Correcting SLD Icing Parameters: A Ridge Regression Method Fusing Icing Wind Tunnel Data and Numerical Priors

To explore the significant systematic deviations of FENSAP-ICE numerical simulations under supercooled large droplet (SLD) conditions, a ridge regression correction method that integrates numerical priors and domain-knowledge-aided features for ice shape geometric parameters is presented in this manuscript. The FENSAP-ICE predictions of eight geometric ice shape parameters are incorporated as numerical priors into the machine learning model, transforming the learning objective from “predicting from scratch” to “correcting systematic bias.” Six engineering auxiliary features are constructed based on SLD icing physics to provide physically meaningful adjustable dimensions for small-sample modeling. A two-stage model combining Logistic Regression classification and Ridge Regression is designed for zero-ice cases on the lower-surface icing limit. Evaluated via Leave-One-Out Cross-Validation on 29 sets of NACA0012 airfoil SLD icing wind tunnel experimental data, the improved system reduces the sMAPE of total ice area from 79.47% to 34.65%, lower-surface ice horn angle from 105.19% to 28.08%, upper-surface icing limit from 61.75% to 35.48%, and average ice thickness from 42.12% to 20.89%, all compared with FENSAP-ICE predictions. Ablation experiments further reveal that the introduction of the numerical prior alone reduces prediction error by approximately 10 percentage points, serving as the primary performance driver. The proposed method features low computational cost and strong physical consistency, providing a practical bias-correction framework for SLD ice shape prediction under small-sample conditions. Furthermore, to address the potential optimistic bias arising from small-sample cross-validation, nested cross-validation together with multiple linear baseline models are additionally employed to verify the robustness and relative competitiveness of the proposed correction method.