Jose I. Aizpurua

Ibai Ramirez, Jokin Alcibar, Joel Pino et al.

Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ) capabilities. Most existing PINN-based prognostics approaches are deterministic or account only for epistemic uncertainty, limiting their suitability for risk-aware decision-making. This work introduces a heteroscedastic Bayesian Physics-Informed Neural Network (B-PINN) framework that jointly models epistemic and aleatoric uncertainty, yielding full predictive posteriors for spatiotemporal insulation material ageing estimation. The approach integrates Bayesian Neural Networks (BNNs) with physics-based residual enforcement and prior distributions, enabling probabilistic inference within a physics-informed learning architecture. The framework is evaluated on transformer insulation ageing application, validated with a finite-element thermal model and field measurements from a solar power plant, and benchmarked against deterministic PINNs, dropout-based PINNs (d-PINNs), and alternative B-PINN variants. Results show that the proposed B-PINN provides improved predictive accuracy and better-calibrated uncertainty estimates than competing approaches. A systematic sensitivity study further analyzes the impact of boundary-condition, initial-condition, and residual sampling strategies on accuracy, calibration, and generalization. Overall, the findings highlight the potential of Bayesian physics-informed learning to support uncertainty-aware prognostics and informed decision-making in transformer asset management.

Ibai Ramirez, Joel Pino, David Pardo et al.

Transformers are crucial for reliable and efficient power system operations, particularly in supporting the integration of renewable energy. Effective monitoring of transformer health is critical to maintain grid stability and performance. Thermal insulation ageing is a key transformer failure mode, which is generally tracked by monitoring the hotspot temperature (HST). However, HST measurement is complex, costly, and often estimated from indirect measurements. Existing HST models focus on space-agnostic thermal models, providing worst-case HST estimates. This article introduces a spatio-temporal model for transformer winding temperature and ageing estimation, which leverages physics-based partial differential equations (PDEs) with data-driven Neural Networks (NN) in a Physics Informed Neural Networks (PINNs) configuration to improve prediction accuracy and acquire spatio-temporal resolution. The computational accuracy of the PINN model is improved through the implementation of the Residual-Based Attention (PINN-RBA) scheme that accelerates the PINN model convergence. The PINN-RBA model is benchmarked against self-adaptive attention schemes and classical vanilla PINN configurations. For the first time, PINN based oil temperature predictions are used to estimate spatio-temporal transformer winding temperature values, validated through PDE numerical solution and fiber optic sensor measurements. Furthermore, the spatio-temporal transformer ageing model is inferred, which supports transformer health management decision-making. Results are validated with a distribution transformer operating on a floating photovoltaic power plant.

Jone Ugarte-Valdivielso, Jose I. Aizpurua, Manex Barrenetxea-Iñarra

Transformers are one of the key assets in AC distribution grids and renewable power integration. During transformer energization inrush currents appear, which lead to transformer degradation and can cause grid instability events. These inrush currents are a consequence of the transformer's magnetic core saturation during its connection to the grid. Transformer cores are normally modelled by the Jiles-Atherton (JA) model which contains five parameters. These parameters can be estimated by metaheuristic-based search algorithms. The parameter initialization of these algorithms plays an important role in the algorithm convergence. The most popular strategy used for JA parameter initialization is a random uniform distribution. However, techniques such as parameter initialization by Probability Density Functions (PDFs) have shown to improve accuracy over random methods. In this context, this research work presents a framework to assess the impact of different parameter initialization strategies on the performance of the JA parameter estimation for inrush current studies. Depending on available data and expert knowledge, uncertainty levels are modelled with different PDFs. Moreover, three different metaheuristic-search algorithms are employed on two different core materials and their accuracy and computational time are compared. Results show an improvement in the accuracy and computational time of the metaheuristic-based algorithms when PDF parameter initialization is used.

