Prediction of future capacity and internal resistance of Li-ion cells from one cycle of input data

There is a large demand for models able to predict the future capacity retention and internal resistance (IR) of Lithium-ion battery cells with as little testing as possible. We provide a data-centric model accurately predicting a cell’s entire capacity and IR trajectory from one single cycle of input data. This represents a significant reduction in the amount of input data needed over previous works. Our approach characterises the capacity and IR curve through a small number of key points, which, once predicted and interpolated, describe the full curve. With this approach the remaining useful life is predicted with an 8.6% mean absolute percentage error when the input-cycle is within the first 100 cycles

Online Lifetime Prediction for Lithium-Ion Batteries with Cycle-by-Cycle Updates, Variance Reduction, and Model Ensembling

This project was funded by an industry-academia grant EPSRC EP/R511687/1 awarded by EPSRC & University of Edinburgh program Impact Acceleration Account (IAA). R. Ibraheem is a Ph.D. student in EPSRC’s MAC-MIGS Centre for Doctoral Training. MAC-MIGS is supported by the UK’s Engineering and Physical Science Research Council (grant number EP/S023291/1). G. dos Reis acknowledges support from the Faraday Institution [grant number FIRG049]. Publisher Copyright: © 2023 by the authors.Lithium-ion batteries have found applications in many parts of our daily lives. Predicting their remaining useful life (RUL) is thus essential for management and prognostics. Most approaches look at early life prediction of RUL in the context of designing charging profiles or optimising cell design. While critical, said approaches are not directly applicable to the regular testing of cells used in applications. This article focuses on a class of models called ‘one-cycle’ models which are suitable for this task and characterized by versatility (in terms of online prediction frameworks and model combinations), prediction from limited input, and cells’ history independence. Our contribution is fourfold. First, we show the wider deployability of the so-called one-cycle model for a different type of battery data, thus confirming its wider scope of use. Second, reflecting on how prediction models can be leveraged within battery management cloud solutions, we propose a universal Exponential-smoothing (e-forgetting) mechanism that leverages cycle-to-cycle prediction updates to reduce prediction variance. Third, we use this new model as a second-life assessment tool by proposing a knee region classifier. Last, using model ensembling, we build a “model of models”. We show that it outperforms each underpinning model (from in-cycle variability, cycle-to-cycle variability, and empirical models). This ‘ensembling’ strategy allows coupling explainable and black-box methods, thus giving the user extra control over the final model.publishersversionpublishe

Path-based splitting methods for SDEs and machine learning for battery lifetime prognostics

In the first half of this Thesis, we present the numerical analysis of splitting methods for stochastic differential equations (SDEs) using a novel path-based approach. The application of splitting methods to SDEs can be viewed as replacing the driving Brownian-time path with a piecewise linear path, producing a ‘controlled-differential-equation’ (CDE). By Taylor expansion of the SDE and resulting CDE, we show that the global strong and weak errors of splitting schemes can be obtained by comparison of the iterated integrals in each. Matching all integrals up to order p+1 in expectation will produce a weak order p+0.5 scheme, and in addition matching the integrals up to order p+0.5 strongly will produce a strong order p scheme. In addition, we present new splitting methods utilising the ‘space-time’ L´evy area of Brownian motion which obtain global strong Oph1.5q and Oph2q weak errors for a class of SDEs satisfying a commutativity condition. We then present several numerical examples including Multilevel Monte Carlo. In the second half of this Thesis, we present a series of papers focusing on lifetime prognostics for lithium-ion batteries. Lithium-ion batteries are fuelling the advancing renewable-energy based world. At the core of transformational developments in battery design, modelling and management is data. We start with a comprehensive review of publicly available datasets. This is followed by a study which explores the evolution of internal resistance (IR) in cells, introducing the original concept of ‘elbows’ for IR. The IR of cells increases as a cell degrades and this often happens in a non-linear fashion: where early degradation is linear until an inflection point (the elbow) is reached followed by increased rapid degradation. As a follow up to the exploration of IR, we present a model able to predict the full IR and capacity evolution of a cell from one charge/discharge cycle. At the time of publication, this represented a significant reduction (100x) in the number of cycles required for prediction. The published paper was the first to show that such results were possible. In the final paper, we consider experimental design for battery testing. Where we focus on the important question of how many cells are required to accurately capture statistical variation

