Structural Identifiability Analysis of Fractional Order Models with Applications in Battery Systems

This paper presents a method for structural identifiability analysis of fractional order systems by using the coefficient mapping concept to determine whether the model parameters can uniquely be identified from input-output data. The proposed method is applicable to general non-commensurate fractional order models. Examples are chosen from battery fractional order equivalent circuit models (FO-ECMs). The battery FO-ECM consists of a series of parallel resistors and constant phase elements (CPEs) with fractional derivatives appearing in the CPEs. The FO-ECM is non-commensurate if more than one CPE is considered in the model. Currently, estimation of battery FO-ECMs is performed mainly by fitting in the frequency domain, requiring costly electrochemical impedance spectroscopy equipment. This paper aims to analyse the structural identifiability of battery FO-ECMs directly in the time domain. It is shown that FO-ECMs with finite numbers of CPEs are structurally identifiable. In particular, the FO-ECM with a single CPE is structurally globally identifiable.

[1]  A. Oustaloup.  La dérivation non entière , 1995 .

[2]  YangQuan Chen,et al.  Fractional order control - A tutorial , 2009, 2009 American Control Conference.

[3]  Gérard Bloch,et al.  Identifiability of discrete-time nonlinear systems: The local state isomorphism approach , 2008, Autom..

[4]  Joseph J. DiStefano,et al.  On the relationships between structural identifiability and the controllability, observability properties , 1977 .

[5]  David A. Howey,et al.  Model identification and parameter estimation for LiFePO 4 batteries , 2013 .

[6]  K R Godfrey,et al.  Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods. , 1990, Mathematical biosciences.

[7]  Seyed Mohammad Mahdi Alavi,et al.  Structural identifiability of battery equivalent circuit models , 2015, ArXiv.

[8]  H. Rabitz,et al.  Similarity transformation approach to identifiability analysis of nonlinear compartmental models. , 1989, Mathematical biosciences.

[9]  J. M. Hof.  Structural identifiability of linear compartmental systems , 1998, IEEE Trans. Autom. Control..

[10]  Claudio Cobelli,et al.  Global identifiability of nonlinear models of biological systems , 2001, IEEE Transactions on Biomedical Engineering.

[11]  K. Cole,et al.  Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics , 1941 .

[12]  E. Barsoukov,et al.  Impedance spectroscopy : theory, experiment, and applications , 2005 .

[13]  Luigi Fortuna,et al.  Fractional Order Systems: Modeling and Control Applications , 2010 .

[14]  Lennart Ljung,et al.  Perspectives on system identification , 2010, Annu. Rev. Control..

[15]  Karl Johan Åström,et al.  BOOK REVIEW SYSTEM IDENTIFICATION , 1994, Econometric Theory.

[16]  David A. Howey,et al.  Time-domain fitting of battery electrochemical impedance models , 2015 .

[17]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[18]  Hosam K. Fathy,et al.  Maximizing Parameter Identifiability of an Equivalent-Circuit Battery Model Using Optimal Periodic Input Shaping , 2014 .

[19]  C. Cobelli,et al.  Parameter and structural identifiability concepts and ambiguities: a critical review and analysis. , 1980, The American journal of physiology.

[20]  J. Jorcin,et al.  CPE analysis by local electrochemical impedance spectroscopy , 2006 .

[21]  M. Krstić,et al.  Adaptive Partial Differential Equation Observer for Battery State-of-Charge/State-of-Health Estimation Via an Electrochemical Model , 2014 .

[22]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[23]  Dirk Uwe Sauer,et al.  Adaptive estimation of the electromotive force of the lithium-ion battery after current interruption for an accurate state-of-charge and capacity determination , 2013 .

[24]  Ursula Klingmüller,et al.  Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood , 2009, Bioinform..

[25]  Mohammad Saleh Tavazoei,et al.  Identifiability of fractional order systems using input output frequency contents. , 2010, ISA transactions.

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

[27]  Seth Sullivant,et al.  Structural Identifiability of Viscoelastic Mechanical Systems , 2013, PloS one.

[28]  J. Randles.  Kinetics of rapid electrode reactions , 1947 .

[29]  U. Troeltzsch,et al.  Characterizing aging effects of lithium ion batteries by impedance spectroscopy , 2006 .

[30]  Stefan Streif,et al.  Nonlinear observability and identifiability of single cells in battery packs , 2013, 2013 IEEE International Conference on Control Applications (CCA).

[31]  J. Willems,et al.  Parametrizations of linear dynamical systems: Canonical forms and identifiability , 1974 .

[32]  Yucai Zhu,et al.  Multivariable System Identification For Process Control , 2001 .

[33]  D. Sauer,et al.  Characterization of high-power lithium-ion batteries by electrochemical impedance spectroscopy. II: Modelling , 2011 .

[34]  D. Howey,et al.  Battery internal temperature estimation by combined impedance and surface temperature measurement , 2014 .

[35]  Gregory L. Plett,et al.  Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs Part 1. Background , 2004 .

[36]  L. Guzzella,et al.  Experiment-driven electrochemical modeling and systematic parameterization for a lithium-ion battery cell , 2010 .

[37]  R. Bellman,et al.  On structural identifiability , 1970 .

[38]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[39]  Hosam K. Fathy,et al.  Genetic identification and fisher identifiability analysis of the Doyle–Fuller–Newman model from experimental cycling of a LiFePO4 cell , 2012 .

[40]  Dennis S. Bernstein,et al.  NONINVASIVE BATTERY-HEALTH DIAGNOSTICS USING RETROSPECTIVE-COST IDENTIFICATION OF INACCESSIBLE SUBSYSTEMS , 2012 .

[41]  Le Yi Wang,et al.  Enhanced Identification of Battery Models for Real-Time Battery Management , 2011, IEEE Transactions on Sustainable Energy.

[42]  J. Ross Macdonald,et al.  Applicability and power of complex nonlinear least squares for the analysis of impedance and admittance data , 1982 .

[43]  Hosam K. Fathy,et al.  Fisher identifiability analysis for a periodically-excited equivalent-circuit lithium-ion battery model , 2014, 2014 American Control Conference.

[44]  Seth Sullivant,et al.  Identifiable reparametrizations of linear compartment models , 2013, J. Symb. Comput..

[45]  B. Boukamp.  A Nonlinear Least Squares Fit procedure for analysis of immittance data of electrochemical systems , 1986 .