Predicting Battery Capacity Fade Using Probabilistic Machine Learning Models With and Without Pre-Trained Priors

Abstract: Lithium-ion batteries are a key energy storage technology driving revolutions in mobile electronics, electric vehicles and renewable energy storage. Capacity retention is a vital performance measure that is frequently utilized to assess whether these batteries have approached their end-of-life. Machine learning (ML) offers a powerful tool for predicting capacity degradation based on past data, and, potentially, prior physical knowledge, but the degree to which an ML prediction can be trusted is of significant practical importance in situations where consequential decisions must be made based on battery state of health. This study explores the efficacy of fully Bayesian machine learning in forecasting battery health with the quantification of uncertainty in its predictions. Specifically, we implemented three probabilistic ML approaches and evaluated the accuracy of their predictions and uncertainty estimates: a standard Gaussian process (GP), a structured Gaussian process (sGP), and a fully Bayesian neural network (BNN). In typical applications of GP and sGP, their hyperparameters are learned from a single sample while, in contrast, BNNs are typically pre-trained on an existing dataset to learn the weight distributions before being used for inference. This difference in methodology gives the BNN an advantage in learning global trends in a dataset and makes BNNs a good choice when training data is available. However, we show that pre-training can also be leveraged for GP and sGP approaches to learn the prior distributions of the hyperparameters and that in the case of the pre-trained sGP, similar accuracy and improved uncertainty estimation compared to the BNN can be achieved. This approach offers a framework for a broad range of probabilistic machine learning scenarios where past data is available and can be used to learn priors for (hyper)parameters of probabilistic ML models.

• The paper introduces pre-training for GP and sGP models to improve forecast accuracy and uncertainty quantification in battery capacity fade predictions.
• It compares traditional and pre-trained frameworks using both physics-based simulated data and experimental lithium-ion battery datasets.
• Empirical results demonstrate that pre-trained BNNs notably reduce MAPE to as low as 1.56% under limited context scenarios.

Predicting Battery Capacity Fade Using Probabilistic Machine Learning Models With and Without Pre-Trained Priors

This paper investigates the application of probabilistic machine learning techniques to predict the capacity fade of lithium-ion batteries, a significant concern in their utilization across various sectors. The study places emphasis on three probabilistic models: Gaussian Processes (GP), Structured Gaussian Processes (sGP), and Bayesian Neural Networks (BNN), analyzing their ability to provide accurate forecasts while quantifying predictive uncertainty.

Key Contributions and Methodology

The research outlines a comparison between standard and pre-trained probabilistic models. Traditionally, GPs and sGPs have been employed in single-shot configurations, where each sample is independently used to train the model. In contrast, BNNs commonly utilize pre-training to improve inference efficiency. This work introduces pre-training to GP and sGP methodologies, hypothesizing that informed priors can enhance their predictive accuracy and uncertainty assessments.

The models were evaluated using both simulated data sets, generated via physics-based battery models, and experimental datasets sourced from lithium-ion battery performance studies. Specifically:

• Gaussian Process (GP): A non-parametric method leveraging learned hyperparameters and observational noise for capacity fade predictions.
• Structured Gaussian Process (sGP): An extension of GP, incorporating a phenomenological model to initiate the mean function, promising improvements in prediction accuracy through incorporating physical insights into battery behavior.
• Bayesian Neural Network (BNN): Employs distributions over weights rather than fixed values, allowing for integration of Bayesian inference through sampling methods like Hamiltonian Monte Carlo.

Results

The study presents numerical results demonstrating the benefits of pre-training, notably for the sGP and BNN models. Pre-training exhibited improved accuracy in forecasts, particularly evident in challenging use cases such as limited context scenarios:

• Pre-trained BNNs demonstrated substantial improvements in Mean Absolute Percentage Error (MAPE), achieving up to a reduction to 1.56% in simulated datasets at 50% of context utilization.
• Pre-trained sGPs showed enhanced prediction accuracy and well-calibrated uncertainty bounds across various context lengths, indicating their potential in applications where uncertainty quantification is critical.

Generically, the pre-training led to significant reductions in prediction errors and more reliable uncertainty estimations compared to non-pre-trained models.

Implications and Future Research Directions

The application of probabilistic machine learning offers attractive prospects for battery health prognostics due to its ability to incorporate prior knowledge from empirical data and simulations. The incorporation of pre-trained priors is particularly impactful, allowing models to efficiently leverage historical data and enhance predictions without excessive data requirements for new tests.

Looking forward, the methodologies developed here can be applied to larger datasets with additional features, such as charge energy or cell resistance, potentially improving the model's predictive horizon and fidelity. The study also opens pathways for integrating deeper physical models within sGP frameworks, offering avenues for improved interpretability and physical insight in battery health predictions.

This research contributes substantially to the field of battery prognostics, particularly in its exploration of pre-trained probabilistic models, setting the stage for more reliable and informative health predictions in energy storage systems.