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Automated feature extraction and selection for data-driven models of rapid battery capacity fade and end of life

Samuel Greenbank, David A. Howey

arXiv:2101.04440v2eess.SYcs.SY

TL;DR

Forecasting lithium-ion battery degradation is challenging, particularly when rapid late-life fade begins and usage varies. This paper automates feature selection for Gaussian process models of capacity change, then uses those estimates to predict capacity trajectories and battery-life milestones. Across the considered datasets, it reports low capacity, knee-point, and end-of-life prediction errors.

  • Problem

    Battery ageing involves interacting mechanisms and varied usage, while available measurements and manually chosen inputs can limit data-driven forecasting of late-life degradation.

    Source: §I · p. 1

  • Method

    The method automatically extracts and selects usage features, models capacity changes with Gaussian process regression, and sums the estimates to predict the capacity-fade trajectory.

    Source: §I · p. 1, §III · p. 2

  • Results

    Knee-point forecast errors were 0.45 days or 2.6% across 600 predictions; median percentage errors for end-of-life predictions were 1.3%.

    Source: §VI · p. 8, §V · p. 8

  • Takeaways & Limitations

    Consistent selection and performance of voltage features suggest that time spent in specific state-of-charge ranges affected degradation rate in the datasets studied.

    Source: §V · p. 7

    The approach cannot eliminate the need for comprehensive ageing data to end of life, and may not predict accurately outside its training-data range.

    Source: §V · p. 8

Abstract

from arXiv · show

Lithium-ion cells may experience rapid degradation in later life, especially with more extreme usage protocols. The onset of rapid degradation is called the `knee point', and forecasting it is important for the safe and economically viable use for batteries. We propose a data-driven method that uses automated feature selection to produce inputs for a Gaussian process regression model that estimates changes in battery health, from which the entire capacity fade trajectory, knee point and end of life may be predicted. The feature selection procedure flexibly adapts to varying inputs and prioritises those that impact degradation. For the datasets considered, it was found that calendar time and time spent in specific voltage regions had a strong impact on degradation rate. The approach produced median root mean square errors on capacity estimates under 1\%, and also produced median knee point and end of life prediction errors of 2.6\% and 1.3\% respectively.

I. INTRODUCTION

Battery degradation forecasting is complicated by changing use, interacting ageing mechanisms, and the difficulty of choosing informative inputs. The paper proposes automated feature selection and evaluates it on two battery datasets.

I. INTRODUCTION

  • Battery ageing depends on varied and interacting factors, while users can measure only a limited set of signals, making flexible feature extraction important.Prior work used manually chosen small feature sets, while usage may vary over a battery's life.Source: §I · p. 1
  • Forecasting the knee point matters because it marks rapid late-life degradation, when cells may need replacement and may raise safety concerns.Earlier data-driven work estimated knee timing or cycle life to 80% capacity as point estimates rather than from full health trajectories.Source: §I · p. 1
  • The method automatically extracts and selects degradation-relevant features for Gaussian process regression, without requiring users to prespecify drivers, and can handle changing usage profiles.The authors also describe the process as interpretable and computationally scalable.Source: §I · pp. 1–2

II. DATA SOURCES

  • The study uses two open-source datasets: 135 A123 cells with varied fast-charging protocols and 45 follow-up cells cycled to 80% of nominal capacity.After removing cells with identified experimental errors and selecting lifetimes of 15–40 days, 147 cells remained.Source: §II · p. 2

III. METHODS

The method converts battery-use data into selected features, models capacity changes with Gaussian process regression, and sums those changes to reconstruct capacity fade. Feature extraction uses data-driven usage regions and time intervals suited to the datasets studied.

III. METHODS

  • Gaussian process regression maps selected features to capacity changes, which are summed piecewise over time to reconstruct the capacity-fade trajectory.The health metric is discharge capacity, though resistance could be used instead; the supervised method requires regular health measurements.Source: §III · p. 2

A. Feature Extraction

  • 12-hour feature intervals balanced computational speed and performance for these datasets; 1-hour intervals slowed computation, while 24-hour intervals tended to miss rapid ageing changes.The authors caution that this interval choice may differ for other data.Source: A. Feature Extraction · pp. 2–3
  • Usage-region features are defined from training data by partitioning six input streams at the 1st, 33rd, 67th, and 99th percentiles; Fig. 3 illustrates voltage histograms and example features.The six streams include current, voltage, temperature, absolute current, power, and absolute power; time and square root of time are also included as features.Source: A. Feature Extraction · p. 3, Figure 3 · p. 3
  • 74 feature types reduced 1.08×10^8 raw time points to 7,386 feature rows, with V2,3—the proportion of time between 3.12 V and 3.51 V—most commonly selected.The feature-selection stage is described as reducing the candidate set to approximately five feature types.Source: A. Feature Extraction · p. 3
  • The features capture usage that can drive ageing, such as prolonged high state of charge or intensive cycling, unlike health-output metrics that may not capture ageing drivers.Test features assume perfect knowledge of future cell use, but not future health; test usage need not match training usage.Source: A. Feature Extraction · p. 3

B. Feature Selection

Feature selection prioritizes inputs associated with battery-health change while limiting redundancy. The method directly ranks individual features and checks whether selected features span training and test data.

