{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T15:04:14Z","timestamp":1789398254198,"version":"build-2803163510"},"reference-count":35,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T00:00:00Z","timestamp":1789344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the 2025 Guangdong Provincial Key Discipline Research Enhancement Project","award":["2025ZDJS129"],"award-info":[{"award-number":["2025ZDJS129"]}]},{"name":"the 2025 Guangdong Provincial Education Science Planning Project","award":["2025GXJK0504"],"award-info":[{"award-number":["2025GXJK0504"]}]},{"name":"the Guangzhou Education Bureau Graduate Student Scientific Research Project","award":["2024312026"],"award-info":[{"award-number":["2024312026"]}]},{"award":["2024312026"],"award-info":[{"award-number":["2024312026"]}],"id":[{"id":"https:\/\/ror.org\/00479t136","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As core weighing equipment in the logistics and industrial sectors, the accuracy of truck scales is significantly affected by environmental noise, sensor errors, and nonlinear factors. This paper proposes an adaptive smoothing-constrained broad learning system (PSO-MCC-SCBLS) to enhance the precision and robustness of truck-scale weighing. Particle swarm optimization (PSO) is employed to optimize the number of feature windows, feature nodes, enhancement nodes, and the smoothing coefficient of the SCBLS; the maximum correntropy criterion (MCC) replaces the minimum mean square error (MMSE) criterion for training the output-weight matrix; and a smoothing constraint derived from the physical continuity of the weighing system is introduced to improve generalization in small-sample scenarios. The method was validated on real data from an 8-channel, 40-ton truck scale under a corrected evaluation protocol that uses group-wise five-fold cross-validation, selects all hyperparameters by an inner cross-validation on the training folds only, and matches the effective regularization strength across MCC and non-MCC variants. A complete component ablation over the seven BLS-family variants (BLS, MCC-BLS, SCBLS, PSO-BLS, PSO-SCBLS, PSO-MCC-BLS and the full model) is reported alongside RBLS, CatBoost, CNN_Attention and LSTM, together with anti-interference tests under a composite Gaussian-plus-impulsive disturbance injected in three scenarios: disturbed calibration only (A), disturbed calibration and deployment (B), and disturbed deployment only (C). The results delimit the contribution of each component. Automated structural search is the one component whose benefit is large and consistent, reducing clean-data RMSE by 47.7% over a plain BLS. On clean data the full model does not lead: PSO-MCC-BLS attains the lowest RMSE (0.0209\u00d7103 kg) while the full model records 0.0292\u00d7103 kg, indicating that under a leakage-free protocol this calibration task is already close to a low-complexity regime. The advantage of the full model is specific and is reported as such: in Scenario B at a noise ratio of 0.5 it achieves the lowest RMSE (1.7670\u00d7103 kg) and the best Friedman rank among all eleven models (p&lt;0.05), whereas at the weaker intensity and in Scenario C the deep-learning baselines lead. Once the effective regularization is matched, the MCC term contributes negligibly on this dataset, so the observed robustness is attributable to the tuned BLS-family model as a whole rather than to correntropy weighting in isolation.<\/jats:p>","DOI":"10.3390\/s26185827","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T14:15:04Z","timestamp":1789395304000},"page":"5827","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Adaptive Smoothing-Constrained Broad Learning System for Truck-Scale Weighing"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9163-2542","authenticated-orcid":false,"given":"Jing","family":"Ling","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Guangzhou Maritime University, Guangzhou 510725, China"},{"name":"School of Electronic and Electrical Engineering, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"given":"Jinru","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronic and Electrical Engineering, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"}]},{"given":"Zhimin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic and Electrical Engineering, Ningxia University, Yinchuan 750021, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"software","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"}]},{"given":"Haijun","family":"Lin","sequence":"additional","affiliation":[{"name":"College of Engineering and Design, Hunan Normal University, Changsha 410081, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"supervision","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"}]},{"given":"Dan","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Guangzhou Maritime University, Guangzhou 510725, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"16997","DOI":"10.1109\/JSEN.2021.3080120","article-title":"A method for nonlinear error compensation of load cell based on neural network with second derivative constraints","volume":"21","author":"Lin","year":"2021","journal-title":"IEEE Sens. 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