Learning battery model parameter dynamics from data with recursive Gaussian process regression

Estimating state of health is a critical function of a battery management system but remains challenging due to the variability of operating conditions and usage requirements of real applications. As a result, techniques based on fitting equivalent circuit models may exhibit inaccuracy at extremes of performance and over long-term ageing, or instability of parameter estimates. Pure data-driven techniques, on the other hand, suffer from lack of generality beyond their training dataset. In this paper, we propose a hybrid approach combining data- and model-driven techniques for battery health estimation. Specifically, we demonstrate a Bayesian data-driven method, Gaussian process regression, to estimate model parameters as functions of states, operating conditions, and lifetime. Computational efficiency is ensured through a recursive approach yielding a unified joint state-parameter estimator that learns parameter dynamics from data and is robust to gaps and varying operating conditions. Results show the efficacy of the method, on both simulated and measured data, including accurate estimates and forecasts of battery capacity and internal resistance. This opens up new opportunities to understand battery ageing in real applications.

[1]  M. Marinescu,et al.  Lithium-Ion Battery Degradation: Measuring Rapid Loss of Active Silicon in Silicon–Graphite Composite Electrodes , 2022, ACS applied energy materials.

[2]  Yiming Wan,et al.  State-of-charge dependent equivalent circuit model identification for batteries using sparse Gaussian process regression , 2022, Journal of Process Control.

[3]  G. Offer,et al.  A composite electrode model for lithium-ion batteries with silicon/graphite negative electrodes , 2022, Journal of Power Sources.

[4]  Charles W. Monroe,et al.  Multiscale coupling of surface temperature with solid diffusion in large lithium-ion pouch cells , 2021, Communications Engineering.

[5]  David A. Howey,et al.  Automated Feature Extraction and Selection for Data-Driven Models of Rapid Battery Capacity Fade and End of Life , 2021, IEEE Transactions on Industrial Informatics.

[6]  A. Jossen,et al.  Low-effort determination of heat capacity and thermal conductivity for cylindrical 18650 and 21700 lithium-ion cells , 2021 .

[7]  W. Bessler,et al.  Grey-box modelling of lithium-ion batteries using neural ordinary differential equations , 2021, Energy Informatics.

[8]  Antti Aitio,et al.  Predicting battery end of life from solar off-grid system field data using machine learning , 2021, Joule.

[9]  Anna G. Stefanopoulou,et al.  The challenge and opportunity of battery lifetime prediction from field data , 2021, Joule.

[10]  Anuradha M. Annaswamy,et al.  Online capacity estimation of lithium-ion batteries with deep long short-term memory networks , 2021, Journal of Power Sources.

[11]  Micah S. Ziegler,et al.  Determinants of lithium-ion battery technology cost decline , 2021, Energy & Environmental Science.

[12]  A. Valero,et al.  Summary and critical review of the International Energy Agency’s special report: The role of critical minerals in clean energy transitions , 2021 .

[13]  D. Sauer,et al.  Timeseries data of a drive cycle aging test of 28 high energy NCA/C+Si round cells of type 18650 , 2021 .

[14]  D. Sauer,et al.  The development of stationary battery storage systems in Germany – A market review , 2020, Journal of Energy Storage.

[15]  Antti Aitio,et al.  Bayesian Parameter Estimation Applied to the Li-ion Battery Single Particle Model with Electrolyte Dynamics , 2020, IFAC-PapersOnLine.

[16]  Arno Solin,et al.  Hilbert space methods for reduced-rank Gaussian process regression , 2014, Stat. Comput..

[17]  Jorn M. Reniers,et al.  Review and performance comparison of mechanical-chemical degradation models for lithium-ion batteries , 2019, Journal of The Electrochemical Society.

[18]  David Howey,et al.  Augmented State Observer for Simultaneous Estimation of Charge State and Crossover in Self-Discharging Disproportionation Redox Flow Batteries , 2019, 2019 IEEE Conference on Control Technology and Applications (CCTA).

[19]  Michael A. Osborne,et al.  Battery health prediction under generalized conditions using a Gaussian process transition model , 2018, Journal of Energy Storage.

[20]  Michael A. Osborne,et al.  Gaussian Process Regression for In Situ Capacity Estimation of Lithium-Ion Batteries , 2017, IEEE Transactions on Industrial Informatics.

[21]  Andrew Gordon Wilson,et al.  GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration , 2018, NeurIPS.

[22]  Patrick Kofod Mogensen,et al.  Optim: A mathematical optimization package for Julia , 2018, J. Open Source Softw..

