label >(16)</label> </div> </div></div><div class='html-p'>The correlation coefficient reflects the strength and direction of correlation between variables. <a href="#processes-12-02571-t002" class="html-table">Table 2</a> shows the general pattern of correlation coefficients and strength of correlation [<a href="#B27-processes-12-02571" class="html-bibr">27</a>,<a href="#B28-processes-12-02571" class="html-bibr">28</a>,<a href="#B29-processes-12-02571" class="html-bibr">29</a>,<a href="#B30-processes-12-02571" class="html-bibr">30</a>].</div><div class='html-p'>A heat map of correlation coefficients using data from the normal operating conditions of well number z70-01-3060601 in a certain oil field is shown in <a href="#processes-12-02571-f004" class="html-fig">Figure 4</a>. According to the correlation coefficient, it can be seen that the voltage, current, and power correlation is higher than 0.91, and the correlation of current and torque is 0.95, so the voltage, power, and torque signals are discarded; the correlation of current and load is 0.20; the correlation of current and oil pressure is 0.49; and the correlation of load and speed is 0.44. In the case that voltage, power, torque, and oil pressure are discarded, the correlation of current, load, speed, and oil pressure is the lowest, that is, 3.48. It can be concluded that the 4-dimensional signals of current, load, speed, and oil pressure can be used as the signal feature.</div></section><section id='sec3dot3dot2-processes-12-02571' type=''><h4 class='' data-nested='3'> 3.3.2. Extraction Data Feature</h4><div class='html-p'>Statistical features can comprehensively describe the original signal state from different perspectives, which can quantitatively reflect the degree of signal dispersion, change, and asymmetry, and play an important role in fault diagnosis research.</div><div class='html-p'>Based on the fault mechanistic analysis, we chose the mean, variance, and peak-to-peak value (as shown in <a href="#processes-12-02571-t003" class="html-table">Table 3</a>) as data features:</div><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>The mean monitors the signal center trend, which can be the most intuitive representation of the signal changes. For example, an extremely low load mean value could mean oil rod break off; an extremely high value could mean pump jamming.</div></dd><dt id=''>(2)</dt><dd><div class='html-p'>The variance monitors the distribution trend of the signal around the mean value, which can help us better understand the fluctuation of the parameters and trend changes. For example, a high variance could mean waxing of oil pipes.</div></dd><dt id=''>(3)</dt><dd><div class='html-p'>The peak-to-peak value can be used to describe the magnitude of change of a parameter over a period of time, and can better reflect the fluctuation of the parameter. For example, a high peak-to-peak could mean stator degumming.</div></dd></dl><div class='html-p'>The effective features extracted by the multidimensional feature extraction model are shown in <a href="#processes-12-02571-t004" class="html-table">Table 4</a>.</div></section></section></section><section id='sec4-processes-12-02571' type=''><h2 data-nested='1'> 4. Experiments</h2><div class='html-p'>We chose 10 common types of faults, shown in <a href="#processes-12-02571-t005" class="html-table">Table 5</a>, and we set the number of clusters to 10.</div><dl class='html-order'><dt id=''>(1)</dt><dd><div class='html-p'>Comparative experiment I</div></dd></dl><div class='html-p'>In order to verify the effectiveness of the effective feature, comparison experiments are conducted using the extracted features (Feature Set-1, <a href="#processes-12-02571-t006" class="html-table">Table 6</a>) and remaining features (Feature Set-2, <a href="#processes-12-02571-t007" class="html-table">Table 7</a>) except for the extracted features, respectively. First, the dimensions of the two feature sets are reduced to 2 dimensions using principal component analysis (PCA), and then the K-means algorithm is used to cluster.</div><div class='html-p'>K-means is computationally efficient, especially when the number of clusters and dimensions are not too large. This makes it suitable for large datasets. The output of K-means, i.e., the cluster centroids, is straightforward to interpret. Each centroid represents the average of all points in that cluster, which can help explain the result of each cluster.</div><div class='html-p'>The clustering results are shown in <a href="#processes-12-02571-f005" class="html-fig">Figure 5</a>. It shows that using the Feature Set-1, the data can be effectively classified into 10 classes. Points clustered into one category represent data for one type of fault. The smaller the intra-class distance and the larger the inter-class distance, the better the clustering is, and accordingly, the clearer the distinction among different faults. Different colors correspond to different types of faults. The pump leakage (green cluster) and the oil pipe leakage (light-blue cluster) are similar, so they are closer in the clustering results. However, using Feature Set-2, the data can be classified into only 5 classes, and the intra-class spacing is large and the inter-class spacing is small, so that the clustering results are not effective. Therefore, it can be concluded that the effective features can be extracted using the proposed multidimensional feature extraction model.</div><div class='html-p'>The Calinski–Harabasz Index (CHI) measures how good the clustering is by the ratio of interclass scatter to intraclass scatter. A higher CHI represents better clustering, as it means that there is more variability between classes as well as more compactness within classes. <a href="#processes-12-02571-f006" class="html-fig">Figure 6</a> shows the CHI of different feature sets with the number of clusters ranging from 4 to 10. It can be seen that Feature Set-1 determined the right cluster number, which means Feature Set-1 is effective for fault diagnosis.