A Grey-Box Surrogate Feature Engineering Approach Based on GP-ANN for Digital Twin Applications

This study proposes a sequential Hybrid GP-ANN architecture based on the concept of autonomous feature engineering for multi-output performance prediction of single-phase induction motors, serving as a high-fidelity surrogate model ready for digital twin integration. The required high-resolution motor dataset (88,375 samples) was generated using a parametric sweep approach with Ansys RMxprt. In the proposed architecture, Genetic Programming (GP) is not positioned as a final predictor but as an analytical filter that discovers hidden physical relationships in raw input data and converts them into super features, thereby structurally eliminating the polynomial explosion risk and scale sensitivity that arise when raw data are modelled directly. The nonlinear physical relationships discovered autonomously by GP are added to the network input matrix as mathematical vectors, breaking the black-box structure of standard artificial neural networks and transforming it into a physics-inspired grey-box model. The nonlinear terms discovered by GP are fed into the network after independent Z-score normalisation to preserve gradient stability. To comprehensively evaluate this framework, its predictive performance is benchmarked against industry-standard machine learning algorithms, including Random Forest (RF), Support Vector Regression (SVR), and Extreme Gradient Boosting (XGBoost). Results on variation-based unseen test data show that the hybrid model achieves competitive prediction accuracy relative to XGBoost—matching or exceeding it for Output Torque and Input Current, and remaining broadly comparable for Output Power, though XGBoost achieves substantially lower RMSE for Efficiency and Power Factor—while additionally offering transparent mathematical traceability, reducing error rates (RMSE) by 42.1% to 66.1% per parameter compared to the standard ANN. The model achieves an R2 score of 0.9879 for the power factor parameter, where conventional approaches struggle. To rigorously validate the interpretability of this grey-box architecture, a global Permutation Feature Importance (PFI) analysis was conducted, showing that the GP-derived super features collectively account for 61.46% of the decision logic, outweighing the combined contribution of the raw inputs (38.54%). Furthermore, the autonomous feature engineering layer is found to reduce the learning burden on the ANN, allowing it to converge to a substantially lower error floor within the same fixed epoch budget. With an online inference time below 0.02 ms, the proposed architecture offers a robust methodological infrastructure for sustainable motor digital twins through a balanced trade-off between prediction accuracy and computational efficiency.