  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.