</div><div class='html-p'>In order to further verify the validity of the model, we reran k-means with 8 different initial random seeds, SVM with 8 different ε-SVR values, and (DBSCAN) with 8 different bandwidths and summarized the results with the test results of K-means, and the average of accuracy and root-mean-square error (RMSE) for different datasets after clustering are shown in <a href="#processes-12-02571-f007" class="html-fig">Figure 7</a> and <a href="#processes-12-02571-t008" class="html-table">Table 8</a>. It can be seen that, for Feature Set-1, all three methods have high average accuracy and low RMSE for diagnosis results. Therefore, using FDM and MDFEM, we can select effective fault data and extract effective fault features, which have high-quality clustering performance for fault diagnosis.</div><dl class='html-order'><dt id=''>(2)</dt><dd><div class='html-p'>Comparative experiment II</div></dd></dl><div class='html-p'>In order to verify the validity of multi-source signals, this section uses a single signal to extract features for experiments. The mean, variance, and peak-to-peak value of current, load, rotational speed, and oil pressure are extracted, respectively, constituting Feature Set-3 to Feature Set-6 (<a href="#processes-12-02571-t009" class="html-table">Table 9</a>, <a href="#processes-12-02571-t010" class="html-table">Table 10</a>, <a href="#processes-12-02571-t011" class="html-table">Table 11</a> and <a href="#processes-12-02571-t012" class="html-table">Table 12</a>), and then the dimensions of the four feature sets are reduced to 2 dimensions using principal component analysis (PCA); then clustering analysis is carried out using the K-means algorithm, and the clustering results are shown in <a href="#processes-12-02571-f008" class="html-fig">Figure 8</a>.</div><div class='html-p'>Different colors correspond to different types of faults. It shows that the data can only be classified into 4 classes using current or rotational speed signals, respectively, and the intraclass spacing is large, the interclass spacing is small; using a load or oil pressure signal can only divide the data into 3 classes and 2 classes, respectively, and the clustering is not effective. Therefore, it can be concluded that the clustering effect of the features extracted by using a single signal is not effective, and there is a considerable gap with the clustering effect of the effective features extracted in this paper.</div><div class='html-p'><a href="#processes-12-02571-f009" class="html-fig">Figure 9</a> shows the CHI of different feature sets with the number of clusters ranging from 4 to 10. We already set the number of clusters to 10. It can be seen that none of these 4 datasets determined the right cluster number, which means using a single signal to extract fault features has low quality for diagnosis.</div><div class='html-p'>The averages of accuracy and RMSE for different datasets after clustering using different methods are shown in <a href="#processes-12-02571-f010" class="html-fig">Figure 10</a> and <a href="#processes-12-02571-t013" class="html-table">Table 13</a>. It can be seen that when we use a single signal to select an effective fault and extract fault features for diagnosis, we will get a low average of accuracy and a high RMSE, which means we will get a low quality of fault diagnosis.</div></section><section id='sec5-processes-12-02571' type='conclusions'><h2 data-nested='1'> 5. Conclusions</h2><div class='html-p'>This paper proposed a model-driven approach to extract multi-source fault features of a screw pump. Firstly, the screw pump fault mechanism model and the FDM were constructed; then the original multi-dimensional data were cleaned, normalized, sliced, and enhanced, and the FDM was used for data selection to establish an effective data set; then the multi-dimensional fault feature extraction model (MDFEM) was constructed to extract the 4-dimensional featured signal and the 3-dimensional data feature, and the 12-dimensional effective fault features were extracted; finally, experiments were carried out to verify the effectiveness and accuracy of the proposed method.</div><div class='html-p'>We draw the following conclusions: (1) By analyzing the different fault mechanisms of the screw pump, the FDM can be constructed to select the effective data and solve the problem of unclear fault labels and locations; (2) By using MDFEM, we can determine that the 4-dimensional featured signals of the original multi-source signals, such as current, load, rotational speed, and oil pressure, are fault-related, and the 3-dimensional statistic feature of the mean, variance, and peak-to-peak are fault-related; (3) The method proposed in this paper can be used to extract 12-dimensional effective fault features and can achieve a multi-source informational fault diagnosis of a screw pump. After experimental verification, the proposed method can comprehensively use the multi-source information collected at the project site and can accurately and efficiently identify the types of screw pump faults, which has high application value. Due to the limited fault sample data collected in this paper, the next step is to obtain more comprehensive fault sample data as much as possible to improve the accuracy of the method.</div></section> </div> <div class="html-back"> <section class='html-notes'><h2 >Author Contributions</h2><div class='html-p'>Conceptualization, W.W. and J.Q.; methodology, W.W. and J.Q.; software, J.Q.; validation, W.W. and J.Q.; formal analysis, W.W., J.Q., X.X. and M.Z.; investigation, W.W. and J.Q.; resources, W.W., X.X. and K.M.; data curation, J.Q.; writing original draft preparation, J.Q.; writing review and editing, W.W.; visualization, J.Q. and M.Z. All authors have read and agreed to the published version of the manuscript.</div></section><section class='html-notes'><h2>Funding</h2><div class='html-p'>This research received no external funding.