锂电池组容量估计对健康管理、安全运行至关重要。针对现有方法无法描述容量分布随服役时间变化的缺陷，提出建立异方差高斯过程回归(heteroscedastic Gaussian process regression, HGPR)模型，突破经典高斯过程回归概率模型的输出噪声同方差限制，构建新的高斯过程描述服役时间相关的输出噪声。采用电动汽车电池组充电数据构建训练集与测试集，根据容量相关性选择模型输入，采用变分近似法求解HGPR中两个高斯过程的超参数。结果表明，HGPR估计的电池组容量均值的精度优于经典高斯过程回归和神经网络模型，同时，估计的容量标准差随服役时间而增大，提高了预测区间覆盖率。进一步分析了不同特征组合、核函数对估计精度的影响，并揭示了HGPR中两个高斯过程分别对均值和标准差估计的作用。该研究可为锂电池组容量、健康状况不确定建模提供参考。

Accurate capacity estimation of lithium-ion battery packs is crucial for health management and safe operation. The existing methods cannot reflect the variation of capacity distribution with service time. Addressing this problem a heteroscedastic Gaussian process regression (HGPR) model is developed. Different from the standard Gaussian process regression which assumes homoscedasticity variation of the output noise, the HGPR constructs a new Gaussian process to represent the output noise with service time-related variance. The model employs charging data from electric vehicle battery packs to construct training and testing sets, selects inputs through capacity correlation analysis, and employs variational approximation for HGPR hyperparameter optimization. Experimental results demonstrate that HGPR not only achieves higher accuracy in mean capacity estimation compared to Gaussian process regression and neural networks, but also effectively captures the increasing trend of capacity standard deviation over time and improves the interval coverage rate of the estimated distribution. Further analysis reveals the distinct roles of the two Gaussian processes in HGPR for mean and standard deviation estimation, and investigates the influence of different feature combinations and kernel functions on estimation accuracy. This research provides a valuable reference for uncertainty modeling in battery pack capacity and health assessment.