{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:21:24Z","timestamp":1760242884188,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2016,10,11]],"date-time":"2016-10-11T00:00:00Z","timestamp":1476144000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A new fusion sensing (FS) method was proposed by using the improved fractal box dimension (IFBD) and a developed maximum wavelet coefficient (DMWC) for fault sensing of an online power cable. There are four strategies that were used. Firstly, the traditional fractal box dimension was improved to enlarge the feature distances between the different fault classes. Secondly, the IFBD recognition algorithm was proposed by using the improved fractal dimension feature extracted from the three-phase currents for the first stage of fault recognition. Thirdly, the DMWC recognition algorithm was developed based on the K-transform and wavelet analysis to establish the relationship between the maximum wavelet coefficient and the fault class. Fourthly, the FS method was formed by combining the IFBD algorithm and the DMWC algorithm in order to recognize the 10 types of short circuit faults of online power. The designed test system proved that the FS method increased the fault recognition accuracy obviously. In addition, the parameters of the initial angle, transient resistance, and fault distance had no influence on the FS method.<\/jats:p>","DOI":"10.3390\/a9040066","type":"journal-article","created":{"date-parts":[[2016,10,11]],"date-time":"2016-10-11T11:27:28Z","timestamp":1476185248000},"page":"66","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fault Sensing Using Fractal Dimension and Wavelet"],"prefix":"10.3390","volume":"9","author":[{"given":"Mei","family":"Wang","sequence":"first","affiliation":[{"name":"School of Electrical and Control Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Electrical and Control Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanan","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Electrical and Control Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.ins.2014.02.039","article-title":"Power system fault diagnosis based on history driven differential evolution and stochastic time domain simulation","volume":"275","author":"Zhao","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.procs.2016.07.326","article-title":"Application of Wavelet Technique for Fault Classification in Transmission","volume":"92","author":"Prasad","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_3","first-page":"813","article-title":"Investigation on the surface morphology of Si3N4 ceramics by a new fractal dimension calculation method","volume":"387","author":"Jun","year":"2016","journal-title":"Appl. Surf. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.procs.2016.04.100","article-title":"Distributed Fault Detection in Smart Spaces Based on Trust Management","volume":"83","author":"Guclu","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_5","first-page":"1027","article-title":"A novel transmission line protection using DOST and SVM","volume":"19","author":"Bharata","year":"2016","journal-title":"Eng. Sci. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/TPWRS.2020.3007618","article-title":"Fault Detection and Faulty Phase Determination of Transmission Lines Based on Time-Frequency Characteristics of Transient Travelling Waves","volume":"36","author":"Lin","year":"2012","journal-title":"Power Syst. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"271","DOI":"10.3390\/a8020271","article-title":"Dynamics and Fractal Dimension of Steffensen-Type Methods","volume":"8","author":"Chicharro","year":"2015","journal-title":"Algorithms"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"G\u00f3mez, M.J., Castej\u00f3n, C., and Garc\u00eda-Prada, J.C. (2016). Review of Recent Advances in the Application of the Wavelet Transform to Diagnose Cracked Rotors. Algorithms, 9.","DOI":"10.3390\/a9010019"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"685","DOI":"10.3390\/a7040685","article-title":"Fusion of Multiple Pyroelectric Characteristics for Human Body Identification","volume":"7","author":"Zhou","year":"2014","journal-title":"Algorithms"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.ijengsci.2015.06.007","article-title":"A simulation method for permeability of porous media based on multiple fractal model","volume":"95","author":"Tan","year":"2015","journal-title":"Int. J. Eng. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.jaerosci.2015.05.011","article-title":"A bimodal moment method model for submicron fractal-like agglomerates undergoing Brownian coagulation","volume":"88","author":"Yu","year":"2015","journal-title":"J. Aerosol Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1109\/JSTARS.2013.2248134","article-title":"Angle Independence Properties of Fractal Dimension Maps Estimated From SAR Data","volume":"6","author":"Martino","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1049\/iet-spr.2011.0070","article-title":"Fractal dimension, wavelet shrinkage and anomaly detection for mine hunting","volume":"6","author":"Nelson","year":"2012","journal-title":"IET Signal Process."