{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T05:17:00Z","timestamp":1771305420045,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T00:00:00Z","timestamp":1765152000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Road and Bridge Research Institute in Warsaw","award":["PWS 1032"],"award-info":[{"award-number":["PWS 1032"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>The FWD is commonly used to conduct a non-destructive evaluation of the capacity of the pavement. The layered pavement is loaded locally by falling weight, and deflection is recorded at many points. Based on these results, if the pavement geometry is known, the mechanical properties of the pavement may be determined using the back-calculation approach. Analytical, numerical, or ML methods can be used for back-calculation. An analytical solution for a multi-layered structure leads to non-linear relationships for the thickness or stiffness of each layer, but provides an accurate solution. The other methods, like numerical or ML methods, are just approximation methods with different levels of accuracy. In this paper, the accuracy of the XGBoost ML regression model in predicting mechanical and geometrical pavement parameters was estimated. The database was generated from a static analytical solution of an axially symmetrical problem implemented in the form of JPav software and then explored by training regression models to predict the moduli and thickness of pavement layers. Two other databases were created using PCA (Principal Component Analysis) and FDM-like (Feature Difference Method) to compare models trained with the complete deflection database. The results showed that models trained with the complete deflection database had the best average prediction performance compared to the other two. In contrast, models trained with the database pre-processed by PCA showed a similar predicting performance to that of the previous models, but with a slight loss in precision. Models trained with the database pre-processed by the FDM-like approach exhibited excellent prediction on some features but performed worse on the rest. The primary objective of this work is to develop a model that enables the determination of pavement layer thickness and moduli from the deflections obtained in FWD tests. The analysis carried out allowed us to conclude that it is possible to obtain some pavement variables from the deflections, while others require a more sophisticated approach.<\/jats:p>","DOI":"10.3390\/app152412943","type":"journal-article","created":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T14:52:24Z","timestamp":1765205544000},"page":"12943","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Estimation of the XGBoost Regression Model Used in the Prediction of Pavement\u2019s Mechanical and Geometrical Parameters Based on Static Interpretation of the FWD Test"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3171-8504","authenticated-orcid":false,"given":"Marcin Daniel","family":"Gajewski","sequence":"first","affiliation":[{"name":"Road and Bridge Research Institute, 03-302 Warsaw, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-1978-846X","authenticated-orcid":false,"given":"Pengyuan","family":"Xia","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering, Warsaw University of Technology, 00-637 Warsaw, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4244-6150","authenticated-orcid":false,"given":"Beata","family":"Gajewska","sequence":"additional","affiliation":[{"name":"Institute of Civil Engineering, Warsaw University of Life Sciences\u2014SGGW, 02-776 Warsaw, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7555-1195","authenticated-orcid":false,"given":"Jorge","family":"Pais","sequence":"additional","affiliation":[{"name":"Department of Civil Engineering, University of Minho, 4800-058 Guimar\u00e3es, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9587-0417","authenticated-orcid":false,"given":"Miko\u0142aj","family":"Miecznikowski","sequence":"additional","affiliation":[{"name":"Faculty of Civil Engineering, Warsaw University of Technology, 00-637 Warsaw, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,8]]},"reference":[{"key":"ref_1","unstructured":"(2025, October 23). TOI World Desk World\u2019s largest road networks 2024: The United States and India take top spots (Updated: 23 October 2024, 11:20 IST). The Times of India 2024. Available online: https:\/\/timesofindia.indiatimes.com\/world\/us\/worlds-largest-road-networks-2024-the-united-states-and-india-takes-top-spots\/articleshow\/114419565.cms."