Model Parametrization and Adaptation Based on the Invariance of Support Vectors With Applications to Battery State-of-Health Monitoring

Support vector regression (SVR) algorithms have been applied to the identification of many nonlinear dynamic systems due to their excellent approximation and generalization capability. However, the standard SVR algorithm involves an iterative optimization process, which is often computationally expensive and inefficient. For applications such as the battery state-of-health (SOH) monitoring, where the identification algorithm needs to be applied repeatedly for multiple cells because of the variation in model dynamics (due to battery aging and cell-to-cell difference), the computational burden could pose difficulties for real-time or onboard implementation. In this paper, the battery V -Q curve identification problem for SOH monitoring is studied. Based on experimental battery aging data, we develop a model parametrization and adaptation framework utilizing the simple structure of SVR representation with determined support vectors (SVs) so that the model parameters can be estimated in real time. Through mathematical analysis and simulations using a mechanistic battery aging model, it is shown that the SVs of the battery models stay invariant, even when the batteries age or vary. The invariance of the SVs is verified using experimental aging data. Consequently, the resulting model for the battery V -Q curve can be directly incorporated into the battery management system (BMS) and adapted online for SOH monitoring. Moreover, the general characteristics of the data that could maintain the SVR invariance are identified. The proposed automated model parametrization process (via an optimization algorithm) can be extended to nonlinear dynamic systems with the given properties.

[1]  Xuning Feng,et al.  Using probability density function to evaluate the state of health of lithium-ion batteries , 2013 .

[2]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[3]  Zhao Lu,et al.  Linear programming support vector regression with wavelet kernel: A new approach to nonlinear dynamical systems identification , 2009, Math. Comput. Simul..

[4]  Susan M. Schoenung,et al.  Long- vs. short-term energy storage technologies analysis : a life-cycle cost study : a study for the DOE energy storage systems program. , 2003 .

[5]  Alexander J. Smola,et al.  Support Vector Regression Machines , 1996, NIPS.

[6]  Bor Yann Liaw,et al.  CHAPTER FIFTEEN – A Roadmap to Understand Battery Performance in Electric and Hybrid Vehicle Operation , 2010 .

[7]  Zhao Lu,et al.  Linear Programming SVM-ARMA $_{\rm 2K}$ With Application in Engine System Identification , 2011, IEEE Transactions on Automation Science and Engineering.

[8]  Jens Groot,et al.  State-of-Health Estimation of Li-ion Batteries: Cycle Life Test Methods , 2012 .

[9]  Renato D. C. Monteiro,et al.  A geometric view of parametric linear programming , 1992, Algorithmica.

[10]  A. Gretton,et al.  Support vector regression for black-box system identification , 2001, Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563).

[11]  T. Horiba,et al.  State Analysis of Lithium-Ion Batteries Using Discharge Curves , 2008 .

[12]  Horst E. Friedrich,et al.  Market Prospects of Electric Passenger Vehicles , 2010 .

[13]  Alireza Khaligh,et al.  Battery, Ultracapacitor, Fuel Cell, and Hybrid Energy Storage Systems for Electric, Hybrid Electric, Fuel Cell, and Plug-In Hybrid Electric Vehicles: State of the Art , 2010, IEEE Transactions on Vehicular Technology.

[14]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[15]  Matthieu Dubarry,et al.  Identify capacity fading mechanism in a commercial LiFePO4 cell , 2009 .

[16]  Michael A. Roscher,et al.  Detection of Utilizable Capacity Deterioration in Battery Systems , 2011, IEEE Transactions on Vehicular Technology.

[17]  I. Bloom,et al.  Differential voltage analyses of high-power, lithium-ion cells: 1. Technique and application , 2005 .

[18]  Alexander J. Smola,et al.  Learning with Kernels: support vector machines, regularization, optimization, and beyond , 2001, Adaptive computation and machine learning series.

[19]  Aaron Smith.  A HIGH PRECISION STUDY OF LI-ION BATTERIES , 2012 .

[20]  Antoni Szumanowski,et al.  Battery Management System Based on Battery Nonlinear Dynamics Modeling , 2008, IEEE Transactions on Vehicular Technology.

[21]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[22]  Zhe Li,et al.  A comparative study of commercial lithium ion battery cycle life in electrical vehicle: Aging mechanism identification , 2014 .

[23]  Bernhard Schölkopf,et al.  Semiparametric Support Vector and Linear Programming Machines , 1998, NIPS.

[24]  Yunqian Ma,et al.  Practical selection of SVM parameters and noise estimation for SVM regression , 2004, Neural Networks.

[25]  Xiaosong Hu,et al.  A comparative study of equivalent circuit models for Li-ion batteries , 2012 .

[26]  B. Schölkopf,et al.  Linear programs for automatic accuracy control in regression. , 1999 .

[27]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[28]  M. Armand,et al.  Building better batteries , 2008, Nature.

[29]  Jinbo Bi,et al.  Dimensionality Reduction via Sparse Support Vector Machines , 2003, J. Mach. Learn. Res..

[30]  Jonghoon Kim,et al.  State-of-Charge Estimation and State-of-Health Prediction of a Li-Ion Degraded Battery Based on an EKF Combined With a Per-Unit System , 2011, IEEE Transactions on Vehicular Technology.

[31]  Tatsuo Horiba,et al.  Capacity-fading prediction of lithium-ion batteries based on discharge curves analysis , 2011 .

[32]  John Newman,et al.  I. A simplified model for determining capacity usage and battery size for hybrid and plug-in hybrid electric vehicles , 2008 .

[33]  D. Sauer,et al.  Dynamic electric behavior and open-circuit-voltage modeling of LiFePO4-based lithium ion secondary batteries , 2011 .

[34]  Bernhard E. Boser,et al.  A training algorithm for optimal margin classifiers , 1992, COLT '92.

[35]  Vojtech Svoboda,et al.  A roadmap to understand battery performance in electric and hybrid vehicle operation , 2007 .

[36]  David R. Musicant,et al.  Large Scale Kernel Regression via Linear Programming , 2002, Machine Learning.

[37]  Gérard Bloch,et al.  Support vector regression from simulation data and few experimental samples , 2008, Inf. Sci..

[38]  John N. Tsitsiklis,et al.  Introduction to linear optimization , 1997, Athena scientific optimization and computation series.

[39]  A. J. Smith,et al.  Delta Differential Capacity Analysis , 2012 .

[40]  J. Bernard,et al.  A Simplified Electrochemical and Thermal Aging Model of LiFePO4-Graphite Li-ion Batteries: Power and Capacity Fade Simulations , 2013 .

[41]  Jun Xu,et al.  Online battery state of health estimation based on Genetic Algorithm for electric and hybrid vehicle applications , 2013 .

[42]  Huei Peng,et al.  On-board state of health monitoring of lithium-ion batteries using incremental capacity analysis with support vector regression , 2013 .

[43]  Huei Peng,et al.  A unified open-circuit-voltage model of lithium-ion batteries for state-of-charge estimation and state-of-health monitoring , 2014 .

[44]  M. Dubarry,et al.  Incremental Capacity Analysis and Close-to-Equilibrium OCV Measurements to Quantify Capacity Fade in Commercial Rechargeable Lithium Batteries , 2006 .

[45]  Matthieu Dubarry,et al.  Synthesize battery degradation modes via a diagnostic and prognostic model , 2012 .

[46]  B. Dunn,et al.  Electrical Energy Storage for the Grid: A Battery of Choices , 2011, Science.

[47]  Alex Smola,et al.  Kernel methods in machine learning , 2007, math/0701907.