</div></section><section class='html-notes'><h2 >Data Availability Statement</h2><div class='html-p'>The data and materials supporting the results are included within the article.</div></section><section id='html-ack' class='html-ack'><h2 >Acknowledgments</h2><div class='html-p'>We are very grateful to the reviewers and editors for their contributions to improving this manuscript.</div></section><section class='html-notes'><h2 >Conflicts of Interest</h2><div class='html-p'>Author Xiangru Xu and Kaifu Mi were employed by the company Beijing Petroleum Machinery Co., Ltd. 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data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g001-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f001"></a> </div> </div> <div class="html-fig_description"> <b>Figure 1.</b> Screw pump fault diagnosis framework. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f001"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f001"> <div class="html-caption"> <b>Figure 1.</b> Screw pump fault diagnosis framework.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g001.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g001.png" alt="Processes 12 02571 g001" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g001.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f002"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f002"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g002.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g002.png" alt="Processes 12 02571 g002" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g002-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f002"></a> </div> </div> <div class="html-fig_description"> <b>Figure 2.</b> Screw pump fault data model. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f002"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f002"> <div class="html-caption"> <b>Figure 2.</b> Screw pump fault data model.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g002.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g002.png" alt="Processes 12 02571 g002" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g002.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f003"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f003"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g003.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g003.png" alt="Processes 12 02571 g003" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g003-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f003"></a> </div> </div> <div class="html-fig_description"> <b>Figure 3.</b> Slide sampling method. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f003"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f003"> <div class="html-caption"> <b>Figure 3.</b> Slide sampling method.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g003.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g003.png" alt="Processes 12 02571 g003" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g003.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f004"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f004"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g004.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g004.png" alt="Processes 12 02571 g004" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g004-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f004"></a> </div> </div> <div class="html-fig_description"> <b>Figure 4.</b> Heat map of signal correlation coefficients. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f004"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f004"> <div class="html-caption"> <b>Figure 4.</b> Heat map of signal correlation coefficients.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g004.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g004.png" alt="Processes 12 02571 g004" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g004.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f005"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f005"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g005.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g005.png" alt="Processes 12 02571 g005" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g005-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f005"></a> </div> </div> <div class="html-fig_description"> <b>Figure 5.</b> Results of comparison of Experiment I. (<b>a</b>) Clustering results of Feature Set-1; (<b>b</b>) clustering results of Feature Set-2. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f005"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f005"> <div class="html-caption"> <b>Figure 5.</b> Results of comparison of Experiment I. (<b>a</b>) Clustering results of Feature Set-1; (<b>b</b>) clustering results of Feature Set-2.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g005.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g005.png" alt="Processes 12 02571 g005" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g005.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f006"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f006"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g006.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g006.png" alt="Processes 12 02571 g006" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g006-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f006"></a> </div> </div> <div class="html-fig_description"> <b>Figure 6.</b> CHI of different feature sets with the number of clusters. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f006"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f006"> <div class="html-caption"> <b>Figure 6.</b> CHI of different feature sets with the number of clusters.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g006.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g006.png" alt="Processes 12 02571 g006" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g006.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f007"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f007"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g007.