A FEM-Based Machine Learning Framework for Online Stress Field Estimation in Hydropower Regulating Rings

Data-driven surrogate methods are increasingly applied to real-time structural health monitoring of critical engineering systems, but their use is often limited by the computational cost of high-fidelity finite element (FEM) simulations. This work proposes an FEM-based machine learning framework combining FEM, Principal Component Analysis (PCA), and Random Forest regression to reconstruct full-field von Mises stress distributions of a hydropower regulating ring from a reduced set of proximity sensor measurements. A calibrated 3D FEM model generated a representative dataset of operating conditions using a Design of Experiments (DOE) sampling strategy, reducing the simulation space. The resulting stress fields were reduced using a single global PCA model, and the retained principal components were predicted by a single Random Forest model trained on the guide vane opening and four displacement sensors installed on the turbine unit. Stress reconstruction was obtained via inverse PCA transformation and validated against FEM results through a leave-one-opening-out cross-validation, in which each guide vane opening was entirely withheld from training. The method achieved an average PSNR of 17.4 dB and SSIM of 0.837 across the eleven withheld openings, with 8 to 9 PCA components sufficient to preserve over 95% of the cumulative explained variance. A sensitivity analysis of the ensemble size showed that 100 decision trees provide accuracy comparable to larger ensembles at lower computational cost, and a feature importance analysis revealed the guide vane opening as the dominant predictor, with the four sensors providing complementary, fine-grained corrections. The framework enables near real-time reconstruction, requiring approximately 1.5 s per condition versus several hours for FEM. These results show that combining physics-based modeling with machine learning enables efficient structural monitoring for predictive maintenance and operational decision-making in hydroelectric systems.