A systematic approach for doing an a priori identifiability study of dynamical nonlinear models.

This paper presents a method for investigating, through an automatic procedure, the (lack of) structural identifiability of dynamical models parameters. This method takes into account constraints on parameters and returns parameters whose estimations turn unidentifiable parameters into identifiable ones. It is based on (i) an equivalence between an extension of the notion of identifiability and the existence of solutions of algebraic systems, (ii) the use of symbolic computations for testing their existence. This method is described in details and is applied to two examples, the last one involving 12 parameters.

[1]  Marisa C Eisenberg,et al.  Determining identifiable parameter combinations using subset profiling. , 2014, Mathematical biosciences.

[2]  M J Chappell,et al.  Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems. , 2000, Mathematical biosciences.

[3]  Stefan Weijers,et al.  A procedure for selecting best identifiable parameters in calibrating activated sludge model no. 1 to full-scale plant data , 1997 .

[4]  Ghislaine Joly-Blanchard,et al.  Equivalence and identifiability analysis of uncontrolled nonlinear dynamical systems , 2004, Autom..

[5]  Christopher W. Brown.  QEPCAD B: a program for computing with semi-algebraic sets using CADs , 2003, SIGS.

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

[7]  E. Walter,et al.  Global approaches to identifiability testing for linear and nonlinear state space models , 1982 .

[8]  J. L. Rabinowitsch.  Zum Hilbertschen Nullstellensatz , 1930 .

[9]  J. Chase,et al.  Structural identifiability analysis of a cardiovascular system model. , 2016, Medical engineering & physics.

[10]  Maria Pia Saccomani,et al.  Parameter identifiability of nonlinear systems: the role of initial conditions , 2003, Autom..

[11]  K R Godfrey,et al.  Structural identifiability of the parameters of a nonlinear batch reactor model. , 1992, Mathematical biosciences.

[12]  Maria Pia Saccomani,et al.  DAISY: A new software tool to test global identifiability of biological and physiological systems , 2007, Comput. Methods Programs Biomed..

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

[14]  T. Glad,et al.  An Algebraic Approach to Linear and Nonlinear Control , 1993 .

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

[16]  Maria Pia Saccomani,et al.  Examples of testing global identifiability of biological and biomedical models with the DAISY software , 2010, Comput. Biol. Medicine.

[17]  Ghislaine Joly-Blanchard,et al.  Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor , 2005 .

[18]  Nicolette Meshkat,et al.  An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases. , 2009, Mathematical biosciences.

[19]  Peter Reichert,et al.  Practical identifiability of ASM2d parameters--systematic selection and tuning of parameter subsets. , 2002, Water research.

[20]  Neil D. Evans,et al.  Three novel approaches to structural identifiability analysis in mixed-effects models , 2016, Comput. Methods Programs Biomed..

[21]  Keith R. Godfrey,et al.  Structural identifiability of non-linear systems using linear/non-linear splitting , 2003 .

[22]  Michel Petitot,et al.  An Algorithm to Test Identifiability of Non-Linear Systems , 2001 .

[23]  R Choquet,et al.  A hybrid symbolic-numerical method for determining model structure. , 2012, Mathematical biosciences.

[24]  Johan Karlsson,et al.  Minimal output sets for identifiability. , 2012, Mathematical biosciences.

[25]  Nicolette Meshkat,et al.  Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations. , 2011, Mathematical biosciences.

[26]  Ghislaine Joly-Blanchard,et al.  Some effective approaches to check the identifiability of uncontrolled nonlinear systems , 2001 .

[27]  Keith R. Godfrey,et al.  Identifiability of uncontrolled nonlinear rational systems , 2002, Autom..

[28]  Nicolette Meshkat,et al.  On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation , 2014, PloS one.

[29]  Jukka Ranta,et al.  Procedures for parameter and state estimation of microbial growth process models , 1982, Autom..

[30]  Marisa C. Eisenberg,et al.  Parameter identifiability and identifiable combinations in generalized Hodgkin-Huxley models , 2015, Neurocomputing.

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

[32]  M. Fliess,et al.  Nonlinear observability, identifiability, and persistent trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[33]  Shaohua Wu,et al.  Mean-Squared-Error Methods for Selecting Optimal Parameter Subsets for Estimation , 2012 .

[34]  M. Aziz-Alaoui,et al.  The chikungunya disease: modeling, vector and transmission global dynamics. , 2011, Mathematical biosciences.

[35]  Bican Xia,et al.  DISCOVERER: a tool for solving semi-algebraic systems , 2007, ACCA.

[36]  Thibault Gateau,et al.  Operator Engagement During Prolonged Simulated UAV Operation , 2016 .

[37]  J. D. Stigter,et al.  A fast algorithm to assess local structural identifiability , 2015, Autom..