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g007.png" alt="Processes 12 02571 g007" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g007-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f007"></a> </div> </div> <div class="html-fig_description"> <b>Figure 7.</b> Diagnosis results for different datasets after clustering: (<b>a</b>) average of accuracy; (<b>b</b>) RMSE. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f007"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f007"> <div class="html-caption"> <b>Figure 7.</b> Diagnosis results for different datasets after clustering: (<b>a</b>) average of accuracy; (<b>b</b>) RMSE.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g007.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g007.png" alt="Processes 12 02571 g007" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g007.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f008"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f008"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g008.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g008.png" alt="Processes 12 02571 g008" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g008-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f008"></a> </div> </div> <div class="html-fig_description"> <b>Figure 8.</b> Results of comparison of Experiment II. (<b>a</b>) Clustering results of Feature Set-3; (<b>b</b>) clustering results of Feature Set-4; (<b>c</b>) clustering results of Feature Set-5; (<b>d</b>) clustering results of Feature Set-6. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f008"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f008"> <div class="html-caption"> <b>Figure 8.</b> Results of comparison of Experiment II. (<b>a</b>) Clustering results of Feature Set-3; (<b>b</b>) clustering results of Feature Set-4; (<b>c</b>) clustering results of Feature Set-5; (<b>d</b>) clustering results of Feature Set-6.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g008.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g008.png" alt="Processes 12 02571 g008" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g008.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f009"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f009"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g009.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g009.png" alt="Processes 12 02571 g009" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g009-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f009"></a> </div> </div> <div class="html-fig_description"> <b>Figure 9.</b> CHI of different feature sets with the number of clusters. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f009"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f009"> <div class="html-caption"> <b>Figure 9.</b> CHI of different feature sets with the number of clusters.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g009.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g009.png" alt="Processes 12 02571 g009" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g009.png" /></div> </div> <div class="html-fig-wrap" id="processes-12-02571-f010"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f010"> <img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g010.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g010.png" alt="Processes 12 02571 g010" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g010-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#fig_body_display_processes-12-02571-f010"></a> </div> </div> <div class="html-fig_description"> <b>Figure 10.</b> Diagnosis results for different datasets after clustering: (<b>a</b>) average of accuracy; (<b>b</b>) RMSE. <!-- <p><a class="html-figpopup" href="#fig_body_display_processes-12-02571-f010"> Click here to enlarge figure </a></p> --> </div> </div> <div class="html-fig_show mfp-hide" id="fig_body_display_processes-12-02571-f010"> <div class="html-caption"> <b>Figure 10.</b> Diagnosis results for different datasets after clustering: (<b>a</b>) average of accuracy; (<b>b</b>) RMSE.</div> <div class="html-img"><img data-large="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g010.png" data-original="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g010.png" alt="Processes 12 02571 g010" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-g010.png" /></div> </div> <div class="html-table-wrap" id="processes-12-02571-t001"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t001'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t001"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 1.</b> Some fault data. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t001"> <div class="html-caption"><b>Table 1.</b> Some fault data.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' > </th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Waxing of Oil Pipe</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Stator Degumming</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Pump Leakage</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Current-time diagram</td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i001'><img alt="Processes 12 02571 i001" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i001.png" /></span></td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i002'><img alt="Processes 12 02571 i002" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i002.png" /></span></td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i003'><img alt="Processes 12 02571 i003" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i003.png" /></span></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Load-time diagram</td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i004'><img alt="Processes 12 02571 i004" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i004.png" /></span></td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i005'><img alt="Processes 12 02571 