Jokin Alcibar, Jose I. Aizpurua, Ekhi Zugasti

Batteries are a key enabling technology for the decarbonization of transport and energy sectors. The safe and reliable operation of batteries is crucial for battery-powered systems. In this direction, the development of accurate and robust battery state-of-health prognostics models can unlock the potential of autonomous systems for complex, remote and reliable operations. The combination of Neural Networks, Bayesian modelling concepts and ensemble learning strategies, form a valuable prognostics framework to combine uncertainty in a robust and accurate manner. Accordingly, this paper introduces a Bayesian ensemble learning approach to predict the capacity depletion of lithium-ion batteries. The approach accurately predicts the capacity fade and quantifies the uncertainty associated with battery design and degradation processes. The proposed Bayesian ensemble methodology employs a stacking technique, integrating multiple Bayesian neural networks (BNNs) as base learners, which have been trained on data diversity. The proposed method has been validated using a battery aging dataset collected by the NASA Ames Prognostics Center of Excellence. Obtained results demonstrate the improved accuracy and robustness of the proposed probabilistic fusion approach with respect to (i) a single BNN model and (ii) a classical stacking strategy based on different BNNs.

Jokin Alcibar, Jose I. Aizpurua, Ekhi Zugastia et al.

Health monitoring of remote critical infrastructure is a complex and expensive activity due to the limited infrastructure accessibility. Inspection drones are ubiquitous assets that enhance the reliability of critical infrastructures through improved accessibility. However, due to the harsh operation environment, it is crucial to monitor their health to ensure successful inspection operations. The battery is a key component that determines the overall reliability of the inspection drones and, with an appropriate health management approach, contributes to reliable and robust inspections. In this context, this paper presents a novel hybrid probabilistic approach for battery end-of-discharge (EOD) voltage prediction of Li-Po batteries. The hybridization is achieved in an error-correction configuration, which combines physics-based discharge and probabilistic error-correction models to quantify the aleatoric and epistemic uncertainty. The performance of the hybrid probabilistic methodology was empirically evaluated on a dataset comprising EOD voltage under varying load conditions. The dataset was obtained from real inspection drones operated on different flights, focused on offshore wind turbine inspections. The proposed approach has been tested with different probabilistic methods and demonstrates 14.8% improved performance in probabilistic accuracy compared to the best probabilistic method. In addition, aleatoric and epistemic uncertainties provide robust estimations to enhance the diagnosis of battery health-states.

Adrian Villalobos, Iban Barrutia, Rafael Pena-Alzola et al.

Semiconductor devices, especially MOSFETs (Metal-oxide-semiconductor field-effect transistor), are crucial in power electronics, but their reliability is affected by aging processes influenced by cycling and temperature. The primary aging mechanism in discrete semiconductors and power modules is the bond wire lift-off, caused by crack growth due to thermal fatigue. The process is empirically characterized by exponential growth and an abrupt end of life, making long-term aging forecasts challenging. This research presents a comprehensive comparative assessment of different forecasting methods for MOSFET failure forecasting applications. Classical tracking, statistical forecasting and Neural Network (NN) based forecasting models are implemented along with novel Temporal Fusion Transformers (TFTs). A comprehensive comparison is performed assessing their MOSFET ageing forecasting ability for different forecasting horizons. For short-term predictions, all algorithms result in acceptable results, with the best results produced by classical NN forecasting models at the expense of higher computations. For long-term forecasting, only the TFT is able to produce valid outcomes owing to the ability to integrate covariates from the expected future conditions. Additionally, TFT attention points identify key ageing turning points, which indicate new failure modes or accelerated ageing phases.

Ibai Ramirez, Jokin Alcibar, Joel Pino et al.

Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited, partly due to the complexity of incorporating partial differential equations (PDEs) for ageing physics and the scarcity of robust uncertainty quantification methods. This work introduces a Bayesian Physics-Informed Neural Network (B-PINN) framework for probabilistic prognostics estimation. By embedding Bayesian Neural Networks into the PINN architecture, the proposed approach produces principled, uncertainty-aware predictions. The method is applied to a transformer ageing case study, where insulation degradation is primarily driven by thermal stress. The heat diffusion PDE is used as the physical residual, and different prior distributions are investigated to examine their impact on predictive posterior distributions and their ability to encode a priori physical knowledge. The framework is validated against a finite element model developed and tested with real measurements from a solar power plant. Results, benchmarked against a dropout-PINN baseline, show that the proposed B-PINN delivers more reliable prognostic predictions by accurately quantifying predictive uncertainty. This capability is crucial for supporting robust and informed maintenance decision-making in critical power assets.