},{"key":"ref_14","first-page":"1459","article-title":"Face Recognition under Varying Illumination with Logarithmic Fractal Analysis","volume":"21","author":"Reza","year":"2014","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1109\/TIP.2015.2413298","article-title":"Fractal Analysis for Reduced Reference Image Quality Assessment","volume":"24","author":"Xu","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_16","first-page":"295","article-title":"The fractal dimension of software networks as a global quality metric","volume":"245","author":"Tumu","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S1674-5264(09)60060-0","article-title":"Application of fractal theory in detecting low current faults of power distribution system in coal mines","volume":"19","author":"Liu","year":"2009","journal-title":"Min Sci. Technol. (China)"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1049\/iet-gtd.2013.0200","article-title":"Design and implementation of a wavelet analysis-based shunt fault detection and identification module for transmission lines application","volume":"8","author":"Usama","year":"2014","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_19","first-page":"291","article-title":"Series Arc Fault Identification Method Based on Energy Produced by Wavelet Transformation and Neural Network","volume":"29","author":"Zhang","year":"2014","journal-title":"Trans. China Electrotech. Soc."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1049\/iet-gtd.2014.0788","article-title":"Transmission line fault detection and localisation methodology using PMU measurements","volume":"9","author":"Gopakumar","year":"2015","journal-title":"IET Gener. Transm. Distrib."},{"key":"ref_21","first-page":"110","article-title":"Transient Fault Locating Method Based on Line Voltage and Zero-mode Current in Non-solidly Earthed Network","volume":"32","author":"Zhang","year":"2012","journal-title":"Proc. CSEE"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.procs.2016.07.326","article-title":"Application of Wavelet Technique for Fault Classification in Transmission Systems","volume":"92","author":"Prasad","year":"2016","journal-title":"Procedia Comput. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.cnsns.2016.06.034","article-title":"A new fractional wavelet transform","volume":"44","author":"Dai","year":"2017","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4515","DOI":"10.1016\/j.ins.2010.08.006","article-title":"Complex system fault diagnosis based on a fuzzy robust wavelet support vector classifier and an adaptive Gaussian particle swarm optimization","volume":"180","author":"Wu","year":"2010","journal-title":"Inf. Sci."},{"key":"ref_25","first-page":"111","article-title":"Line and Segment Online Location of Single-phase-to-earth Fault in the Ungrounded Neutral System","volume":"37","author":"Zheng","year":"2013","journal-title":"Autom. Electr. Power Syst."},{"key":"ref_26","first-page":"1990","article-title":"A Hybrid Framework for Fault Detection, Classification, and Location\u2014Part I: Concept, Structure, and Methodology","volume":"26","author":"Jiang","year":"2011","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"25648","DOI":"10.3390\/s151025648","article-title":"Compressive Sensing of Roller Bearing Faults via Harmonic Detection from Under-Sampled Vibration Signals","volume":"15","author":"Tang","year":"2015","journal-title":"Sensors"},{"key":"ref_28","first-page":"10777","article-title":"Multiple Leader Candidate and Competitive Position Allocation for Robust Formation against Member Robot Faults","volume":"15","author":"Wook","year":"2015","journal-title":"Sensors"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1302","DOI":"10.1109\/JSTARS.2015.2507859","article-title":"A Remote Sensing Fusion Method Based on the Analysis Sparse Model","volume":"9","author":"Han","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.cageo.2015.09.022","article-title":"A remote sensing fusion method based on feedback sparse component analysis","volume":"85","author":"Xu","year":"2015","journal-title":"Comput. Geosci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.isprsjprs.2015.02.015","article-title":"Remote sensing image fusion via wavelet transform and sparse representation","volume":"104","author":"Cheng","year":"2015","journal-title":"ISPRS J. Photogramm. Remote Sens."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/9\/4\/66\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:32:42Z","timestamp":1760211162000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/9\/4\/66"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,11]]},"references-count":31,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,12]]}},"alternative-id":["a9040066"],"URL":"https:\/\/doi.org\/10.3390\/a9040066","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2016,10,11]]}}}