i005" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i005.png" /></span></td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i006'><img alt="Processes 12 02571 i006" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i006.png" /></span></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Rotate speed-time diagram</td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i007'><img alt="Processes 12 02571 i007" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i007.png" /></span></td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i008'><img alt="Processes 12 02571 i008" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i008.png" /></span></td><td align='center' valign='middle' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i009'><img alt="Processes 12 02571 i009" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i009.png" /></span></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Oil pressure-time diagram</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i010'><img alt="Processes 12 02571 i010" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i010.png" /></span></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i011'><img alt="Processes 12 02571 i011" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i011.png" /></span></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><span class='html-fig-inline' id='processes-12-02571-i012'><img alt="Processes 12 02571 i012" data-lsrc="/processes/processes-12-02571/article_deploy/html/images/processes-12-02571-i012.png" /></span></td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t002"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t002'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t002"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 2.</b> Correlation table. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t002"> <div class="html-caption"><b>Table 2.</b> Correlation table.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Relevance</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Negative Value</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Positive Value</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Irrelevant</td><td align='center' valign='middle' class='html-align-center' >−0.09~0.00</td><td align='center' valign='middle' class='html-align-center' >0.00~0.09</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Low relevance</td><td align='center' valign='middle' class='html-align-center' >−0.50~0.10</td><td align='center' valign='middle' class='html-align-center' >0.10~0.50</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >High relevance</td><td align='center' valign='middle' class='html-align-center' >−0.80~−0.50</td><td align='center' valign='middle' class='html-align-center' >0.50~0.80</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Significant relevance</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−0.90~−10</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.9~1</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t003"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t003'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t003"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 3.</b> Characteristics of statistics. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t003"> <div class="html-caption"><b>Table 3.</b> Characteristics of statistics.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Feature Name</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Formula</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Mean</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mover> <mi mathvariant="normal">x</mi> <mo>−</mo> </mover> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mrow> <msub> <mi>N</mi> <mi>s</mi> </msub> </mrow> </mfrac> </mstyle> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <msub> <mi>N</mi> <mi>s</mi> </msub> </mrow> </msubsup> <mi>x</mi> <mfenced> <mi>i</mi> </mfenced> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Variance</td><td align='center' valign='middle' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mrow> <msub> <mi>N</mi> <mi>s</mi> </msub> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mstyle> <msubsup> <mstyle mathsize="140%" displaystyle="true"> <mo>∑</mo> </mstyle> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <msub> <mi>N</mi> <mi>s</mi> </msub> </mrow> </msubsup> <msup> <mrow> <mfenced> <mrow> <mi>x</mi> <mfenced> <mi>i</mi> </mfenced> <mo>−</mo> <mover> <mi mathvariant="normal">x</mi> <mo>−</mo> </mover> </mrow> </mfenced> </mrow> <mn>2</mn> </msup> </mrow> </semantics> </math></td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Peak-to-peak value</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><math display='inline'> <semantics> <mrow> <mi>max</mi> <mfenced> <mrow> <mi>x</mi> <mfenced> <mi>i</mi> </mfenced> </mrow> </mfenced> <mo>−</mo> <mi>min</mi> <mfenced> <mrow> <mi>x</mi> <mfenced> <mi>i</mi> </mfenced> </mrow> </mfenced> </mrow> </semantics> </math></td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t004"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t004'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t004"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 4.</b> Effective characteristics. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t004"> <div class="html-caption"><b>Table 4.</b> Effective characteristics.