Multivariable Fractional Polynomials for lithium-ion batteries degradation models under dynamic conditions

Longevity and safety of lithium-ion batteries are facilitated by efficient monitoring and adjustment of the battery operating conditions. Hence, it is crucial to implement fast and accurate algorithms for State of Health (SoH) monitoring on the Battery Management System. The task is challenging due to the complexity and multitude of the factors contributing to the battery capacity degradation, especially because the different degradation processes occur at various timescales and their interactions play an important role. Data-driven methods bypass this issue by approximating the complex processes with statistical or machine learning models: they rely solely on the available cycling data, while remaining agnostic to the underlying real physical processes. This paper proposes a data-driven approach which is understudied in the context of battery degradation, despite being characterised by simplicity and ease of computation: the Multivariable Fractional Polynomial (MFP) regression. Models are trained from historical data of one exhausted cell and used to 1Corresponding author. Department of Mathematics, University of Oslo, 0851 Oslo, Norway, clarabe@math.uio.no 2Department of Mathematics, University of Oslo, 0851 Oslo, Norway, azzeddib@math.uio.no 3Department of Mathematics, University of Oslo, 0851 Oslo, Norway, glad@math.uio.no 4Department of Mathematics, University of Oslo, 0851 Oslo, Norway; DNV GL Group Technology and Research, 1322 Høvik, Norway, erik.vanem@dnvgl.com 5Department of Mathematics, University of Oslo, 0851 Oslo, Norway, debin@math.uio.no 1 ar X iv :2 10 2. 08 11 1v 2 [ st at .A P] 2 9 N ov 2 02 1 predict the SoH of other cells. The data are provided by the NASA Ames Prognostics Center of Excellence, and are characterised by varying loads which simulate dynamic operating conditions. Two hypothetical scenarios are considered: one assumes that a recent observed capacity measurement is known, the other is based only on the nominal capacity of the cell. It was shown that the degradation behaviour of the batteries under examination is influenced by their historical data, as supported by the low prediction errors achieved (root mean squared errors ranging from 1.2% to 7.22% when considering data up to the battery End of Life). Moreover, we offer a multi-factor perspective where the degree of impact of each different factor to ageing acceleration is analysed. Finally, we compare with a Long Short-Term Memory Neural Network and other works from the literature on the same dataset. We conclude that the MFP regression is effective and competitive with contemporary works, and provides several additional advantages e.g. in terms of interpretability, generalisability, and implementability.