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2187","DOI":"10.1016\/j.jclepro.2015.09.080","article-title":"Life cycle assessment of pavements: Reviewing research challenges and opportunities","volume":"112","author":"Azarijafari","year":"2016","journal-title":"J. Clean. Prod."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"425","DOI":"10.7409\/rabdim.021.025","article-title":"Research on the influence of pavement unevenness on heavy vehicles \u2019 axle loads variations with the use of TSD deflectometer","volume":"20","author":"Harasim","year":"2021","journal-title":"Roads Bridges Drog. I Most."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1515\/rjti-2015-0015","article-title":"Application of GPR and FWD in Assessing Pavement Bearing Capacity","volume":"2","author":"Rukavina","year":"2013","journal-title":"Rom. J. Transp. Infrastruct."},{"key":"ref_5","first-page":"61","article-title":"Determining pavement structural number from FWD testing","volume":"1448","author":"Rohde","year":"1994","journal-title":"Transp. Res. Rec."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"30","DOI":"10.3141\/1806-04","article-title":"Feasibility of backcalculation procedures based on dynamic FWD response data","volume":"1806","author":"Guzina","year":"2005","journal-title":"Transp. Res. Rec."},{"key":"ref_7","unstructured":"Kanai, T., Matsui, K., and Himeno, K. (2005, January 25\u201327). Applicability of Static and Dynamic Analytical Methods to Structural Evaluation of Flexible Pavements Using FWD Data. Proceedings of the Seventh International Conference on the Bearing Capacity of Roads, Railways and Airfields, Trondheim, Norway."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/j.conbuildmat.2018.05.082","article-title":"Comparative study on using static and dynamic finite element models to develop FWD measurement on flexible pavement structures","volume":"176","author":"Hamim","year":"2018","journal-title":"Constr. Build. Mater."},{"key":"ref_9","unstructured":"Siddharthan, R.V., Hajj, E.Y., Sebaaly, P.E., and Nitharsan, R. (2015). Formulation and Application of 3D-Move: A Dynamic Pavement Analysis Program, University of Nevada. Report: FHWA-RD-WRSC-UNR-201506."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1179\/1938636212Z.0000000009","article-title":"Consistency and accuracy of selected FWD backcalculation software for computing layer modulus of airport pavements","volume":"7","author":"Tarefder","year":"2013","journal-title":"Int. J. Geotech. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Miani, M., Dunnhofer, M., Rondinella, F., Manthos, E., Valentin, J., Micheloni, C., and Baldo, N. (2021). Bituminous mixtures experimental data modeling using a hyperparameters-optimized machine learning approach. Appl. Sci., 11.","DOI":"10.3390\/app112411710"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"132709","DOI":"10.1016\/j.conbuildmat.2023.132709","article-title":"Improved predictions of asphalt concretes\u2019 dynamic modulus and phase angle using decision-tree based categorical boosting model","volume":"400","author":"Rondinella","year":"2023","journal-title":"Constr. Build. Mater."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"27","DOI":"10.7409\/rabdim.025.001","article-title":"Mechanical performance prediction of asphalt mixtures: A baseline study of linear and non-linear regression compared with neural network modeling","volume":"24","author":"Baldo","year":"2025","journal-title":"Roads Bridges Drog. I Most."},{"key":"ref_14","first-page":"1195","article-title":"Predicting flexural-creep stiffness in bending beam rheometer (BBR) experiments using advanced super learner machine learning techniques","volume":"10","author":"Roshan","year":"2024","journal-title":"Res. Eng. Struct. Mater."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Rondinella, F., Oreto, C., Abbondati, F., and Baldo, N. (2024). A Deep Neural Network Approach towards Performance Prediction of Bituminous Mixtures Produced Using Secondary Raw Materials. Coatings, 14.","DOI":"10.3390\/coatings14080922"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1650945","DOI":"10.1155\/2018\/1650945","article-title":"Analysis of the Mechanical Behaviour of Asphalt Concretes Using Artificial Neural Networks","volume":"2018","author":"Baldo","year":"2018","journal-title":"Adv. Civ. Eng."