{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T20:29:13Z","timestamp":1773692953196,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:00:00Z","timestamp":1760140800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology Project of the Jiangxi Provincial Department of Transportation, China","award":["2023C0017"],"award-info":[{"award-number":["2023C0017"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Skid resistance is a key factor in road safety, directly affecting vehicle stability and braking efficiency. To enhance predictive accuracy, this study develops a multilayer perceptron (MLP) model for forecasting the Sideway Force Coefficient (SFC) of asphalt pavements and systematically examines the role of activation functions and optimizers. Seven activation functions (Sigmoid, Tanh, ReLU, Leaky ReLU, ELU, Mish, Swish) and three optimizers (SGD, RMSprop, Adam) are evaluated using regression metrics (MSE, RMSE, MAE, R2) and loss-curve analysis. Results show that ReLU and Mish provide notable improvements over Sigmoid, with ReLU increasing goodness of fit and accuracy by 13\u201315%, and Mish further enhancing nonlinear modeling by 12\u201314%. For optimizers, Adam achieves approximately 18% better performance than SGD, offering faster convergence, higher accuracy, and stronger stability, while RMSprop shows moderate performance. The findings suggest that combining ReLU or Mish with Adam yields highly precise and robust predictions under multi-source heterogeneous inputs. This study offers a reliable methodological reference for intelligent pavement condition monitoring and supports safety management in highway transportation systems.<\/jats:p>","DOI":"10.3390\/sym17101708","type":"journal-article","created":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:13:27Z","timestamp":1760361207000},"page":"1708","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Prediction of Skid Resistance of Asphalt Pavements on Highways Based on Machine Learning: The Impact of Activation Functions and Optimizer Selection"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiaoyun","family":"Wan","sequence":"first","affiliation":[{"name":"Jiangxi Ganyue Expressway Co., Ltd., Nanchang 330025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqing","family":"Yu","sequence":"additional","affiliation":[{"name":"Jiangxi Ganyue Expressway Co., Ltd., Nanchang 330025, China"},{"name":"Jiangxi Provincial Key Laboratory of Pavement Performance Evolution and Life Extension of Highway Subgrade, Nanchang 330038, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maomao","family":"Chen","sequence":"additional","affiliation":[{"name":"Jiangxi Ganyue Expressway Co., Ltd., Nanchang 330025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haixin","family":"Ye","sequence":"additional","affiliation":[{"name":"Jiangxi Ganyue Expressway Co., Ltd., Nanchang 330025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhanghong","family":"Liu","sequence":"additional","affiliation":[{"name":"Jiangxi Ganyue Expressway Co., Ltd., Nanchang 330025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1327-7338","authenticated-orcid":false,"given":"Qifeng","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Transport & Communications, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1080\/14680629.2016.1261723","article-title":"Pavement skid resistance consideration in rain-related wet-weather speed limits determination","volume":"19","author":"Chu","year":"2016","journal-title":"Road Mater. Pavement Des."},{"key":"ref_2","first-page":"38","article-title":"Measurement of anti-slide performance of tunnel road surface and its effect on driving safety","volume":"25","author":"Yang","year":"2006","journal-title":"J. Chongqing Jiaotong Univ. (Nat. Sci.)"},{"key":"ref_3","unstructured":"Huang, X.M., and Ma, T. (2024). Skid Resistance Analysis Based on Tire-Asphalt Pavement Coupling: Theory and Practice, China Communications Press. (In Chinese)."},{"key":"ref_4","first-page":"32","article-title":"Research status and progress for skid resistance performance of asphalt pavements","volume":"32","author":"Huang","year":"2019","journal-title":"China J. Highw. Transp."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.jreng.2021.12.001","article-title":"Determination and prediction of pavement skid resistance\u2014Connecting research and practice","volume":"1","author":"Fwa","year":"2021","journal-title":"J. Road Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1080\/10298436.2017.1309191","article-title":"A laboratory procedure for predicting skid and polishing resistance of road surfaces","volume":"20","author":"Hofko","year":"2017","journal-title":"Int. J. Pavement Eng."},{"key":"ref_7","first-page":"32","article-title":"Review on detection and prediction methods for pavement skid resistance","volume":"21","author":"Tan","year":"2021","journal-title":"J. Traffic Transp. