Wind Turbine Gearbox Oil Temperature Forecasting Using Stochastic Differential Equations and Multi-Objective Grey Modeling

This study develops and evaluates three complementary predictive modeling frameworks for gearbox oil temperature forecasting: Stochastic Differential Equation (SDE) modeling with iterative Markov correction, multi-objective genetic algorithm-enhanced grey modeling (MOGA-GM(1,N)), and multi-output Gaussian Process Regression (MO-GPR). The study used supervisory control and data acquisition (SCADA) data from a 1.5 MW wind turbine gearbox, comprising 14 temperature measurements spanning 789 operational hours. The SDE framework partitions temperature evolution into deterministic aging effects and stochastic environmental perturbations, achieving a fitting accuracy of 2.5% and testing accuracy of 8.0% after thirty iterative corrections. The MOGA-GM(1,N) approach optimizes weight coefficients through the dual objective of minimizing the posterior difference ratio and maximizing small error probability, attaining first-class accuracy classification (C=0.06; P=0.99) while identifying mechanical loads and rotational speeds as dominant thermal drivers. MO-GPR demonstrates competitive performance with uncertainty quantification capabilities, achieving RMSE values of 2.51–7.48 depending on training SCADA data proportions. Comparative analysis shows that the iteratively refined SDE methodachieves the best prediction accuracy in this case study for continuous thermal trajectory forecasting, while MOGA-GM(1,N) excels at wear source diagnostics and operational factor analysis. The proposed framework addresses persistent challenges in wind turbine condition monitoring, including extreme nonlinearity, discontinuous data, and unpredictable thermal spikes. The results suggest potential for implementation in preventive maintenance systems, enabling timely intervention before critical thermal thresholds that precipitate component failure.