Lithium-ion battery data and where to find it

Lithium-ion batteries are fuelling the advancing renewable-energy based world. At the core of transformational developments in battery design, modelling and management is data. In this work, the datasets associated with lithium batteries in the public domain are summarised. We review the data by mode of experimental testing, giving particular attention to test variables and data provided. Alongside highlighted tools and platforms, over 30 datasets are reviewed

Automatic method for the estimation of li-ion degradation test sample sizes required to understand cell-to-cell variability

This project was funded by an industry-academia collaborative grant EPSRC EP/R511687/1 awarded by Engineering and Physical Sciences Research Council (EPSRC) & University of Edinburgh United Kingdom program Impact Acceleration Account (IAA). P. Dechent was supported by Bundesministerium für Bildung und Forschung Germany ( BMBF 03XP0302C ). Publisher Copyright: © 2022 The Author(s)The testing of battery cells is a long and expensive process, and hence understanding how large a test set needs to be is very useful. This work proposes an automated methodology to estimate the smallest sample size of cells required to capture the cell-to-cell variability seen in a larger population. We define cell-to-cell variation based on the slopes of a linear regression model applied to capacity fade curves. Our methodology determines a sample size which estimates this variability within user specified requirements on precision and confidence. The sample size is found using the distributional properties of the slopes under a normality assumption, and an implementation of the approach is available on GitHub. For the five datasets in the study, we find that a sample size of 8–10 cells (at a prespecified precision and confidence) captures the cell-to-cell variability of the larger datasets. We show that prior testing knowledge can be leveraged with machine learning models to operationally optimise the design of new cell-testing, leading up to a 75% reduction in experimental costs.publishersversionpublishe

Elbows of internal resistance rise curves in Li-ion cells

The degradation of lithium-ion cells with respect to increases of internal resistance (IR) has negative implications for rapid charging protocols, thermal management and power output of cells. Despite this, IR receives much less attention than capacity degradation in Li-ion cell research. Building on recent developments on ‘knee’ identification for capacity degradation curves, we propose the new concepts of ‘elbow-point’ and ‘elbow-onset’ for IR rise curves, and a robust identification algorithm for those variables. We report on the relations between capacity’s knees, IR’s elbows and end of life for the large dataset of the study. We enhance our discussion with two applications. We use neural network techniques to build independent state of health capacity and IR predictor models achieving a mean absolute percentage error (MAPE) of 0.4% and 1.6%, respectively, and an overall root mean squared error below 0.0061. A relevance vector machine, using the first 50 cycles of life data, is employed for the early prediction of elbow-points and elbow-onsets achieving a MAPE of 11.5% and 14.0%, respectively

Algorithmic complexity stratification for congenital heart disease patients

Background: Congenital Heart Disease (CHD) encompasses a huge variety of rare diagnoses that range in complexity and comorbidity. To help build clinical guidelines, plan health services and conduct statistically powerful research on such a disparate set of diseases there have been various attempts to group pathologies into mild, moderate, or severe disease. So far, however, these complexity scores have required manual specialist input for every case, and are therefore missing in large databases where this is impractical, or quickly outdated when guidelines are revised. Methods: We used the up-to-date European Society of Cardiology guidelines to create an algorithm to assign complexity scores to CHD patients using only their diagnosis list. Two CHD specialists then independently assigned complexity scores to a random sample of patients. Results: Our algorithm was 96% accurate where both specialists agreed on a complexity score; this occurred 68% of the time overall, and 79% of the time in moderate or complex CHD. The algorithm “failed” mainly when diagnoses were insufficiently specific, usually for septal defects (where size was unspecified), or where complexity depends on the procedure performed (e.g. atrial/arterial switch for transposition of the great arteries). Conclusions: We were able to algorithmically determine the complexity scores of a majority of patients with CHD based on their diagnosis list alone. This could allow for automatic complexity scoring of most patients in large CHD databases, for example our own Registry of the Congenital Heart Alliance of Australia and New Zealand. This will facilitate targeted research into the management, outcomes and burden of CHD