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Current</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Load</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Rotate Speed</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Oil Pressure</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' > </th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Mean</td><td align='center' valign='middle' class='html-align-center' >Cm</td><td align='center' valign='middle' class='html-align-center' >Lm</td><td align='center' valign='middle' class='html-align-center' >Sm</td><td align='center' valign='middle' class='html-align-center' >Pm</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Variance</td><td align='center' valign='middle' class='html-align-center' >Cv</td><td align='center' valign='middle' class='html-align-center' >Lv</td><td align='center' valign='middle' class='html-align-center' >Sv</td><td align='center' valign='middle' class='html-align-center' >Pv</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Peak-to-peak value</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Cp</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Lp</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Sp</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Pp</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t005"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t005'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t005"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 5.</b> Common types of faults. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t005"> <div class="html-caption"><b>Table 5.</b> Common types of faults.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Fault Number</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Type of Fault</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Reason</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >0</td><td align='center' valign='middle' class='html-align-center' >Oil rod break-off</td><td align='center' valign='middle' class='html-align-center' >Excessive torque/tension</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >1</td><td align='center' valign='middle' class='html-align-center' >Oil pipe leakage</td><td align='center' valign='middle' class='html-align-center' >Oil pipe corrosion</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >2</td><td align='center' valign='middle' class='html-align-center' >Oil pipe break-off</td><td align='center' valign='middle' class='html-align-center' >Anti-rotation anchor damage</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >3</td><td align='center' valign='middle' class='html-align-center' >Waxing of oil pipe</td><td align='center' valign='middle' class='html-align-center' >High wax content in oil wells</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >4</td><td align='center' valign='middle' class='html-align-center' >Stator swelling</td><td align='center' valign='middle' class='html-align-center' >Liquid-absorbing, expanding</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >5</td><td align='center' valign='middle' class='html-align-center' >Stator Degumming</td><td align='center' valign='middle' class='html-align-center' >Low bonding strength</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >6</td><td align='center' valign='middle' class='html-align-center' >Pump leakage</td><td align='center' valign='middle' class='html-align-center' >Stator wear and aging</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >7</td><td align='center' valign='middle' class='html-align-center' >Pump jamming</td><td align='center' valign='middle' class='html-align-center' >Excessive surplus</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >8</td><td align='center' valign='middle' class='html-align-center' >High parameters</td><td align='center' valign='middle' class='html-align-center' >Displacement is greater than the fluid supply capacity</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Low parameters</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Insufficient liquid supply capacity</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t006"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t006'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t006"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 6.</b> Feature Set-1. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t006"> <div class="html-caption"><b>Table 6.</b> Feature Set-1.</div> <table > <thead ><tr ><th rowspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Value Features</th><th colspan='4' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Signal Features</th></tr><tr ><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Current</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Load</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rotate Speed</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Oil Pressure</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Mean</td><td align='center' valign='middle' class='html-align-center' >Cm</td><td align='center' valign='middle' class='html-align-center' >Lm</td><td align='center' valign='middle' class='html-align-center' >Sm</td><td align='center' valign='middle' class='html-align-center' >Pm</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Variance</td><td align='center' valign='middle' class='html-align-center' >Cv</td><td align='center' valign='middle' class='html-align-center' >Lv</td><td align='center' valign='middle' class='html-align-center' >Sv</td><td align='center' valign='middle' class='html-align-center' >Pv</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Peak-to-peak value</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Cp</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Lp</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Sp</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Pp</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t007"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t007'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t007"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 7.</b> Feature Set-2. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t007"> <div class="html-caption"><b>Table 7.</b> Feature Set-2.