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Battery health prediction under generalized conditions using a Gaussian process transition model
Robert R. Richardson, Michael A. Osborne, David A. Howey
TL;DR
Battery health prediction must remain accurate despite complex degradation and varying operating conditions. The paper introduces a Bayesian non-parametric Gaussian process transition model that predicts capacity changes from usage, achieving accurate nonlinear capacity-fade predictions with quantified uncertainty. Its best reported normalised root mean square error is 4.3%.
Problem
Battery degradation is complex, while accurate health prediction is needed for reliable operation, maintenance, and energy-storage valuation.
Method
A Bayesian non-parametric Gaussian process transition model predicts capacity changes from current, voltage, and temperature usage sequences represented by fixed-size feature vectors.
Results
4.3% best-case normalised root mean square error was reported, with accurate nonlinear capacity-fade prediction and uncertainty estimates.
Takeaways & Limitations
The model provides a generalized battery health model that can predict capacity fade across varied usage scenarios while accounting for prediction uncertainty.
Takeaways & Limitations
Predictive use assumes future current, voltage, and temperature time series are known in advance, and performance depends on sufficient training coverage of input conditions.
Abstract
from arXiv · showhide
Accurately predicting the future health of batteries is necessary to ensure reliable operation, minimise maintenance costs, and calculate the value of energy storage investments. The complex nature of degradation renders data-driven approaches a promising alternative to mechanistic modelling. This study predicts the changes in battery capacity over time using a Bayesian non-parametric approach based on Gaussian process regression. These changes can be integrated against an arbitrary input sequence to predict capacity fade in a variety of usage scenarios, forming a generalised health model. The approach naturally incorporates varying current, voltage and temperature inputs, crucial for enabling real world application. A key innovation is the feature selection step, where arbitrary length current, voltage and temperature measurement vectors are mapped to fixed size feature vectors, enabling them to be efficiently used as exogenous variables. The approach is demonstrated on the open-source NASA Randomised Battery Usage Dataset, with data of 26 cells aged under randomized operational conditions. Using half of the cells for training, and half for validation, the method is shown to accurately predict non-linear capacity fade, with a best case normalised root mean square error of 4.3%, including accurate estimation of prediction uncertainty.
Highlights
The study uses a Gaussian process transition model to predict future battery capacity and uncertainty under varied operating conditions. It maps variable-length measurements to fixed-size inputs and achieves a best-case normalised root mean square error of 4.3%.
- A Gaussian process transition model predicts future battery capacity and its associated uncertainty.
- Arbitrary-length current, voltage and temperature measurements are mapped to fixed-size input vectors for efficient modelling.
- The approach was demonstrated on 26 cells aged under randomized usage conditions.
- 4.3% best-case normalised root mean square error was achieved.
1 Introduction
Battery degradation is difficult to model because complex interacting processes limit mechanistic approaches and varied operating conditions challenge conventional data-driven predictions. The paper introduces a Bayesian non-parametric transition model that predicts capacity changes from battery usage.
- Accurate health and remaining-useful-life prediction matters for reliable operation, maintenance costs, asset valuation, and performance.
- Battery degradation involves complex interacting chemical and mechanical processes, making first-principles physical modelling challenging.
- State of health is represented here by cell capacity, although the outlined methods could also apply to metrics such as internal resistance.
- Conventional parametric approaches require a specified model form and may lose accuracy under different environmental or load conditions.
- Data-driven methods, including Gaussian process regression, offer greater flexibility than pre-specified parametric functions.
- The method builds on prior Gaussian-process health prediction for similarly cycled batteries by targeting varied real-world usage conditions.
- The paper introduces a Bayesian non-parametric transition model that predicts changes in state of health as a function of battery usage rather than directly fitting health to time or cycle count.
2 Method
The method models capacity changes between flexible usage intervals with Gaussian-process regression, after converting variable-length current, voltage, and temperature histories into fixed-size features. It evaluates both capacity-change and capacity forecasts, alongside uncertainty calibration, and compares Gaussian processes with gradient boosting.
- 2.1 Transition model: Load patterns are time-series segments between successive capacity measurements, allowing variable durations and multiple charge-discharge events.
- 2.1 Transition model: The regression maps selected load-pattern features to measured capacity differences using a latent function plus independent Gaussian noise.
- 2.2 Input feature extraction: Arbitrary-length current, voltage, and temperature histories are mapped to fixed-size feature vectors for regression.
