{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T09:14:06Z","timestamp":1781946846600,"version":"3.54.5"},"reference-count":20,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T00:00:00Z","timestamp":1747267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Accurate current sensing in rectangular conductors is challenged by mechanical deformations, including eccentricity (X\/Y-axis shifts) and inclination (Z-axis tilt), which distort magnetic field distributions and induce measurement errors. To address this, we propose a bio-inspired error compensation strategy integrating an elliptically configured Hall sensor array with a hybrid Grey Wolf Optimizer (GWO)-enhanced backpropagation neural network. The eccentric displacement and tilt angle of the conductor are quantified via a three-dimensional magnetic field reconstruction and current inversion modeling. A dual-stage optimization framework is implemented: first, establishing a BP neural network for real-time conductor state estimations, and second, leveraging the GWO\u2019s swarm intelligence to refine network weights and thresholds, thereby avoiding local optima and enhancing the robustness against asymmetric field patterns. The experimental validation under extreme mechanical deformations (X\/Y-eccentricity: \u00b18 mm; Z-tilt: \u00b115\u00b0) demonstrates the strategy\u2019s efficacy, achieving a 65.07%, 45.74%, and 76.15% error suppression for X-, Y-, and Z-axis deviations. The elliptical configuration reduces the installation footprint by 72.4% compared with conventional circular sensor arrays while maintaining a robust suppression of eccentricity- and tilt-induced errors, proving critical for space-constrained applications, such as electric vehicle powertrains and miniaturized industrial inverters. This work bridges bio-inspired algorithms and adaptive sensing hardware, offering a systematic solution to mechanical deformation-induced errors in high-density power systems.<\/jats:p>","DOI":"10.3390\/s25103116","type":"journal-article","created":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T04:39:16Z","timestamp":1747283956000},"page":"3116","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Robust Current Sensing in Rectangular Conductors: Elliptical Hall-Effect Sensor Array Optimized via Bio-Inspired GWO-BP Neural Network"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1685-1593","authenticated-orcid":false,"given":"Yue","family":"Tang","sequence":"first","affiliation":[{"name":"School of Internet of Things Engineering, Wuxi University, Wuxi 214105, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiajia","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Internet of Things Engineering, Wuxi University, Wuxi 214105, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1515\/teme-2019-0032","article-title":"Contactless measurement of electric current using magnetic sensors","volume":"86","author":"Ripka","year":"2019","journal-title":"TM-Tech. 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