Prediction of Shear-Wave Velocity from CPTu Data Using Robust Tanh Normalization and Quadratic Vector Regression

Abstract

Shear-wave velocity (Vs) is widely used for dynamic ground characterization, but existing CPT/CPTu-based correlations often exhibit limited transferability across soil types and geological settings. This study proposes a transparent prediction framework that combines robust tanh normalization with an explicit Quadratic Vector Regression (QVR) formulation for direct Vs estimation from four primary CPTu inputs: corrected cone resistance (, sleeve friction (), pore pressure (), and depth (z). The inputs are robustly scaled using the training median and interquartile range and mapped into a bounded (-1,1) feature space before being represented by first-order and feature-wise quadratic terms. The framework was evaluated using the North Sea database of Stuyts et al. (2024) and the multi-regional D1 database of Zhang et al. (2026). On the North Sea hold-out test set, QVR improved R² from 0.105 to 0.257 and reduced MAE from 39.13 to 35.89 m/s relative to the stress-dependent correlation of Stuyts et al. (2024). Comparable or improved performance was also obtained for additional held-out North Sea profiles. In cross-dataset evaluation from the North Sea training set to the D1 subsets, QVR achieved R² = 0.221–0.259, with performance comparable to SVR, DNN, and XGBoost despite its substantially simpler closed-form structure. Conversely, models trained on D1 showed degraded performance when transferred to the small North Sea hold-out set, indicating persistent dataset-dependent transfer limitations. Overall, the results show that a meaningful component of the multivariate CPTu–Vs relationship can be represented by a compact explicit quadratic formulation after robust bounded transformation, while broader transferability requires strictly site-independent validation.