Bayesian Inference in Non-Markovian State-Space Models with Applications to Battery Fractional-Order Systems
Journal
IEEE Transactions on Control Systems Technology
Journal Volume
26
Journal Issue
2
Pages
497-506
Date Issued
2018
Author(s)
Abstract
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 noncommensurate 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. Two examples are provided. In a first example, the approach is applied to identify a battery commensurate FO model with a single constant phase element (CPE) by using real data. We compare the proposed approach to an instrumental variable method. Then, we consider a noncommensurate FO model with more than one CPE and synthetic data sets, investigating how the proposed method enables the study of various effects on parameter identification, such as the data length, the magnitude of the input signal, the choice of prior, and the measurement noise. ? 2017 IEEE.
Subjects
Bayesian networks
Differential equations
Electric batteries
Inference engines
Markov processes
Monte Carlo methods
State space methods
Time domain analysis
Computational challenges
Constant phase element
Discrete time-domain
Fractional-order systems
Instrumental variable methods
Non-Markovian settings
Particle markov chain monte carlo
State - space models
Parameter estimation
Type
journal article