A Probabilistic Data-Driven Ensemble Approach for Battery Remaining Useful Life (RUL) Prognostics
- 1School of Civil Aviation, Northwestern Polytechnical University, Xi’an 710072, China
- 2Department of Mathematics, SUNY Buffalo State University, Buffalo, NY 14212, USA
Abstract
This study proposes a probabilistic data-driven ensemble framework for the remaining useful life (RUL) prognostics of lithium-ion batteries. This work addresses the limitations of single-model and deterministic methods by integrating Bayesian neural networks (BNNs), LSTM/Transformer architectures, Wiener process–based stochastic degradation modeling, and gradient boosting within a unified uncertainty-aware architecture. Unlike prior ensembles that fuse models with fixed weights, the proposed framework makes the fusion itself adaptive: each base model’s contribution is recomputed online from the degradation stage, operating-condition similarity, and recent residuals, and every prediction carries a decomposed epistemic and aleatoric uncertainty. Three primary contributions distinguish this work: (1) a novel dynamic ensemble weighting mechanism that adaptively adjusts each base model’s contribution as a function of degradation stage, operating-condition similarity, and recent prediction residuals; (2) a principled decomposition of total predictive uncertainty into epistemic and aleatoric components, combined with temperature scaling and an empirical analysis of when scalar calibration succeeds and fails; and (3) validation across four benchmark datasets (NASA PCoE, CALCE, MIT, and XJTU) comprising 197 cells and approximately 140,000 charge–discharge cycles (178 cells with an observed end of life). At these benchmarks, the proposed adaptive ensemble achieved a mean RMSE of 80.3 cycles, an MAE of 51.7 cycles, the best MAPE of all evaluated models (29.9%), and a CRPS of 40.4 cycles, reducing RMSE by 28.2% relative to a simple-average ensemble (Wilcoxon’s test: p < 0.001) and outperforming the LSTM, Transformer, BNN, and Wiener-PINN base learners individually; its point accuracy is statistically indistinguishable from the strongest single learner (gradient boosting, p = 0.20), while additionally providing decomposed epistemic/aleatoric uncertainty. Uncalibrated ensemble intervals were reliably conservative (PICP@95% = 99.1%); a single temperature-scaling parameter fitted on the small validation sets transferred imperfectly to unseen cells (PICP@95% = 78.1%), and this brittleness of scalar calibration under cell-level distribution shift is quantified and discussed. These results support adaptive ensembling for risk-aware battery management while identifying calibration under distribution shift as an open problem.
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BibTeX
@article{zhi2026probabilistic,
title = {{A Probabilistic Data-Driven Ensemble Approach for Battery Remaining Useful Life (RUL) Prognostics}},
author = {Guozhu Zhi and Fahad Abul Kalam and Zhenbao Liu and Mahabub Sultan and Abu Said Md Taher Bin Faisal Prodhan},
journal = {Batteries},
year = {2026},
month = oct,
doi = {10.3390/batteries12100390},
url = {https://www.mdpi.com/2313-0105/12/10/390},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Probabilistic Data-Driven Ensemble Approach for Battery Remaining Useful Life (RUL) Prognostics
AU - Guozhu Zhi
AU - Fahad Abul Kalam
AU - Zhenbao Liu
AU - Mahabub Sultan
AU - Abu Said Md Taher Bin Faisal Prodhan
PY - 2026
DA - 2026/10/02
JO - Batteries
DO - 10.3390/batteries12100390
UR - https://www.mdpi.com/2313-0105/12/10/390
AB - This study proposes a probabilistic data-driven ensemble framework for the remaining useful life (RUL) prognostics of lithium-ion batteries. This work addresses the limitations of single-model and deterministic methods by integrating Bayesian neural networks (BNNs), LSTM/Transformer architectures, Wiener process–based stochastic degradation modeling, and gradient boosting within a unified uncertainty-aware architecture. Unlike prior ensembles that fuse models with fixed weights, the proposed framework makes the fusion itself adaptive: each base model’s contribution is recomputed online from the degradation stage, operating-condition similarity, and recent residuals, and every prediction carries a decomposed epistemic and aleatoric uncertainty. Three primary contributions distinguish this work: (1) a novel dynamic ensemble weighting mechanism that adaptively adjusts each base model’s contribution as a function of degradation stage, operating-condition similarity, and recent prediction residuals; (2) a principled decomposition of total predictive uncertainty into epistemic and aleatoric components, combined with temperature scaling and an empirical analysis of when scalar calibration succeeds and fails; and (3) validation across four benchmark datasets (NASA PCoE, CALCE, MIT, and XJTU) comprising 197 cells and approximately 140,000 charge–discharge cycles (178 cells with an observed end of life). At these benchmarks, the proposed adaptive ensemble achieved a mean RMSE of 80.3 cycles, an MAE of 51.7 cycles, the best MAPE of all evaluated models (29.9%), and a CRPS of 40.4 cycles, reducing RMSE by 28.2% relative to a simple-average ensemble (Wilcoxon’s test: p < 0.001) and outperforming the LSTM, Transformer, BNN, and Wiener-PINN base learners individually; its point accuracy is statistically indistinguishable from the strongest single learner (gradient boosting, p = 0.20), while additionally providing decomposed epistemic/aleatoric uncertainty. Uncalibrated ensemble intervals were reliably conservative (PICP@95% = 99.1%); a single temperature-scaling parameter fitted on the small validation sets transferred imperfectly to unseen cells (PICP@95% = 78.1%), and this brittleness of scalar calibration under cell-level distribution shift is quantified and discussed. These results support adaptive ensembling for risk-aware battery management while identifying calibration under distribution shift as an open problem.
SN - 2313-0105
ER -