- 2.2 Input feature extraction: Features encode assumed ageing drivers, including elapsed time, charge throughput, and time spent within selected current, voltage, and temperature ranges.
- 2.4 Evaluation: The model evaluates capacity-change RMSE, actual-capacity RMSE, and calibration of predicted credible intervals.
- 2.6 Gradient boosting: Gradient boosting provides a comparison model using quantile regression for approximate prediction intervals, without a full covariance matrix.
3 Dataset
The study uses 26 NASA battery cells grouped by randomized cycling procedures, with capacity measured through periodic 2 A characterization tests. The dataset spans varied operating conditions and cell-group capacity trajectories.
- The NASA repository randomizes battery load profiles to better represent practical battery usage.The dataset explores ranges of time, charge throughput, current, voltage, and temperature.
- 26 of 28 available cells were used, grouped into 7 groups of 4 with different randomized cycling procedures.Cells 16 and 17 were omitted because spurious data produced cycles with negative duration.
- 950 discharge curves were available across all cells, providing approximately 34 capacity measurements per cell.Capacity was evaluated from periodic 2 A charge-discharge characterization tests between cell-voltage limits.
- Capacity was calculated by integrating current from each 2 A charge curve, and its evolution differed substantially across cell groups.The measured capacities for similarly cycled cells are plotted against time in Figure 4.
- Table 3 summarizes the distinct NASA load profiles assigned to the cell groups.
4 Results
Six transition-model configurations were trained on even-numbered cells and tested on odd-numbered cells. The best configuration used Gaussian process regression with a Matérn kernel and achieved the lowest reported capacity-prediction errors.
- Six model configurations were compared using even-numbered cells for training and odd-numbered cells for testing.The split includes mappings between inputs and capacity drops across the training cells.
- Model 1 used a Matérn-kernel Gaussian process with the preceding 6 load patterns as inputs and without total elapsed time.
- Model 2 used only the current load pattern and added total elapsed time to capture long-term trends.
- Models 3 and 4 replaced the Matérn kernel with a linear kernel, while Models 5 and 6 replaced Gaussian processes with gradient boosting.The linear-kernel models provide a simpler comparison case.
- 4.3% normalised capacity prediction error was achieved by Model 1, with RMSE∆Q of 0.0201 Ah and RMSEQ of 0.07 Ah.Model 1 was the best-performing of the six tested cases.
- Figure 6 presents capacity trajectories for every test cell using Model 1.
5 Discussion
Model 1 accurately predicted nonlinear capacity trajectories and generally contained true capacity within its ±2σ uncertainty intervals. The discussion also identifies feature-history benefits, model-comparison weaknesses, and dependence on representative training coverage.
- A calibration score close to 0.954 indicated reasonable, slightly over-cautious uncertainty estimates for Model 1.True capacity generally remained within the plotted ±2σ interval.
- Model 1 predicted both positive and negative capacity differences, including some occasional capacity increases such as cell 7 near day 140.The physical cause of these increases was unclear, but accounting for them matters because real measurements may show similar behavior.
- Model 1’s superiority over Model 2 suggests that previous load-pattern inputs contain information unavailable from total elapsed time alone.
- Linear-kernel models performed considerably worse and showed over-confidence, indicating that simple linear input combinations were insufficient for this dataset.
- Gradient-boosting models were slightly less accurate in mean prediction than Models 1 and 2 and were also erroneously overconfident.
- Performance may deteriorate when training cells do not cover the tested groups, because the model would extrapolate beyond the training input space.The reported even/odd split placed at least one training cell in each of the seven cycling groups.
6 Conclusions
The paper develops a Bayesian non-parametric battery health model that predicts capacity changes from usage and reports accurate mean capacity predictions. Time elapsed and charge throughput dominate the inputs, while future prediction assumes the input time series are known in advance.
- Gaussian process regression with a Matérn kernel provided the best-performing approach for estimating capacity change as a function of battery usage.
- Within 5% relative accuracy, the best-case mean capacity predictions matched actual values.
- Time elapsed and charge throughput were the dominant inputs despite the dataset spanning a wide range of temperatures and currents.
- Figure 6 compares true capacity trajectories with mean predictions and displays uncertainty using a blue ±2σ credibility region.
- Linear-kernel Gaussian process models produced very inaccurate predictions when inputs were combined naively through a simple linear combination.
- Predictive use assumes future current, voltage, and temperature time series are known perfectly, motivating evaluation on larger datasets and improved input modelling.