On the Use of Cramer-Rao Lower Bound for Least-Variance Circuit Parameters Identification of Li-ion Cells
arxiv(2024)
摘要
Electrochemical Impedance Spectroscopy (EIS) and Equivalent Circuit Models
(ECMs) are widely used to characterize the impedance and estimate parameters of
electrochemical systems such as batteries. We use a generic ECM with ten
parameters grouped to model different frequency regions of the Li-ion cell's
impedance spectrum. We derive a noise covariance matrix from the measurement
model and use it to assign weights for the fitting technique. The paper
presents two formulations of the parameters identification problem. Using the
properties of the ECM EIS spectra, we propose a method to initialize ECM
parameters for the Complex Non-linear Least Squares (CNLS) technique. The paper
proposes a novel algorithm for designing the EIS experiments by applying the
theory on Cramer-Rao Lower Bound (CRLB) and Fisher Information Matrix (FIM) to
the identification problem. We show that contributions to the FIM elements
strongly depend on the frequencies at which EIS is performed. Hence, the
algorithm aims to adjust frequencies such that the most information about
parameters is collected. This is done by minimizing the highest variance of ECM
parameters defined by CRLB. Results of a numerical experiment show that the
estimator is efficient, and frequency adjustment leads to more accurate ECM
parameters' identification.
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