B. Feature Selection

  • The method ranks individual features rather than PCA combinations, since its goal is to select and interpret inputs directly.Capacity fade is often smooth, and the cells considered had two or three distinct phases, suggesting only a small feature set may be needed.Source: B. Feature Selection · p. 4
  • Removing highly similar features avoids redundant inputs that may add computational complexity without improving health prediction.The selection procedure prioritizes features that affect battery health; prior work found calendar time and charge throughput particularly significant.Source: B. Feature Selection · p. 4
  • Features are selected iteratively by correlation with capacity change, removing candidates whose shared correlation exceeds 0.85 until the user-specified number is reached.The feature count trades accuracy against complexity.Source: B. Feature Selection · p. 4
  • Successful selection should yield strong overlap between training and test data across selected features and capacity changes.Figure 5 illustrates this criterion with the first three selected features; its purple test data overlaps the grey training data.Source: B. Feature Selection · p. 5, Figure 5 · p. 5

C. Gaussian Process Regression

Gaussian process regression maps selected inputs to capacity transitions, which are summed to model capacity fade. Automatic relevance determination allows a separate lengthscale for each input feature.

C. Gaussian Process Regression

  • Gaussian process regression maps selected input features to capacity transitions, using a flexible model that makes few assumptions about the fitted function.The model uses a Matérn 5/2 covariance function and fits hyperparameters on training data by maximum marginal likelihood.Source: C. Gaussian Process Regression · p. 5
  • Automatic relevance determination assigns each input feature its own lengthscale hyperparameter, alongside a covariance-magnitude hyperparameter.Test inputs unseen during fitting produce capacity-transition predictions with associated ±2σ credible intervals.Source: C. Gaussian Process Regression · p. 5
  • Selected features form an approximate linear model, which the Gaussian process improves into a nonlinear model of capacity fade.Source: C. Gaussian Process Regression · p. 5

D. Knee Point Identification

Predicted capacity transitions are summed over time to form capacity-fade profiles, from which the knee point is identified.

D. Knee Point Identification

E. Evaluation Metrics

Evaluation uses capacity-profile and capacity-transition errors, plus percentage errors for end of life and knee-point timing. Median and 95th-percentile values are reported, with mean errors also quoted for comparison.

E. Evaluation Metrics

  • RMSE_Q measures error in predicted capacity profiles, while RMSE_∆Q measures error using capacity-transition data alone.The transition metric is included because a single poor transition prediction can substantially influence profile RMSE.Source: E. Evaluation Metrics · p. 5
  • End-of-life percentage error measures the percentage difference between predicted and observed end-of-life time.Source: E. Evaluation Metrics · p. 5
  • Knee-point prediction accuracy is evaluated as a percentage error using knee-point position in time.Source: E. Evaluation Metrics · p. 5
  • Evaluation reports the median and 95th percentile for all metrics, and also quotes mean errors for comparison.Source: E. Evaluation Metrics · p. 5

F. Trial Setup

The evaluation combined a large-scale cross-validation test with tests of limited late-life data, feature count, and feature-correlation thresholds.

F. Trial Setup

  • The large-scale test used 20 randomly sampled datasets, each with 100 training cells and 47 test cells, to quantify general performance through k-fold cross-validation.The evaluation used temperature, voltage, and current data from 147 cells across four batches, with lifetimes of 15–40 days.Source: F. Trial Setup · p. 5
  • The limited late-life data test used 10 test cells and 30 training cells, varying the number of cells with full-life data from 3 to 30.This setup replicated a scenario with limited full-life data.Source: F. Trial Setup · p. 6, Figure 7 · p. 6
  • Separate tests varied the maximum shared feature correlation from 1 to 0.7 and compared models using 1, 2, 3, 4, 5, or 10 features against a time-only baseline.Correlation tests used 20 repeats at each of 16 test points, with 50 training and 50 test cells.Source: F. Trial Setup · p. 6

IV. RESULTS

Voltage-region features were selected most consistently, while calendar time also ranked among the most frequently selected inputs and showed evidence of relevance to capacity transitions.

A. Feature prioritisation

  • V2,3 was selected in every trial; V1,2 was selected second in 19 trials and omitted in the remainder, while calendar time was selected 18 times.These were the most commonly selected features in the process and datasets described.Source: A. Feature prioritisation · p. 6
  • Calendar time typically had a GP length-scale of around 7 days across data spanning 0–40 days, suggesting this input is relevant to capacity fade.GP length-scale hyperparameters provide an estimate of the relevance of down-selected features for predicting capacity transitions.Source: A. Feature prioritisation · p. 6
  • Tables III and IV summarize the large-scale trial results, with Table IV reporting results in units of time (days).The supplied passages do not provide the tables' cell values.Source: Table III · p. 6, Table IV · p. 6

B. Kneepoint and end of life predictions

The model produced low capacity-profile errors and comparatively accurate end-of-life and knee-point forecasts. Its reported performance also varied with feature count, correlation threshold, sampling rate, and the amount of late-life training data.