},{"key":"ref_17","unstructured":"Pereira, P., and Pais, J. (2024, January 24\u201326). Artificial Neural Network Models for the Wander Effect for Connected and Autonomous Vehicles to Minimize Pavement Damage. Proceedings of the 10th International Conference on Maintenance and Rehabilitation of Pavements. MAIREPAV 2024, Guimaraes, Portugal. Lecture Notes in Civil Engineering."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"143","DOI":"10.3311\/PPci.2201","article-title":"Optimization of resilient modulus prediction from FWD results using artificial neural network","volume":"58","author":"Tarawneh","year":"2014","journal-title":"Period. Polytech. Civ. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1080\/10298436.2017.1309197","article-title":"Development of ANN-GA program for backcalculation of pavement moduli under FWD testing with viscoelastic and nonlinear parameters","volume":"20","author":"Li","year":"2019","journal-title":"Int. J. Pavement Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3099","DOI":"10.1080\/10298436.2021.1883016","article-title":"Application of a hybrid neural network structure for FWD backcalculation based on LTPP database","volume":"23","author":"Han","year":"2022","journal-title":"Int. J. Pavement Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"437","DOI":"10.7409\/rabdim.024.021","article-title":"Optimisation of BELLS3 model coefficients to increase the precision of asphalt layer temperature calculations in FWD and TSD measurements","volume":"23","author":"Sudyka","year":"2024","journal-title":"Roads Bridges Drog. I Most."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4231","DOI":"10.1007\/s12205-021-2306-9","article-title":"Tree-Based Ensemble Methods: Predicting Asphalt Mixture Dynamic Modulus for Flexible Pavement Design","volume":"25","author":"Worthey","year":"2021","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_23","unstructured":"Nielsen, D. (2016). Tree Boosting With XGBoost Why Does XGBoost Win \u201cEvery\u201d Machine Learning Competition?. [Master\u2019s Thesis, Norwegian University of Science and Technology]."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"133523","DOI":"10.1016\/j.conbuildmat.2023.133523","article-title":"Developing an improved extreme gradient boosting model for predicting the international roughness index of rigid pavement","volume":"408","author":"Wang","year":"2023","journal-title":"Constr. Build. Mater."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"123642","DOI":"10.1016\/j.conbuildmat.2021.123642","article-title":"An eXtreme Gradient Boosting model for predicting dynamic modulus of asphalt concrete mixtures","volume":"295","author":"Ali","year":"2021","journal-title":"Constr. Build. Mater."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"570","DOI":"10.4236\/ojce.2024.144031","article-title":"Machine Learning Models for Pavement Structural Condition Prediction: A Comparative Study of Random Forest (RF) and eXtreme Gradient Boosting (XGBoost)","volume":"14","author":"Ahmed","year":"2024","journal-title":"Open J. Civ. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"140610","DOI":"10.1016\/j.conbuildmat.2025.140610","article-title":"A novel maintenance decision model for asphalt pavement considering crack causes based on random forest and XGBoost","volume":"477","author":"Zhu","year":"2025","journal-title":"Constr. Build. Mater."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1063\/1.1707558","article-title":"The General Theory of Stresses and Displacements in Layered Systems. I","volume":"16","author":"Burmister","year":"1945","journal-title":"J. Appl. Phys."},{"key":"ref_29","unstructured":"Jemio\u0142o, S., and Szwed, A. (2017). Zagadnienia Statyki Spr\u0119\u017cystych P\u00f3\u0142przestrzeni Warstwowych, Oficyna Wydawnicza Politechniki Warszawskiej. Wydanie II."},{"key":"ref_30","unstructured":"Chatti, K., Kutay, M.E., Lajnef, N., Zaabar, I., Varma, S., and Lee, H.S. (2017). FHWA-HRT-15-063 Enhanced Analysis of Falling Weight Deflectometer Data for Use With Mechanistic-Empirical Flexible Pavement Design and Analysis and Recommendations for Improvements to Falling Weight Deflectometers, U.S. Department of Transportation, Federal Highway Administration."},{"key":"ref_31","unstructured":"De Pascalis, R. (2010). The Semi-Inverse Method in Solid Mechanics: Theoretical Underpinnings and Novel Applications. [Ph.D. Thesis, Universit\u2019e Pierre et Marie Curie and Universit\u00e0 del Salento]."},{"key":"ref_32","unstructured":"Timoshenko, S., and Goodier, J.N. (1970). Theory of Elasticity, McGraw-Hill Inc."