Data Worth of Measurement Quantities and Uncertainty Considerations in Lithium-Ion Battery Modeling

Because of their favorable properties like, e.g., high energy density, lithium-ion batteries are ubiquitous in modern societies. Still, some security aspects, like thermal runaway, are not yet fully solved [1]. As a first step towards an early-alert system that can warn the user of an imminent thermal runaway we investigate some of the stochastic aspects of thermal battery model predictions.

Numerical system modeling is inherently challenged by system uncertainties. These uncertainties stem from incomplete knowledge about parameter values, error-prone measurements and the imperfect mathematical description of the real system. The latter results in differences between predicted model output and the behavior of the real system. This phenomenon is called model structural error.

We present a minimally intrusive methodology that allows to handle model errors of an existing thermal-electrochemical battery model in a stochastically rigorous way. Moreover, we investigate the explanatory power of different measurement quantities on the temperature profile inside of the battery.

An existing, thermal-electrochemical battery model (DENIS [2]) of a LiFePO₄ cell is extended by an additional, stochastically motivated model for the model structural error. The parameters for this error model are determined by means of a Monte Carlo maximum likelihood approach. That is, the residuals between experimental discharge curves at low temperatures and the model predictions are used to evaluate the likelihood of different error model parameter sets.

Based on this stochastic system description a particle filter is implemented. Instead of a single model run, several parallel runs are computed. This yields a probability density function of the temperature distribution inside of the battery. Online measurement data can be used to update the system state and to decrease the uncertainty of future predictions. In comparison to Kalman filters, the use of a particle filter allows for a wide choice of error models beyond Gaussian and linear system assumptions.

The development of this methodology is extended by a data worth analysis. By application of the PreDIA (“Preposterior Data Impact Assessor”) method [3] we investigate the explanatory power of different measurement quantities on the temperature profile inside of the battery. Voltage, discharge current and temperature measurements are considered and for the latter also different sensor locations are examined.

The dynamics of the stochastic system description and the relative data worth of the different measurement quantities are interpreted and an outlook towards an early-alert system that builds upon the presented methodology is presented.

[1] Bandhauer, Todd M., Srinivas Garimella, and Thomas F. Fuller. "A critical review of thermal issues in lithium-ion batteries." Journal of the Electrochemical Society 158.3 (2011): R1-R25.

[2] Neidhardt, Jonathan P., et al. "A Flexible Framework for Modeling Multiple Solid, Liquid and Gaseous Phases in Batteries and Fuel Cells." Journal of The Electrochemical Society 159.9 (2012): A1528-A1542.

[3] Leube, P. C., A. Geiges, and W. Nowak. "Bayesian assessment of the expected data impact on prediction confidence in optimal sampling design." Water Resources Research 48.2 (2012).