</div> <table > <thead ><tr ><th rowspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Value Features</th><th colspan='4' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Signal Features</th></tr><tr ><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Current</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Load</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Rotate Speed</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Oil Pressure</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Kurtosis</td><td align='center' valign='middle' class='html-align-center' >Ck</td><td align='center' valign='middle' class='html-align-center' >Lk</td><td align='center' valign='middle' class='html-align-center' >Sk</td><td align='center' valign='middle' class='html-align-center' >Pk</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Impulse</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Ci</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Li</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Si</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Pi</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t008"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t008'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t008"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 8.</b> The average of accuracy and RMSE for different datasets. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t008"> <div class="html-caption"><b>Table 8.</b> The average of accuracy and RMSE for different datasets.</div> <table > <thead ><tr ><th rowspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Datasets</th><th colspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >K-Means</th><th colspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SVM</th><th colspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DBSCAN</th></tr><tr ><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average of Accuracy (%)</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >RMSE</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average of Accuracy (%)</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >RMSE</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average of Accuracy (%)</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >RMSE</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Feature Set-1</td><td align='center' valign='middle' class='html-align-center' >95.3</td><td align='center' valign='middle' class='html-align-center' >0.002</td><td align='center' valign='middle' class='html-align-center' >91.2</td><td align='center' valign='middle' class='html-align-center' >0.012</td><td align='center' valign='middle' class='html-align-center' >92.6</td><td align='center' valign='middle' class='html-align-center' >0.005</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Feature Set-2</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >75.7</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.091</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >64.5</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.156</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >71.9</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.076</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t009"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t009'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t009"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 9.</b> Feature Set-3. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t009"> <div class="html-caption"><b>Table 9.</b> Feature Set-3.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Value Features</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Current</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Mean</td><td align='center' valign='middle' class='html-align-center' >Cm</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Variance</td><td align='center' valign='middle' class='html-align-center' >Cv</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Peak-to-peak value</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Cp</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t010"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t010'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t010"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 10.</b> Feature Set-4. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t010"> <div class="html-caption"><b>Table 10.</b> Feature Set-4.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Value Features</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Load</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Mean</td><td align='center' valign='middle' class='html-align-center' >Lm</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Variance</td><td align='center' valign='middle' class='html-align-center' >Lv</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Peak-to-peak value</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Lp</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t011"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t011'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t011"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 11.</b> Feature Set-5. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t011"> <div class="html-caption"><b>Table 11.</b> Feature Set-5.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Value Features</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Rotate Speed</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Mean</td><td align='center' valign='middle' class='html-align-center' >Sm</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Variance</td><td align='center' valign='middle' class='html-align-center' >Sv</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Peak-to-peak value</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Sp</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t012"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t012'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t012"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 12.</b> Feature Set-6. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t012"> <div class="html-caption"><b>Table 12.</b> Feature Set-6.