},{"key":"ref_33","unstructured":"Timoshenko, S., and Woinowsky-Krieger, S. (1959). Theory of Plates and Shells, New Age International Publishers."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Chan, J.Y.L., Leow, S.M.H., Bea, K.T., Cheng, W.K., Phoong, S.W., Hong, Z.W., and Chen, Y.L. (2022). Mitigating the Multicollinearity Problem and Its Machine Learning Approach: A Review. Mathematics, 10.","DOI":"10.3390\/math10081283"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3360","DOI":"10.1080\/10494820.2021.1928235","article-title":"Enhancing the prediction of student performance based on the machine learning XGBoost algorithm","volume":"31","author":"Asselman","year":"2023","journal-title":"Interact. Learn. Environ."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016, January 13\u201317). XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_37","unstructured":"(2025, November 27). Optuna: A Hyperparameter Optimization Framework\u2014Optuna 4.3.0 Documentation. Available online: https:\/\/optuna.readthedocs.io\/en\/v4.3.0\/."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Akiba, T., Sano, S., Yanase, T., Ohta, T., and Koyama, M. (2019). Optuna: A Next-generation Hyperparameter Optimization Framework. arXiv.","DOI":"10.1145\/3292500.3330701"},{"key":"ref_39","unstructured":"Bergstra, J., Bardenet, R., Bengio, Y., and K\u00e9gl, B. (2025, November 27). Algorithms for Hyper-Parameter Optimization. Available online: https:\/\/www.researchgate.net\/publication\/216816964_Algorithms_for_Hyper-Parameter_Optimization."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1162\/106365601750190398","article-title":"Completely derandomized self-adaptation in evolution strategies","volume":"9","author":"Hansen","year":"2001","journal-title":"Evol. Comput."},{"key":"ref_41","unstructured":"Jamieson, K., and Talwalkar, A. (2016, January 9\u201311). Non-stochastic Best Arm Identification and Hyperparameter Optimization. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, Cadiz, Spain."},{"key":"ref_42","unstructured":"(2025, November 27). XGBoost Documentation\u2014Xgboost 3.0.2 Documentation. Available online: https:\/\/xgboost.readthedocs.io\/en\/latest\/."},{"key":"ref_43","unstructured":"Hooker, S., Erhan, D., Kindermans, P.J., and Kim, B. (2019). A benchmark for interpretability methods in deep neural networks. Adv. Neural Inf. Process. Syst., 32."},{"key":"ref_44","unstructured":"Mechelli, A., and Vieira, S. (2020). Chapter 12\u2014Principal component analysis. Machine Learning, Academic Press."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"25967","DOI":"10.1029\/98JD01168","article-title":"First difference method: Maximizing station density for the calculation of long-term global temperature change","volume":"103","author":"Peterson","year":"1998","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"196","DOI":"10.3846\/1822-427X.2009.4.196-202","article-title":"Use of Fwd Deflection Basin Parameters (SCI, BDI, BCI) for Pavement Condition Assessment","volume":"4","author":"Talvik","year":"2009","journal-title":"Balt. J. Road Bridge Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"127","DOI":"10.3141\/1655-17","article-title":"Determination of Bedrock Depth from Falling Weight Deflectometer Data","volume":"1655","author":"Chen","year":"1999","journal-title":"Transp. Res. Rec."},{"key":"ref_48","unstructured":"Rohde, G.T., and Smith, R.E. (1991). Determining Depth to Apparent Stiff Layer from FWD Data, Texas Transportation Institut, Texas A&M Universit. Available online: https:\/\/static.tti.tamu.edu\/tti.tamu.edu\/documents\/1159-1.pdf."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Biecek, P., and Burzykowski, T. (2021). Explanatory Model Analysis: Explore, Explain, and Examine Predictive Models, Chapman and Hall\/CRC.","DOI":"10.1201\/9780429027192"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"3789","DOI":"10.1029\/1998JD100042","article-title":"Sensitivity analysis: Could better methods be used?","volume":"104","author":"Atmospheres","year":"1999","journal-title":"J. Geophys. Res."}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/15\/24\/12943\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T10:41:28Z","timestamp":1765276888000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/15\/24\/12943"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,8]]},"references-count":50,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["app152412943"],"URL":"https:\/\/doi.org\/10.3390\/app152412943","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,8]]}}}