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wu, J., Wang, X., Wang, L., Zhang, L., Xiao, Q., and Yang, H. (2020). Temperature correction and analysis of pavement skid resistance performance based on RIOHTrack full-scale track. Coatings, 10.","DOI":"10.3390\/coatings10090832"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1080\/14680629.2018.1552619","article-title":"Testing for low-speed skid resistance of road pavements","volume":"21","author":"Han","year":"2018","journal-title":"Road Mater. Pavement Des."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"124411","DOI":"10.1016\/j.conbuildmat.2021.124411","article-title":"Study on the skid resistance of asphalt pavement: A state-of-the-art review and future prospective","volume":"303","author":"Guo","year":"2021","journal-title":"Constr. Build. Mater."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"124729","DOI":"10.1016\/j.conbuildmat.2021.124729","article-title":"Promoting the pavement skid resistance estimation by extracting tire-contacted texture based on 3D surface data","volume":"307","author":"Du","year":"2021","journal-title":"Constr. Build. Mater."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF02823926","article-title":"Development of performance prediction models in flexible pavement using regression analysis method","volume":"10","author":"Kim","year":"2006","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_13","first-page":"944","article-title":"A review of asphalt pavement long-term skid resistance performance based on multi-scale texture evolution characterization","volume":"13","author":"He","year":"2025","journal-title":"Friction"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Kon\u00e9, A., Es-Sabar, A., and Do, M.T. (2023). Application of machine learning models to the analysis of skid resistance data. Lubricants, 11.","DOI":"10.3390\/lubricants11080328"},{"key":"ref_15","first-page":"1234","article-title":"Establishment of probabilistic prediction models for pavement deterioration based on Bayesian neural network","volume":"23","author":"Xiao","year":"2022","journal-title":"Int. J. Pavement Eng."},{"key":"ref_16","first-page":"110217","article-title":"Prediction model for bearing surface friction coefficient in bolted joints based on GA-BP neural network and experimental data","volume":"196","author":"Chen","year":"2024","journal-title":"Tribol. Int."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1177\/0361198118822501","article-title":"Establishment of prediction models of asphalt pavement performance based on a novel data calibration method and neural network","volume":"2673","author":"Yao","year":"2019","journal-title":"Transp. Res. Rec."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2054","DOI":"10.1111\/mice.13063","article-title":"Effective contact texture region aware pavement skid resistance prediction via convolutional neural network","volume":"39","author":"Shi","year":"2024","journal-title":"Comput.-Aided Civ. Infrastruct. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"122786","DOI":"10.1016\/j.eswa.2023.122786","article-title":"Evaluate asphalt pavement frictional characteristics based on IGWO-NGBoost using 3D macro-texture data","volume":"242","author":"Hu","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/j.eij.2022.03.003","article-title":"Smart cities: Fusion-based intelligent traffic congestion control system for vehicular networks using machine learning techniques","volume":"23","author":"Saleem","year":"2022","journal-title":"Egypt. Inform. J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"110638","DOI":"10.1016\/j.measurement.2021.110638","article-title":"Integrated FFT and XGBoost framework to predict pavement skid resistance using automatic 3D texture measurement","volume":"188","author":"You","year":"2022","journal-title":"Measurement"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1080\/10298436.2019.1609673","article-title":"Machine learning approach for pavement performance prediction","volume":"22","author":"Marcelino","year":"2021","journal-title":"Int. J. Pavement Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1061\/JHTRCQ.0000794","article-title":"Pavement surface condition index prediction based on random forest algorithm","volume":"15","author":"Yu","year":"2021","journal-title":"J. Highw. Transp. Res. Dev. (Engl. Ed.)"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"135","DOI":"10.3141\/2589-15","article-title":"Prediction of pavement performance: Application of support vector regression with different kernels","volume":"2589","author":"Ziari","year":"2016","journal-title":"Transp. Res. Rec."},{"key":"ref_25","first-page":"7534970","article-title":"A hybrid model for prediction in asphalt pavement performance based on support vector machine and grey relation analysis","volume":"2020","author":"Wang","year":"2020","journal-title":"J. Adv. Transp."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"04018052","DOI":"10.1061\/(ASCE)CP.1943-5487.0000797","article-title":"Convolutional neural network\u2013based friction model using pavement texture data","volume":"32","author":"Yang","year":"2018","journal-title":"J. Comput. Civ. