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

Bayesian inference in non-Markovian state-space models with applications to fractional order systems

Battery impedance spectroscopy models are given by fractional order (FO) differential equations. In the discrete-time domain, they give rise to state-space models where the latent process is not Markovian. Parameter estimation for these models is therefore challenging, especially for non-commensurate FO models. In this paper, we propose a Bayesian approach to identify the parameters of generic FO systems. The computational challenge is tackled with particle Markov chain Monte Carlo methods, with an implementation specifically designed for the non-Markovian setting. The approach is then applied to estimate the parameters of a battery non-commensurate FO equivalent circuit model. Extensive simulations are provided to study the practical identifiability of model parameters and their sensitivity to the choice of prior distributions, the number of observations, the magnitude of the input signal and the measurement noise