Abstract:
Accurate state-of-charge (SOC) estimation and reliable characterization of prediction uncertainty are essential for the safe operation, efficient energy management, and risk-aware control of lithium-ion battery energy-storage systems. However, temperature variations and dynamic loads intensify the nonlinear and time-varying behavior of batteries, potentially degrading estimation accuracy and prediction reliability. Moreover, most existing data-driven approaches focus on deterministic point estimation and provide limited information regarding the reliability of individual predictions. To address these challenges, a parallel feature-fusion QRCNN–BiGRU–Transformer model, termed PFF-QBT, is proposed to integrate accurate SOC estimation and uncertainty quantification within a unified framework. PFF-QBT adopts a parallel-to-serial architecture to characterize battery dynamics across multiple temporal scales. Battery operating sequences are first processed in parallel by the Quantile Regression Convolutional Neural Network (QRCNN) and bidirectional Gated Recurrent Unit (BiGRU) branches. The QRCNN branch extracts local response patterns and short-term fluctuations induced by rapidly varying loads, thereby enhancing the representation of transient battery behavior. Meanwhile, the BiGRU branch processes the sequences in both forward and backward directions to capture contextual information and bidirectional temporal dependencies associated with SOC evolution. The complementary features extracted by the two branches are subsequently fused and delivered to the Transformer module. Through self-attention, the Transformer adaptively evaluates the relevance of information across time steps and establishes long-range dependencies within the fused sequence. Consequently, the proposed architecture integrates local dynamic patterns, bidirectional temporal correlations, and global contextual information, overcoming the representation limitations of models based on a single feature-extraction mechanism. Quantile regression is embedded into the end-to-end learning framework to extend deterministic SOC estimation to uncertainty-aware prediction without assuming a predefined residual distribution. It enables PFF-QBT to provide a central SOC estimate, together with adaptive bounds that form a 90% prediction interval. The resulting interval characterizes condition-dependent prediction reliability and provides quantitative support for reliability assessment, operational risk identification, and adaptive safety-margin setting. The proposed model is evaluated using lithium-ion battery data collected under the Beijing Bus Dynamic Stress Test (BBDST) and Dynamic Stress Test (DST) profiles at multiple temperatures. These data encompass diverse thermal environments and dynamic current excitations, enabling systematic assessment of model accuracy, robustness, and adaptability under different operating conditions. Point-estimation performance is evaluated using the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R2). In contrast, prediction-interval reliability and sharpness are assessed using the prediction interval coverage probability (PICP) and prediction interval normalized average width (PINAW), respectively. Experimental results demonstrate that PFF-QBT achieves the lowest MAE and RMSE among the evaluated models. Across all test conditions, the average MAE and RMSE are 0.839% and 1.072%, respectively, while the average R2 reaches 99.822%. The minimum MAE and RMSE are 0.753% and 0.897%, respectively, and the maximum R2 reaches 99.897%. Compared with the comparison model, PFF-QBT reduces the average MAE and RMSE by 35.58% and 35.31%, respectively, and improves the average R2 by 0.247 percentage points. Moreover, the generated 90% prediction intervals achieve an average PICP of 90.009%, differing from the nominal coverage level by only 0.009 percentage points, together with an average PINAW of 0.07451. These results demonstrate that PFF-QBT effectively balances point-estimation accuracy, interval reliability, and prediction sharpness. By jointly delivering accurate SOC estimates and reliable prediction intervals, the proposed model comprehensively characterizes battery state and predictive uncertainty, thereby supporting reliability-aware monitoring, operational risk identification, and safety-oriented decision-making in battery management systems.