{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:32:10Z","timestamp":1765960330763,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T00:00:00Z","timestamp":1717718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Planned project of Gansu science and Technology Department","award":["21JR7RA310","2021029"],"award-info":[{"award-number":["21JR7RA310","2021029"]}]},{"name":"Youth Science Fund Project of Lanzhou Jiaotong University","award":["21JR7RA310","2021029"],"award-info":[{"award-number":["21JR7RA310","2021029"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To accurately identify the deflection data collected by a traffic speed deflectometer (TSD) and eliminate the noise in the measured signals, a TSD signal denoising method based on the partial swarm optimization\u2013variational mode decomposition (PSO\u2013VMD) method is proposed. Initially, the VMD algorithm is used for modal decomposition, calculating the correlation coefficients between each decomposed mode and the original signal for modal selection and signal reconstruction; Then, the particle swarm optimization algorithm is utilized to optimize the number of modes K and the value \u03b1 for the VMD algorithm, adopting fuzzy entropy as the affinity function to circumvent effects from sequence decomposition and forecasting accuracy, thus identifying the optimal combination of hyperparameters. Finally, the analysis on simulated signals indicates that the PSO\u2013VMD method secures the best parameters, showing a clear advantage in denoising. Denoising real TSD data validates that the approach proposed herein achieves commendable outcomes in TSD deflection noise reduction, offering a feasible strategy for TSD signal denoising.<\/jats:p>","DOI":"10.3390\/s24123708","type":"journal-article","created":{"date-parts":[[2024,6,7]],"date-time":"2024-06-07T08:05:17Z","timestamp":1717747517000},"page":"3708","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Signal Denoising of Traffic Speed Deflectometer Measurement Based on Partial Swarm Optimization\u2013Variational Mode Decomposition Method"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0201-0611","authenticated-orcid":false,"given":"Chaoyang","family":"Wu","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}]},{"given":"Yiyuan","family":"Duan","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8666-6900","authenticated-orcid":false,"given":"Hao","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"48","DOI":"10.3141\/1806-06","article-title":"New Relationships Between Falling Weight Deflectometer Deflections and Asphalt Pavement Layer Condition Indicators","volume":"1806","author":"Xu","year":"2002","journal-title":"Transp. 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