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Value Features</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Oil Pressure</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Mean</td><td align='center' valign='middle' class='html-align-center' >Pm</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Variance</td><td align='center' valign='middle' class='html-align-center' >Pv</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Peak-to-peak value</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Pp</td></tr></tbody> </table> </div> <div class="html-table-wrap" id="processes-12-02571-t013"> <div class="html-table_wrap_td"> <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href='#table_body_display_processes-12-02571-t013'> <img data-lsrc="https://pub.mdpi-res.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2227-9717/12/11/2571/display" href="#table_body_display_processes-12-02571-t013"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 13.</b> The average of accuracy and RMSE for different datasets. </div> </div> <div class="html-table_show mfp-hide " id="table_body_display_processes-12-02571-t013"> <div class="html-caption"><b>Table 13.</b> The average of accuracy and RMSE for different datasets.</div> <table > <thead ><tr ><th rowspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Datasets</th><th colspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >K-Means</th><th colspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >SVM</th><th colspan='2' align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >DBSCAN</th></tr><tr ><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average of Accuracy (%)</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >RMSE</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average of Accuracy (%)</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >RMSE</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average of Accuracy (%)</th><th align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >RMSE</th></tr></thead><tbody ><tr ><td align='center' valign='middle' class='html-align-center' >Feature Set-3</td><td align='center' valign='middle' class='html-align-center' >74.3</td><td align='center' valign='middle' class='html-align-center' >0.123</td><td align='center' valign='middle' class='html-align-center' >68.3</td><td align='center' valign='middle' class='html-align-center' >0.097</td><td align='center' valign='middle' class='html-align-center' >72.6</td><td align='center' valign='middle' class='html-align-center' >0.135</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Feature Set-4</td><td align='center' valign='middle' class='html-align-center' >71.8</td><td align='center' valign='middle' class='html-align-center' >0.098</td><td align='center' valign='middle' class='html-align-center' >64.5</td><td align='center' valign='middle' class='html-align-center' >0.165</td><td align='center' valign='middle' class='html-align-center' >71.9</td><td align='center' valign='middle' class='html-align-center' >0.145</td></tr><tr ><td align='center' valign='middle' class='html-align-center' >Feature Set-5</td><td align='center' valign='middle' class='html-align-center' >69.5</td><td align='center' valign='middle' class='html-align-center' >0.134</td><td align='center' valign='middle' class='html-align-center' >70.2</td><td align='center' valign='middle' class='html-align-center' >0.126</td><td align='center' valign='middle' class='html-align-center' >68.5</td><td align='center' valign='middle' class='html-align-center' >0.140</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Feature Set-6</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >75.6</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.153</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >71.8</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.103</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >64.3</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.147</td></tr></tbody> </table> </div> </section><section class='html-fn_group'><table><tr id=''><td></td><td><div class='html-p'><b>Disclaimer/Publisher’s Note:</b> The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). 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A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump. <em>Processes</em> <b>2024</b>, <em>12</em>, 2571. https://doi.org/10.3390/pr12112571 </p> <div style="display: block"> <b>AMA Style</b><br> <p> Wen W, Qin J, Xu X, Mi K, Zhou M. A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump. <em>Processes</em>. 2024; 12(11):2571. https://doi.org/10.3390/pr12112571 </p> <b>Chicago/Turabian Style</b><br> <p> Wen, Weigang, Jingqi Qin, Xiangru Xu, Kaifu Mi, and Meng Zhou. 2024. "A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump" <em>Processes</em> 12, no. 11: 2571. https://doi.org/10.3390/pr12112571 </p> <b>APA Style</b><br> <p> Wen, W., Qin, J., Xu, X., Mi, K., & Zhou, M. (2024). A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump. <em>Processes</em>, <em>12</em>(11), 2571. https://doi.org/10.3390/pr12112571 </p> </div> </div> <div class="info-box no-margin"> Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. 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A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump. <em>Processes</em> <b>2024</b>, <em>12</em>, 2571. https://doi.org/10.3390/pr12112571 </p> <div style="display: block"> <b>AMA Style</b><br> <p> Wen W, Qin J, Xu X, Mi K, Zhou M. A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump. <em>Processes</em>. 2024; 12(11):2571. https://doi.org/10.3390/pr12112571 </p> <b>Chicago/Turabian Style</b><br> <p> Wen, Weigang, Jingqi Qin, Xiangru Xu, Kaifu Mi, and Meng Zhou. 2024. "A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump" <em>Processes</em> 12, no. 11: 2571. https://doi.org/10.3390/pr12112571 </p> <b>APA Style</b><br> <p> Wen, W., Qin, J., Xu, X., Mi, K., & Zhou, M. (2024). A Model-Driven Approach to Extract Multi-Source Fault Features of a Screw Pump. <em>Processes</em>, <em>12</em>(11), 2571. https://doi.org/10.3390/pr12112571 </p> </div> </div> <div class="info-box no-margin"> Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. 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