Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning

Abstract

Various modeling techniques are used to predict the capacity fade of Li-ion batteries. Algebraic reduced-order models, which are inherently interpretable and computationally fast, are ideal for use in battery controllers, technoeconomic models, and multiobjective optimizations. For Li-ion batteries with graphite anodes, solid-electrolyte-interphase (SEI) growth on the graphite surface dominates fade. This fade is often modeled using physically informed equations, such as square-root of time for predicting solventdiffusion limited SEI growth, and Arrhenius and Tafel-like equations predicting the temperature and state-of-charge rate dependencies. In some cases, completely empirical relationships are proposed. However, statistical validation is rarely conducted to evaluate model optimality, and only a handful of possible models are usually investigated. This article demonstrates a novel procedure for automatically identifying reduced-order degradation models from millions of algorithmically generated equations via bi-level optimization and symbolic regression. Identified models are statistically validated using cross-validation, sensitivity analysis, and uncertainty quantification via bootstrapping. On a LiFePO 4 /Graphite cell calendar aging data set, automatically identified models utilizing square-root, power law, stretched exponential, and sigmoidal functions result in greater accuracy and lower uncertainty than models identified by human experts, and demonstrate that previously known physical relationships can be empirically "rediscovered" using machine learning.

Early Battery Performance Prediction for Mixed Use Charging Profiles Using Hierarchal Machine Learning

“…The modeling framework presented here could likely account for the impact of rest SOC on long‐term degradation if the rest SOC was varied within the training set. Creating a more robust prediction will require more direct accounting, especially for LLI, as LLI associated with SEI growth is known to vary distinctly with EOC and T [14,31] …”

“…This low level of error holds true even under the situation that different cycling regimes and calendar aging conditions between the training and validation sets For short or intermediate length estimates of life, this level of error would minimally impact prediction purposes. However, as pointed out recently by Gasper et al ., even small prediction errors can lead to sizeable variation when projecting to the 10+ year life need for most automotive and stationary applications [14] . Thus, future work needs to more effectively capture aspects related to calendar aging variations, and to validate model predictions or update model parameters with real‐world, long‐term data whenever possible.…”

“…Life models and prediction techniques can usually be grouped into either data‐driven empirical models or physics‐based models [6,7,10–17] . Physics‐based models need to span many different length scales to fully encapsulate specific electrochemical signatures that are linked to battery performance [17–19] .…”

Symbolic regression for scientific discovery: an application to wind speed forecasting

“…This multi-objective optimization approach proved to yield superior results compared to previous approaches. Additionally, the work presented in [26,17,11] show some real world applications of symbolic regression using genetic algorithms, including business forecasting (e.g. labor cost and product demand) for decision making, as well as complex systems analysis (e.g.…”

Supervised Learning of Synthetic Big Data for Li‐Ion Battery Degradation Diagnosis

“…Empirical models include algebraic equations for capacity prediction [8] as well as more flexible data‐driven machine learning (ML) models [9] . These models have been reported extensively in the literature for both state of health (SOH) estimation [10–14] and remaining useful lifetime (RUL) prediction [15–20] .…”