B. Kneepoint and end of life predictions

  • 2.6% was the median absolute knee-point position error in time, rising to 14% when 95% of results are accounted for.Knee points were estimated from the capacity-fade predictions and compared with observations.Source: B. Kneepoint and end of life predictions · p. 6
  • Performance was reasonably consistent across lifetimes, but knee-point forecasts were less accurate than end-of-life forecasts because slight late-life gradient over-prediction affected the knee calculation.The gradient over-prediction did not significantly alter end-of-life estimates.Source: B. Kneepoint and end of life predictions · p. 6
  • Adding features tended to improve median error, but the 95th-percentile error did not significantly improve beyond three features plus time; time alone performed poorly.Other features were also needed for accurate health prognosis.Source: B. Kneepoint and end of life predictions · pp. 6–7, Table V · p. 6
  • 0.83% was the median RMSEQ, 95% of profiles had RMSEQ < 3.1% capacity, and capacity-transition forecasts had median RMSE of 0.13% capacity.The capacity-profile errors were generally small.Source: B. Kneepoint and end of life predictions · p. 6, Figure 8 · p. 7
  • 1.3% was the median absolute end-of-life forecast percentage error, with a 5.6% 95th percentile and 2.0% mean.Fig. 9 plots predicted versus observed end of life.Source: B. Kneepoint and end of life predictions · p. 6, Figure 9 · p. 7
  • Reducing raw data to one point every 100 seconds left algorithm performance unchanged.Source: B. Kneepoint and end of life predictions · p. 7
  • Median results were accurate with late-life data from 15 cells and relatively consistent with as few as 6 such cells; 95th-percentile errors were around 4% for capacity RMSE, 10% for end-of-life error, and 20% for knee-point error.The limited late-life data test results are presented in Fig. 10.Source: B. Kneepoint and end of life predictions · p. 7
  • A maximum shared correlation threshold of 0.95 showed a distinct improvement in capacity RMSE, while end-of-life and knee-point performance improved more steadily as the threshold changed.Elsewhere in the work, the maximum shared correlation was 0.85.Source: B. Kneepoint and end of life predictions · p. 7

V. DISCUSSION

The approach achieved low median end-of-life error, while knee-point forecasts were generally close to observed timing. The discussion also identifies voltage-region features and feature diversity as important, alongside limits in training-data coverage and uncertainty calibration.

V. DISCUSSION

  • Selected voltage-range features V2,3 and V1,2 strongly suggest that time spent in specific state-of-charge ranges impacted degradation rate.V2,3 was generally prioritized because V3,4 and V1,2 correlated closely with it; as cells degraded, voltage limits were reached sooner, changing time spent across voltage ranges.Source: §V · p. 7
  • 1.3% median percentage error for end-of-life predictions; the large-scale test’s 2.0% mean error was at least a three-fold improvement over similar-data work.The authors suggest training across each cell’s entire life, allowing usage variability, may explain the improvement over point measurements.Source: §V · p. 8
  • Three quarters of knee-point estimates were within one day of the measured value, and 95% of profiles were within two and a half days.The authors attribute these results to accurate capacity forecasts.Source: §V · p. 8
  • Data-driven approaches cannot necessarily predict accurately beyond the range of their training data, and the limited-data test did not remove the need for comprehensive ageing data to end of life.The limited late-life test nevertheless showed versatility with significantly restricted training data.Source: §V · p. 8
  • Reducing the maximum allowed correlation between features improved accuracy, indicating that diverse inputs were crucial for performance.The authors suggest this constraint either avoided overfitting or identified otherwise unobvious features.Source: §V · p. 8
  • The capacity calibration score was 0.42 for the full large-scale trial and up to 0.75 for end-of-life predictions, both below the 0.95 target.Larger end-of-life errors were not matched by larger credible intervals, suggesting overconfident uncertainty estimates.Source: §V · p. 8

VI. CONCLUSIONS

The paper combines automated feature selection with machine learning to forecast battery health, knee points, and end of life. It reports accurate forecasts and interpretable features, while identifying data and uncertainty challenges for future work.

VI. CONCLUSIONS

  • Across 600 predictions, knee-point forecast errors were 0.45 days or 2.6%; half of full-lifetime capacity profiles had root mean square error under 0.83% capacity.The approach also handled lesser data quality and quantity without unduly impacting end-of-life prediction, though more data generally improved performance.Source: §VI · p. 8
  • Further work should investigate feature counts across wider datasets, improve credible intervals, and address datasets without regular health measurements.The authors identify absent regular health measurements as an open challenge, suggesting unsupervised learning or a more general health metric as possible approaches.Source: §VI · p. 8
  • Easily understood selected features provide insight unavailable from black-box machine learning, including how features correlate and which impact degradation.The authors present that insight alongside accurate capacity, end-of-life, and knee-point forecasts.Source: §VI · p. 8
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