This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head’s theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network’s fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox, X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

State-of-the-art Deep Learning (DL) methods based on Supervisory Control and Data Acquisition (SCADA) system data for the detection and prognosis of wind turbine faults require large amounts of failure data for successful training and generalisation, which are generally not available. This limitation prevents benefiting from the superior performance of these methods, especially in SCADA-based failure prognosis. Data augmentation approaches have been proposed in the literature for generating failure data instances within a SCADA sequence to reduce the imbalance between healthy and faulty state data points, which is relevant to fault detection tasks. However, the successful implementation of DL-based failure prognosis methods requires the availability of multiple run-to-failure SCADA sequences. This paper proposes a data-driven method for generating synthetic run-to-failure SCADA sequences with custom operational and environmental conditions and progression of degradation. An Artificial Neural Network (ANN) is trained with signals that represent these factors to reconstruct the SCADA signals. Then, it is used to generate synthetic SCADA datasets based on data available from a wind turbine that experienced a gearbox failure. Synthetic data sets generated are evaluated on the basis of the similarity of their signal distributions, the temporal dynamics within each signal, and the temporal dynamics among different SCADA signals with those in similar field datasets. The results show that the generated synthetic datasets are consistent with their field counterparts, with a comparatively lower diversity in their dynamic behaviour in time.