[23]  Amit Patra,et al.  State of Health Estimation of Lithium-Ion Batteries Using Capacity Fade and Internal Resistance Growth Models , 2018, IEEE Transactions on Transportation Electrification.

[24]  Tarvydas Dalius,et al.  Li-ion batteries for mobility and stationary storage applications , 2018 .

[25]  Yigang He,et al.  Capacity Prognostics of Lithium-Ion Batteries using EMD Denoising and Multiple Kernel RVM , 2017, IEEE Access.

[26]  Hicham Chaoui,et al.  State of Charge and State of Health Estimation for Lithium Batteries Using Recurrent Neural Networks , 2017, IEEE Transactions on Vehicular Technology.

[27]  Michael A. Osborne,et al.  Gaussian process regression for forecasting battery state of health , 2017, 1703.05687.

[28]  Dustin Tran,et al.  Automatic Differentiation Variational Inference , 2016, J. Mach. Learn. Res..

[29]  Gae-won You,et al.  Real-time state-of-health estimation for electric vehicle batteries: A data-driven approach , 2016 .

[30]  Miles Lubin,et al.  Forward-Mode Automatic Differentiation in Julia , 2016, ArXiv.

[31]  I. Villarreal,et al.  Critical review of state of health estimation methods of Li-ion batteries for real applications , 2016 .

[32]  Arno Solin,et al.  Stochastic Differential Equation Methods for Spatio-Temporal Gaussian Process Regression , 2016 .

[33]  Shuichi Adachi,et al.  Simultaneous state of charge and parameter estimation of lithium-ion battery using log-normalized unscented Kalman Filter , 2015, 2015 American Control Conference (ACC).

[34]  Arno Solin,et al.  Spatiotemporal Learning via Infinite-Dimensional Bayesian Filtering and Smoothing: A Look at Gaussian Process Regression Through Kalman Filtering , 2013, IEEE Signal Processing Magazine.

[35]  Simo Särkkä,et al.  Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering , 2012, Computational Statistics.

[36]  Simo Särkkä,et al.  Bayesian Filtering and Smoothing , 2013, Institute of Mathematical Statistics textbooks.

[37]  Simo Särkkä,et al.  Infinite-Dimensional Kalman Filtering Approach to Spatio-Temporal Gaussian Process Regression , 2012, AISTATS.

[38]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[39]  Michael Buchholz,et al.  State-of-health monitoring of lithium-ion batteries in electric vehicles by on-board internal resistance estimation , 2011 .

[40]  Jamie Gomez,et al.  Equivalent circuit model parameters of a high-power Li-ion battery: Thermal and state of charge effects , 2011 .

[41]  J. Vanhatalo,et al.  Approximate inference for disease mapping with sparse Gaussian processes , 2010, Statistics in medicine.

[42]  IL-Song Kim,et al.  A Technique for Estimating the State of Health of Lithium Batteries Through a Dual-Sliding-Mode Observer , 2010, IEEE Transactions on Power Electronics.

[43]  Bhaskar Saha,et al.  Prognostics Methods for Battery Health Monitoring Using a Bayesian Framework , 2009, IEEE Transactions on Instrumentation and Measurement.

[44]  Gregory L. Plett,et al.  Sigma-point Kalman filtering for battery management systems of LiPB-based HEV battery packs Part 2: Simultaneous state and parameter estimation , 2006 .

[45]  Carl E. Rasmussen,et al.  A Unifying View of Sparse Approximate Gaussian Process Regression , 2005, J. Mach. Learn. Res..

[46]  Gregory L. Plett,et al.  Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs: Part 3. State and parameter estimation , 2004 .

[47]  Agathe Girard,et al.  Prediction at an Uncertain Input for Gaussian Processes and Relevance Vector Machines Application to Multiple-Step Ahead Time-Series Forecasting , 2002 .

[48]  C. Rasmussen,et al.  Gaussian Process Priors with Uncertain Inputs - Application to Multiple-Step Ahead Time Series Forecasting , 2002, NIPS.

[49]  M. Doyle,et al.  Simulation and Optimization of the Dual Lithium Ion Insertion Cell , 1994 .

[50]  M. Doyle,et al.  Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell , 1993 .

[51]  R. E. Carlson,et al.  Monotone Piecewise Cubic Interpolation , 1980 .

[52]  C. Striebel,et al.  On the maximum likelihood estimates for linear dynamic systems , 1965 .

[53]  J. Newman,et al.  Theoretical Analysis of Current Distribution in Porous Electrodes , 1962 .