Multi-machine learning framework for the modulus back-calculation of asphalt pavement using measured FWD deflection basin

Pavement modulus is a key parameter for asphalt pavement maintenance decision-making, and falling weight deflectometer (FWD)-based modulus back-calculation is the most common nondestructive method, yet existing models suffer from systematic errors, low accuracy and inefficiency. This study proposed a multi-machine learning (ML) framework for asphalt pavement modulus back-calculation using FWD deflection basin data. A deflection dataset was generated via wave propagation-based forward solution, with deflection basin parameters (DBP) calculated and high-dimensional data reduced to 12 principal components by principal component analysis (PCA). Four ML models (SVR, RF, XGBoost, BPNN) were optimized, and their performance and robustness were evaluated. The BPNN model was compared with the traditional iterative inversion method in terms of accuracy and computational efficiency. Finally, the ML models were validated using the RIOHTrack field data. Quantitative results showed that BPNN outperformed other models for surface and base layer back-calculation, achieving an R² of 0.999 and the minimum MAPE. Meanwhile, XGBoost exhibited the best robustness for subgrade modulus back-calculation with an MAPE of 3.5%. In error robustness tests, XGBoost exhibited higher robustness under general FWD test errors, while BPNN achieved higher prediction accuracy, with R² > 0.94 and MAPE < 10%. Compared with the traditional method, which takes 1.5 h to perform a single calculation, ML models can significantly improve calculation efficiency while ensuring accuracy. The back-calculated modulus matched laboratory-measured lower layer modulus well and effectively reflected modulus degradation with loading cycles, providing an efficient, engineering-applicable ML method for FWD-based modulus back-calculation.