Renewable energy is critical for combating climate change, whose first step is the storage of electricity generated from renewable energy sources. Li-ion batteries are a popular kind of storage units. Their continuous usage through charge-discharge cycles eventually leads to degradation. This can be visualized in plotting voltage discharge curves (VDCs) over discharge cycles. Studies of battery degradation have mostly concentrated on modeling degradation through one scalar measurement summarizing each VDC. Such simplification of curves can lead to inaccurate predictive models. Here we analyze the degradation of rechargeable Li-ion batteries from a NASA data set through modeling and predicting their full VDCs. With techniques from longitudinal and functional data analysis, we propose a new two-step predictive modeling procedure for functional responses residing on heterogeneous domains. We first predict the shapes and domain end points of VDCs using functional regression models. Then we integrate these predictions to perform a degradation analysis. Our approach is fully functional, allows the incorporation of usage information, produces predictions in a curve form, and thus provides flexibility in the assessment of battery degradation. Through extensive simulation studies and cross-validated data analysis, our approach demonstrates better prediction than the existing approach of modeling degradation directly with aggregated data.

翻译：可再生能源对于应对气候变化至关重要，其首要步骤是储存可再生能源产生的电能。锂离子电池是一种常用的储能单元。其通过充放电循环的持续使用最终会导致性能退化。这种退化可通过绘制放电循环中的电压放电曲线（VDC）来可视化。现有的电池退化研究大多集中于通过单一标量测量值（用于概括每条VDC）来建模退化过程。这种曲线简化可能导致预测模型不准确。本文通过建模和预测完整VDC，分析了NASA数据集中可充电锂离子电池的退化行为。借助纵向数据与功能数据分析技术，我们提出了一种针对异构域上功能响应的新型两步预测建模流程。首先，我们使用功能回归模型预测VDC的形态与定义域端点；随后整合这些预测结果进行退化分析。我们的方法具有完全功能性，允许纳入使用信息，以曲线形式生成预测，从而为电池退化评估提供了灵活性。通过大量模拟研究和交叉验证数据分析，本方法相较于直接使用聚合数据建模退化的现有方法，展现出更优的预测性能。