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1080\/15472450.2020.1780922","article-title":"Road surface friction prediction using long short-term memory neural network based on historical data","volume":"26","author":"Pu","year":"2021","journal-title":"J. Intell. Transp. Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2277815","DOI":"10.1080\/10298436.2023.2277815","article-title":"Prediction of the skid-resistance deterioration in asphalt pavement based on peephole\u2013LSTM neural network","volume":"24","author":"Zhan","year":"2023","journal-title":"Int. J. Pavement Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"04021058","DOI":"10.1061\/JPEODX.0000312","article-title":"Machine learning approach to predict international roughness index using long-term pavement performance data","volume":"147","author":"Damirchilo","year":"2021","journal-title":"J. Transp. Eng. Part B Pavements"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1080\/14680629.2024.2373222","article-title":"Artificial intelligence techniques for pavement performance prediction: A systematic review","volume":"26","author":"Kang","year":"2025","journal-title":"Road Mater. Pavement Des."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1177\/03611981221100521","article-title":"Recurrent neural networks for pavement performance forecasting: Review and model performance comparison","volume":"2677","author":"Mers","year":"2023","journal-title":"Transp. Res. Rec."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.neunet.2018.12.010","article-title":"An extensive experimental survey of regression methods","volume":"111","author":"Sirsat","year":"2019","journal-title":"Neural Netw."},{"key":"ref_33","unstructured":"Motamed, M. (2022). Approximation power of deep neural networks: An explanatory mathematical survey. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","article-title":"Multilayer feedforward networks are universal approximators","volume":"2","author":"Hornik","year":"1989","journal-title":"Neural Netw."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1037\/h0042519","article-title":"The perceptron: A probabilistic model for information storage and organization in the brain","volume":"65","author":"Rosenblatt","year":"1958","journal-title":"Psychol. Rev."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_37","first-page":"9","article-title":"Efficient backprop","volume":"Volume 1524","author":"Orr","year":"1998","journal-title":"Neural Networks: Tricks of the Trade"},{"key":"ref_38","unstructured":"Glorot, X., Bordes, A., and Bengio, Y. (2011, January 11\u201313). Deep sparse rectifier neural networks. Proceedings of the 14th International Conference on Artificial Intelligence and Statistics (AISTATS), Fort Lauderdale, FL, USA."},{"key":"ref_39","unstructured":"Haykin, S. (1999). Neural Networks: A Comprehensive Foundation, Prentice Hall. [2nd ed.]."},{"key":"ref_40","unstructured":"Maas, A.L., Hannun, A.Y., and Ng, A.Y. (2013, January 16\u201321). Rectifier nonlinearities improve neural network acoustic models. Proceedings of the 30th International Conference on Machine Learning (ICML), Atlanta, GA, USA."},{"key":"ref_41","unstructured":"Clevert, D.-A., Unterthiner, T., and Hochreiter, S. (2016, January 2\u20134). Fast and accurate deep network learning by exponential linear units (ELUs). Proceedings of the 4th International Conference on Learning Representations (ICLR), San Juan, PR, USA."},{"key":"ref_42","unstructured":"Ramachandran, P., Zoph, B., and Le, Q.V. (May, January 30). Searching for activation functions. Proceedings of the 6th International Conference on Learning Representations (ICLR), Vancouver, BC, Canada."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Misra, D. (2019). Mish: A self-regularized non-monotonic activation function. arXiv.","DOI":"10.5244\/C.34.191"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1214\/aoms\/1177729586","article-title":"A stochastic approximation method","volume":"22","author":"Robbins","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_45","first-page":"26","article-title":"Lecture 6.5\u2014RMSProp: Divide the Gradient by a Running Average of Its Recent Magnitude","volume":"4","author":"Tieleman","year":"2012","journal-title":"Coursera Neural Netw. Mach. Learn."},{"key":"ref_46","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_47","unstructured":"(2019). Specifications for Field Test Methods of Highway Subgrade and Pavement (Standard No. JTG 3450-2019). (In Chinese)."},{"key":"ref_48","unstructured":"(2017). Standards for Quality Inspection and Evaluation of Highway Engineering, Part I: Civil Engineering (Standard No. JTG F80\/1-2017). (In Chinese)."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1708\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:05:50Z","timestamp":1760364350000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/10\/1708"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,11]]},"references-count":48,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["sym17101708"],"URL":"https:\/\/doi.org\/10.3390\/sym17101708","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,11]]}}}