On the Error of Li-ion Battery Parameter Estimation Subject to System Uncertainties

Abstract

Emerging lithium-ion battery systems require high-fidelity electrochemical models for advanced control, diagnostics, and design. Accordingly, battery parameter estimation is an active research domain where novel algorithms are being developed to calibrate complex models from input-output data. Amidst these efforts, little focus has been placed on the fundamental mechanisms governing estimation accuracy, spurring the question, why is an estimate accurate or inaccurate? In response, we derive a generalized estimation error equation under the commonly adopted least-squares objective function, which reveals that the error can be represented as a combination of system uncertainties (i.e., in model, measurement, and parameter) and uncertainty-propagating sensitivity structures in the data. We then relate the error equation to conventional error analysis criteria, such as the Fisher information matrix, Cramér-Rao bound, and parameter sensitivity, to assess the benefits and limitations of each. The error equation is validated through several uni- and bivariate estimations of lithium-ion battery electrochemical parameters using experimental data. These results are also analyzed with the error equation to study the error compositions and parameter identifiability under different data. Finally, we show that adding target parameters to the estimation without increasing the amount of data intrinsically reduces the robustness of the results to system uncertainties. Formula is derived to quantify and analyze battery parameter estimation errors Influences of system uncertainties and estimation bias are considered Mechanisms and data structures propagating uncertainties to error are identified Error magnitude, composition, and dominant source highly depend on data Multivariate estimation is less robust to uncertainties than univariate estimation