基于并行特征融合与分位数回归的锂电池SOC估计

State-of-Charge Estimation for Lithium-Ion Batteries Based on Parallel Feature Fusion and Quantile Regression

  • 摘要: 锂离子电池荷电状态(State of Charge,SOC)的准确估计及不确定性量化,是保障储能系统安全运行和提高电池管理效率的关键。本文针对复杂工况与动态负载,导致SOC估计精度与可信度下降问题,提出一种基于并行特征融合的QRCNN–BiGRU–Transformer(parallel feature-fusion QRCNN–BiGRU–Transformer,PFF-QBT)模型。该模型利用分位数回归卷积神经网络(Quantile Regression Convolutional Neural Network,QRCNN)与双向门控循环单元(Bidirectional Gated Recurrent Unit,BiGRU)并行提取电池运行序列的局部动态特征和双向时序信息,并通过Transformer建模全局依赖关系,实现多层次特征融合,引入分位数回归损失同步构建90%预测区间。最后,在多温度、多工况下进行实验验证。结果表明,所提模型的平均绝对误差(Mean Absolute Error,MAE)和均方根误差(Root Mean Square Error,RMSE)均最低,可低至0.753%和0.897%,决定系数(Coefficient of Determination,R2)可高达99.897%。此外,预测区间覆盖概率(Prediction Interval Coverage Probability,PICP)和归一化平均宽度(Prediction Interval Normalized Average Width,PINAW)的平均值分别为90.009%和0.07451。综上所述,所提方法能够兼顾SOC点预测精度与不确定性表征能力,可为复杂运行环境下电池管理系统的状态监测和安全决策提供依据。

     

    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.

     

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